Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Physics
Suppose your friend is sitting on a sled and asks you to move her across a flat, horizontal field. You have a choice of (a) pushing her from behind by applying a force downward on her shoulders at 30 below the horizontal (Fig. 4.22a) or (b) attaching a rope to the front of the sled and pulling with a force at 30 above the horizontal (Fig. 4.22b). Which option would be easier and why?Physics Review A hockey player strikes a puck, giving it an initial velocity of 10.0 m/s in the positive x-direction. The puck slows uniformly to 6.00 m/s when it has traveled 40.0 m. (a) What is the pucks acceleration? (b) At what velocity is it traveling after 2.00 s? (c) How long does it take to travel 40.0 m? (See Section 2.5.)Four forces act on an object, given by A = 40.0 N east, B = 50.0 north, C = 70.0 N west, and D = 90.0 N south. (a) What is the magnitude of the net force on the object? (b) What is the direction of the force?A force of 30.0 N is applied in the positive x-direction to a block of mass 8.00 kg, at rest on a frictionless surface. (a) What is the blocks acceleration? (b) How fast is it going after 6.00 s? (Sec Sections 2.5 and 4.3.)What would be the acceleration of gravity at the surface of a world with twice Earths mass and twice its radius? (See Section 4.3.)Two monkeys are holding onto a single vine of negligible mass that hangs vertically from a tree, with one monkey a few meters higher than the other. The upper monkey has mass 20.0 kg and the lower monkey mass 10.0 kg. What is the ratio of the tension in the vine above the upper monkey to the tension in the vine between the two monkeys? (Sec Section 4.5.)Two identical strings making an angle of = 30.0 with respect to the vertical support a block of mass m = 15.0 kg (Fig. P4.32). What is the tension in each of the strings?Calculate the normal force on a 15.0 kg block in the following circumstances: (a) The block is resting on a level surface. (b) The block is resting on a surface tilted up at a 30.0 angle with respect to the horizontal. (c) The block is resting on the floor of an elevator that is accelerating upwards at 3.00 m./s2. (d) The block is on a level surface and a force of 125 N is exerted on it at an angle of 30.0 above the horizontal. (Sec Section 1.5.)A horizontal force of 95.0 N is applied to a 60.0.kg crate on a rough, level surface. If the crate accelerates at 1.20 m/s2, what is the magnitude of the force of kinetic friction acting on the crate? (See Section 4.5.)9WUEA block of mass 12.0 kg is sliding at an initial velocity of 8.00 m/s in the positive x-direction. The surface has a coefficient of kinetic friction of 0.300. (a) What is the force of kinetic friction acting on the block? (b) What is the blocks acceleration? (c) How far will it slide before coming to rest?A man exerts a horizontal force of 112 N on a refrigerator of mass 42.0 kg. If the refrigerator doesnt move, what is the minimum coefficient of static friction between the refrigerator and the floor? (See Section 4.6.)An Atwoods machine (Fig. 4.38) consists of two masses: one of mass 3.00 kg and the other of mass 8.00 kg. When released from rest, what is the acceleration of the system?A block of mass m1= 10 kg is on a frictionless table to the left of a second block of mass m2 = 24 kg, attached by a horizontal string (Figure WU4.13). If a horizontal force of 120 N is exerted on the block m2in the positive x-direction, (a) use the system approach to find the acceleration of the two blocks. (b) What is the tension in the string connecting the blocks? (See Section 4.6.) Figure WU4.13A passenger sitting in the rear of a bus claims that she was injured as the driver slammed on the brakes, causing a suitcase to come flying toward her from the front of the bus. If you were the judge in this case, what disposition would you make? Explain.A space explorer is moving through space far from any planet or star. He notices a large rock, taken as a specimen from an alien planet, floating around the cabin of the ship. Should he push it gently, or should he kick it toward the storage compartment? Explain.(a) If gold were sold by weight, would you rather buy it in Denver or in Death Valley? (b) If it were sold by mass, in which of the two locations would you prefer to buy it? Why?If you push on a heavy box that is at rest, you must exert some force to start its motion. Once the box is sliding, why does a smaller force maintain its motion?A ball is held in a persons hand. (a) Identify all the external forces acting on the ball and the reaction to each. (b) If the ball is dropped, what force is exerted on it while it is falling? Identify the reaction force in this case. (Neglect air resistance.)A weight lifter stands on a bathroom scale. (a) As she pumps a barbell up and down, what happens to the reading on the scale? (b) Suppose she is strong enough to actually throw the barbell upward. How does the reading on the scale vary now?(a) What force causes an automobile to move? (b) A propeller-driven airplane? (c) A rowboat?If only one force acts on an object, can it be in equilibrium? Explain.In the: motion picture It Happened One Night (Columbia Pictures, 1934), Clark Gable is standing inside a stationary bus in front of Claudette Colbert, who is seated. The bus suddenly starts moving forward and Clark falls into Claudettes lap. Why did this happen?Analyze the motion of a rock dropped in water in terms of its speed and acceleration as it falls. Assume a resistive force is acting on the rock that increases as the velocity of the rock increases.Identify the action-reaction pairs in the following situations: (a) a man takes a step, (b) a snowball hits a girl in the back, (c) a baseball player catches a ball, (d) a gust of wind strikes a window.Draw a free-body diagram for each of the following objects: (a) a projectile in motion in the presence of air resistance, (b) a rocket leaving the launch pad with its engines operating, and (c) an athlete running along a horizontal track.In a tug-of-war between two athletes, each pulls on the rope with a force of 200 N. What is the tension in the rope? If the rope doesnt move, what horizontal force does each athlete exert against the ground?Suppose you are driving a car at a high speed. Why should you avoid slamming on your brakes when you want to stop in the shortest possible distance? (Newer cars have antilock brakes that avoid this problem.)As a block slides down a frictionless incline, which of the following statements is true? (a) Both its speed and acceleration increase. (b) Its speed and acceleration remain constant. (c) Its speed increases and its acceleration remains constant. (d) Both its speed and acceleration decrease. (e) Its speed increases and its acceleration decreases.A crate remains stationary after it has been placed on a ramp inclined at an angle with the horizontal. Which of the following statements must be true about the magnitude of the frictional force that acts on the crate? (a) It is larger than the weight of the crate. (b) It is at least equal to the weight of the crate. (c) It is equal to sn. (d) It is greater than the component of the gravitational force acting down the ramp. (e) It is equal to the component of the gravitational force acting down the ramp.In Figure 4.4, a locomotive has broken through the wall of a train station. During the collision, what can be said about the force exerted by the locomotive on the wall? (a) The force exerted by the locomotive on the wall was larger than the force the wall could exert on the locomotive. (b) The force exerted by the locomotive on the wall was the same in magnitude as the force exerted by the wall on the locomotive. (c) The force exerted by the locomotive on the wall was less than the force exerted by the wall on the locomotive. (d) The wall cannot be said to exert a force; after all, it broke.If an object is in equilibrium, which of the following statements is not true? (a) The speed of the object remains constant. (b) The acceleration of the object is zero. (c) The net force acting on the object is zero. (d) The object must be at rest. (e) The velocity is constant.A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the acceleration of the truck as its trailer leaks sand at a constant rate through a hole in its bottom? (a) It decreases at a steady rate. (b) It increases at a steady rate. (c) It increases and then decreases. (d) It decreases and then increases. (e) It remains constant.A large crate of mass m is placed on the back of a truck but not tied down. As the truck accelerates forward with an acceleration a, the crate remains at rest relative to the truck. What force causes the crate to accelerate forward? (a) the normal force (b) the force of gravity (c) the force of friction between the crate and the floor of the truck (d) the ma force (e) none of theseWhich of the following statements are true? (a) An astronauts weight is the same on the Moon as on Earth. (b) An astronauts mass is the same on the International Space Station as it is on Earth. (c) Earths gravity has no effect on astronauts inside the International Space Station. (d) An astronauts mass is greater on Earth than on the Moon. (e) None of these statements are true.The heaviest invertebrate is the giant squid, which is estimated to have a weight of about 2 tons spread out over its length of 70 feet. What is its weight in newtons?A football punter accelerates a football from rest to a speed of 10 m/s during the time in which his toe is in contact with the ball (about 0.20 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?A 6.0-kg object undergoes an acceleration of 2.0 m/s2. (a) What is the magnitude of the resultant force acting on it? (b) If this same force is applied to a 4.0-kg object, what acceleration is produced?One or more external forces are exerted on each object enclosed in a dashed box shown in Figure 4.2. Identify the reaction to each of these forces.A bag of sugar weighs 5.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth? Repeat for Jupiter, where g is 2.64 times that on Earth. Find the mass of the bag of sugar in kilograms at each of the three locations.A freight train has a mass of 1.5 107 kg. If the locomotive can exert a constant pull of 7.5 105 N, how long does it take to increase; the speed of the train from rest to 80 km/h?A 75-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 825 N. What is the acceleration of the elevator?Consider a solid metal sphere (S) a few centimeters in diameter and a feather (F). For each quantity in the list that follows, indicate whether the quantity is the same, greater, or lesser in the case of S or in that of F. Explain in each case why you gave the answer you did. Here is the list: (a) the gravitational force, (b) the time it will take to fall a given distance in air, (c) the time it will take to fall a given distance in vacuum, (d) the total force on the object when falling in vacuum.As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 61.0 kg. If this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 6.00 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine (a) the salmons acceleration and (b) the magnitude of the force F during this interval.A 5.0-g bullet leaves the muzzle of a rifle with a speed of 320 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.82-m-long barrel of the rifle?A boat moves through the water with two forces acting on it. One is a 2.00 103-N forward push by the water on the propeller, and the other is a 1.80 103-N resistive force due to the water around the bow. (a) What is the acceleration of the 1.00 103-kg boat? (b) If it starts from rest, how far will the boat move in 10.0 s? (c) What will its velocity be at the end of that time?Two forces are applied to a car in an effort to move it, as shown in Figure P4.12. (a) What is the resultant vector of these two forces? (b) If the car has a mass of 3 000 kg, what acceleration does it have? Ignore friction. Figure P4.12A 970.-kg car starts from rest on a horizontal roadway and accelerates eastward for 5.00 s when it reaches a speed of 25.0 m/s. What is the average force exerted on the car during this time?An object of mass m is dropped from the roof of a building of height h. While the object is falling, a wind blowing parallel to the face of the building exerts a constant horizontal force F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h. (b) Find an expression in terms of m and F for the acceleration ax of the object in the horizontal direction (taken as the positive x-direction). (c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m, g, F, and h. (d) Find the magnitude of the objects acceleration while it is falling, using the variables F, m, and g.After falling from rest from a height of 30.0 m, a 0.500-kg ball rebounds upward, reaching a height of 20.0 m. If the contact between ball and ground lasted 2.00 ms, what average force was exerted on the ball?The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N east. If the boat (including its crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?(a) Find the tension in each cable supporting the 6.00 102-N cat burglar in Figure P4.35. (b) Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the other cables increase, decrease, or stay the same? Why? Figure P4.35A certain orthodontist uses a wire brace to align a patients crooked tooth as in Figure P4.88. The tension in the wire is adjusted to have a magnitude of 18.0 N. Find the magnitude of the net force exerted by the wire on the crooked tooth. Figure P4.38A 150-N bird feeder is supported by three cables as shown in Figure P4.39. Find the tension in each cable. Figure P4.39The leg and cast in Figure P4.40 weigh 220 N (w1). Determine the weight w2 and the angle needed so that no force is exerted on the hip joint by the leg plus the cast. Figure P4.40Two blocks each of mass m are fastened to the top of an elevator as in Figure P4.56. The elevator has an upward acceleration a. The strings have negligible mass, (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b) Compare the two tensions and determine which string would break first if a is made sufficiently large. (c) What are the tensions if the cable supporting the elevator breaks? Figure P4.56Two blocks each of mass m = 3.50 kg are fastened to the top of an elevator as in Figure P4.56. (a) If the elevator has an upward acceleration a = 1.60 m/s2, find the tensions T1 and T2 in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0 N, what maximum acceleration can the elevator have before the upper string breaks?The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire.The systems shown in Figure P4.58 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline in Figure P4.58d are frictionless. Figure P4.58A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s2, find the force exerted by the rope on the bucket.A crate of mass m = 32 kg rides on the bed of a truck attached by a cord to the back of the cab as in Figure P4.34. The cord can with-stand a maximum tension of 68 N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the truck can have before the cord breaks. Figure P4.34Two blocks of masses m and 2m are held in equilibrium on a frictionless incline as in Figure P4.57. In terms of m and , find (a) the magnitude of the tension T1 in the upper cord and (b) the magnitude of the tension T2 in the lower cord connecting the two blocks. Figure P4.57Two packing crates of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.60. The 5.00-kg crate lies on a smooth incline of angle 40.0. Find (a) the acceleration of the 5.00-kg crate and (b) the tension in the string. Figure P4.60Assume the three blocks portrayed in Figure P4.59 move on a frictionless surface and a 42-N force acts as shown on the 3.0-kg block. Determine (a) the acceleration given this system, (b) the tension in the cord connecting the 3.0-kg and the 1.0-kg blocks, and (c) the force exerted by the 1.0-kg block on the 2.0-kg block. Figure P4.59A block of mass m = 5.8 kg is pulled up a = 25 incline as in Figure P4.24 with a force of magnitude F = 32 N. (a) Find the acceleration of the bloc k if the incline is frictionless. (b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.10. Figure P4.24A setup similar to the one shown in Figure P4.53 is often used in hospitals to support and apply a traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted on the leg? Assume the traction force is horizontal. Figure P4.53Two blocks of masses m1 and m2 (m1 m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1 in Figure P4.62. (a) If P is the magnitude of the contact force between the blocks, draw the free-body diagrams for each block. (b) What is the net force on the system consisting of both blocks? (c) What is the net force acting on m1? (d) What is the net force acting on m2? (e) Write the x-component of Newtons second law for each block. (f) Solve the resulting system of two equations and two unknowns, expressing the acceleration a and contact force P in terms of the masses and force. (g) How would the answers change if the force had been applied to m2 instead? (Hint: use symmetry; dont calculate!) Is the contact force larger, smaller, or the same in this case? Why? Figure P4.62A 276-kg glider is being pulled by a 1 950-kg jet along a horizontal runway with an acceleration of a = 2.20 m/s2 to the right as in Figure P4.41. Find (a) the thrust provided by the jets engines and (b) the magnitude of the tension in the cable connecting the jet and glider. Figure P4.41In Figure P4.63, the light, taut, unstretchable cord B joins block 1 and the larger-mass block 2. Cord A exerts a force on block 1 to make it accelerate forward. (a) How does the magnitude of the force exerted by cord A on block 1 compare with the magnitude of the force exerted by cord B on block 2? (b) How does the acceleration of block 1 compare with the acceleration of block 2? (c) Does cord B exert a force on block 1? Explain your answer. Figure P4.63(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater. T or w? (b) When the elevator is moving at a constant velocity upward, which is greater. T or w2 (c) When the elevator is moving upward, but the acceleration is downward, which is greater. T or w? (d) Let the elevator have a mass of 1500 kg and an upward acceleration of 2.5 m/s2. Find T. Is your answer consistent with the answer to part (a)? (e) The elevator of part (d) now moves with a constant upward velocity of 10 m/s. Find T. Is your answer consistent with your answer to part (b)? (f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.50 m/s2. Find T Is your answer consistent with your answer to part (c)?An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg, as shown in Figure P4.64. Find (a) the acceleration of each object and (b) the tension in the cable. Figure P4.64 (Problems 64, 65, andA 1.00 103 car is pulling a 300.-kg trailer. Together, the car and trailer have an acceleration of 2.15 m/s2 in the positive x-direction. Neglecting frictional forces on the trailer, determine (a) the net force on the car, (b) the net force on the trailer, (c) the magnitude and direction of the force exerted by the trailer on the car, and (d) the resultant force exerted by the car on the road.Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley, as in Figure P4.66. Determine (a) the tension in the string, (b) the acceleration of each object, and (c) the distance each object will move in the first second of motion if both objects start from rest. Figure P4.66A dockworker loading crates on a ship finds that a 20.0-kg crate, initially at rest on a horizontal surface, requires a 75.0-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 60.0 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.In Figure P4.64, m1 = 10. kg and m2 = 4.0 kg. The coefficient of static friction between m1 and the horizontal surface is 0.50, and the coefficient of kinetic friction is 0.30. (a) If the system is released from rest, what will its acceleration be? (b) If the system is set in motion with m2 moving downward, what will be the acceleration of the system?A 1.00 103-N crate is being pushed across a level floor at a constant speed by a force F of 3.00 102 N at an angle of 20.0 below the horizontal, as shown in Figure P4.23a. (a) What is the coefficient of kinetic friction between the crate and the floor? (b) If the 3.00 102-N force is instead pulling the block at an angle of 20.0 above the horizontal, as shown in Figure P4.23b, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that found in part (a). Figure P4.23A block of mass 3m is placed on a frictionless horizontal surface, and a second block of mass m is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude F is applied to the first block as in Figure P4.68. (a) Construct free-body diagrams for each block. (b) Identify the horizontal force that causes the block of mass m to accelerate. (c) Assume that the upper block does not slip on the lower block, and find the acceleration of each block in terms of m and F. Figure P4.68Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, a 10 000-kg load sits on the flatbed of a 20 000-kg truck moving at 12.0 m/s. Assume the load is not tied down to the truck and has a coefficient of static friction of 0.500 with the truck bed. (a) Calculate the minimum stopping distance for which the load will not slide forward relative to the truck. (b) Is any piece of data unnecessary for the solution?A crate of mass 45.0 kg is being transported on the flatbed of a pickup truck. The coefficient of static friction between the crate and the trucks flatbed is 0.350, and the coefficient of kinetic friction is 0.320. (a) The truck accelerates forward on level ground. What is the maximum acceleration the truck can have so that the crate does not slide relative to the trucks flatbed? (b) The truck barely exceeds this acceleration and then moves with constant acceleration, with the crate sliding along its bed. What is the acceleration of the crate relative to the ground?Objects with masses m1 = 10.0 kg and m2 = 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.64. If, when the system starts from rest, m2 falls 1.00 m in 1.20 s, determine the coefficient of kinetic friction between raj and the table.A hockey puck struck by a hockey stick is given an initial speed v0 in the positive x-direction. The coefficient of kinetic friction between the ice and the puck is k. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of part (a) to obtain an expression for the distance d the puck slides. The answer should be in terms of the variables v0, k, and g only.The coefficient of static friction between the 3.00-kg crate and the 35.0 incline of Figure P4.31 is 0.300. What minimum force F must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? Figure P4.31A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 80.0 N at an angle of 25.0 above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and floor is 0.300. (a) Find the acceleration of the box. (b) The student now starts moving the box up a 10.0 incline, keeping her 80.0 N force directed at 25.0 above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f = bv. Assume b = 15 kg/s and m = 50 kg. (a) What is the terminal speed the object reaches while falling? (b) Does your answer to part (a) depend on the initial speed of the object? Explain.A car is traveling at 50.0 km/h on a flat highway. (a) If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and the coefficient of friction is 0.600?A 3.00-kg block starts from rest at the top of a 30.0 incline and slides 2.00 m down the incline in 1.50 s. Find (a) the acceleration of the block, (b) the coefficient of kinetic friction between the block and the incline, (c) the frictional force acting on the block, and (d) the speed of the block after it has slid 2.00 m.A 15.0-lb block rests on a horizontal floor, (a) What force does the floor exert on the block? (b) A rope is tied to the block and is run vertically over a pulley. The other end is attached to a free-hanging 10.0-lb object. What now is the force exerted by the floor on the 15.0-lb block? (c) If the 10.0-lb object in part (b) is replaced with a 20.0-lb object, what is the force exerted by the floor on the 15.0-lb block?To meet a U.S. Postal Service requirement, employees footwear must have a coefficient of static friction of 0.500 or more on a specified tile surface. A typical athletic shoe has a coefficient of 0.800. In an emergency, what is the minimum time interval in which a person starting from rest can move 3.00 in on the tile surface if she is wearing (a) footwear meeting the Postal Service minimum and (b) a typical athletic shoe?Objects of masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string dial passes over a frictionless pulley as in Figure P4.70. The object m1 is held at rest on the floor, and m2 rests on a fixed incline of = 40.0. The objects are released from rest, and m2 slides 1.00 m down the incline in 4.00 s. Determine (a) the acceleration of each object, (b) the tension in the string, and (c) the coefficient of kinetic friction between m2 and the incline. Figure P4.70The person in Figure P4.49 weighs 170. lb. Each crutch makes an angle of 22.0 with the vertical (as seen from the front). Half of the persons weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet. Assuming he is at rest and the force exerted by the ground on the crutches acts along the crutches, determine (a) the smallest possible coefficient of friction between crutches and ground and (b) the magnitude of the compression force supported by each crutch. Figure P4.49As a protest against the umpires calls, a baseball pitcher throws a ball straight up into the air at a speed of 20.0 m/s. In the process, he moves his hand through a distance of 1.50 m. If the ball has a mass of 0.150 kg, find the force he exerts on the ball to give it this upward speed.Three objects are connected on a table as shown in Figure P4.73. The coefficient of kinetic friction between the block of mass m2 and the table is 0.350. The objects have masses of m1 = 4.00 kg, m2 = 1.00 kg, and m3 = 2.00 kg as shown, and the pulleys are frictionless. (a) Draw a diagram of the forces on each object. (b) Determine the acceleration of each object, including its direction. (c) Determine the tensions in the two cords. (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain. Figure P4.73The force exerted by the wind on a sailboat is approximately perpendicular 10 the sail and proportional to the component of the wind velocity perpendicular to the sail. For the 800-kg sailboat shown in Figure P4.58. the force exerted by the wind on the sailboat is Fsoil=(550Nm/s)vwind Water exerts a force along the keel (bottom) of the boat that prevents it from moving sideways, as shown in the figure Once the boat starts moving forward, water also exerts a drag force backwards on the boat, opposing the forward motion. If a 17-knot wind (1 knot = 0.514 m/s) is blowing to the east, what is the initial acceleration of the sailboat? Figure P 4.58(a) What is the resultant force exerted by the two cables supporting the traffic light in Figure P4.75? (b) What is the weight of the light? Figure P4.75(a) What is the minimum force of friction required to hold the system of Figure P4.74 in equilibrium? (b) What coefficient of static friction between the 100.-N block and the table ensures equilibrium? (c) If the coefficient of kinetic friction between the 100.-N block and the table is 0.250, what hanging weight should replace the 50.0-N weight to allow the system to move at a constant speed once it is set in motion? Figure P4.74A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.00 m/s. If the coefficient of friction between the sleds runners and the snow is 0.050 0 and the boy and sled together weigh 600. N, how far does the sled travel on the level surface before coming to rest?A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle above the horizontal (Fig. 4.76). She pulls on the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. (a) Draw a free-body diagram of the suitcase. (b) What angle does the strap make with the horizontal? (c) What is the magnitude of the normal force that the ground exerts on the suitcase? Figure P4.76A box rests on the back of a truck. The coefficient of static friction between the box and the bed of the truck is 0.800. (a) When the truck accelerates forward, what force accelerates the box? (b) Find the maximum acceleration the truck can have before the box slides.Three objects are connected by light strings as shown in Figure P4.78. The string connecting the 4.00-kg object and the 5.00-kg object passes over a light frictionless pulley. Determine (a) the acceleration of each object and (b) the tension in the two strings. Figure P4.78A frictionless plane is 10.0 m long and inclined at 35.0. A sled starts at the bottom with an initial speed of 5.00 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed vi. Both sleds reach the bottom of the incline at the same moment. (a) Determine the distance that the first sled traveled up the incline. (b) Determine the initial speed of the second sled.A high diver of mass 70.0 kg steps off a board 10.0 m above the water and falls vertical to the water, starting from rest. If her downward motion is stopped 2.00 s after her feet first touch the water, what average upward force did the water exert on her?A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed steel block wedge (of angle = 30.0) as shown in Figure P4.83. Making use of Table 4.2, determine (a) the acceleration of the two blocks and (b) the tension in the string. Figure P4.83An object of mass m1 hangs from a string that passes over a very light fixed pulley P1 as shown in Figure P4.68. The string connects to a second very light pulley P2. A second string passes around this pulley with one end attached to a wall and the other to an object of mass m2 on a frictionless, horizontal table, (a) If a1 and a2, are the accelerations of m1 and m2, respectively, what is the relation between these accelerations? Find expressions for (b) the tensions in the strings and (c) the accelerations a1 and a2? in terms of the masses m1 and m2. and g. Figure P4.68Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in Figure P4.85, where m1 = 10.0 kg and m2 = 20.0 kg. A force of 50.0 N is applied to the 20.0-kg box. (a) Determine the acceleration of each box and the tension in the string. (b) Repeat the problem for the case where the coefficient of kinetic friction between each box and the surface is 0.10. Figure P4.85Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, C, called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to sn for angles less than C? Explain. What can you definitely say about the magnitude of the friction force for any angle c? (c) Show that the coefficient of static friction is given by s = tan c. (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value c c such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction? Figure P4.82A fisherman poles a boat as he searches for his next catch. He pushes parallel to the length of the light pole, exerting a force of 240 N on the bottom of a shallow lake. The pole lies in the vertical plane containing the boats keel. At one moment, the pole makes an angle of 35.0 with the vertical and the water exerts a horizontal drag force of 47.5 N on the boat, opposite to its forward velocity of magnitude 0.857 m/s. The mass of the boat including its cargo and the worker is 370 kg. (a) The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force. (b) Assume the forces are constant user a short interval of time. Find the velocity of the boat 0.450 s after the moment described, (c) If the angle of the pole with respect to the vertical increased but the exerted force against the bottom remained the same, what would happen to buoyant forte and the acceleration of the boat?A rope with mass m, is attached to a block with mass mb, as in Figure P4.72. Both the rope and the block rest on a horizontal, frictionless surface. The rope does not stretch. The free end of the rope is pulled to the right with a horizontal force F. (a) Draw free-body diagrams for the rope and the block, noting that the tension in the rope is not uniform, (b) Find the acceleration of the system in terms of mb, mT, and F. (c) Find the magnitude of the force the rope exerts on the block, (d) What happens to the force on the block as the ropes mass approaches zero? What can you state about the tension in a light cord joining a pair of moving objects? Figure P4.72A car accelerates down a hill (Fig. P4.87), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m = 0.100 kg) hangs by a string from the cars ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle and (b) the tension in the string. Figure P4.8774APThe parachute on a race car of weight 8 820 N opens at the end of a quarter-mile run when the car is traveling at 35.0 m/s. What total retarding force must be supplied by the parachute to stop the car in a distance of 1.00 103 m?On an airplanes takeoff, the combined action of the air around the engines and wings of an airplane exerts an 8 000-N force on the plane, directed upward at an angle of 65.0 above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. (a) What is the weight of the plane? (b) What is its horizontal acceleration?The board sandwiched between two other boards in Figure P4.91 weighs 95.5 N. If the coefficient of friction between the boards is 0.663, what must be the magnitude of the compression forces (assumed to be horizontal) acting on both sides of the center board to keep it from slipping? Figure P4.91A sled weighing 60.0 N is pulled horizontally across snow so that the coefficient of kinetic friction between sled and snow is 0.100. A penguin weighing 70.0 N rides on the sled, as in Figure P4.86. If the coefficient of static friction between penguin and sled is 0.700, find the maximum horizontal force that can be exerted on the sled before the penguin begins to slide off. Figure P4.86A 72-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.2 m/s in 0.80 s. The elevator travels with this constant speed for 5.0 s, undergoes a uniform negative acceleration for 1.5 s, and then comes to rest What does the spring scale register (a) before the elevator starts to move? (b) During the first 0.80 s of the elevators ascent? (c) While the elevator is traveling at constant speed? (d) During the elevators negative acceleration?A magician pulls a tablecloth from under a 200-g mug located 30.0 cm from the edge of the cloth. The cloth exerts a friction force of 0.100 N on the mug and is pulled with a constant acceleration of 3.00 m/s2. How far does the mug move relative to the horizontal tabletop before the cloth is completely out from under it? Note that the cloth must move more than 30 cm relative to the tabletop during the process.An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P4.88), the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The childs true weight is 320- N, and the chair weighs 160 N. The childs feet are not touching the ground. (a) Show that the acceleration of the system is upward, and find its magnitude. (b) Find the force the child exerts on the chair. Figure P4.88A fire helicopter carries a 620-kg bucket of water at the end of a 20.0-m-long cable. Flying back from a fire at a constant speed of 40.0 m/s, the cable makes an angle of 40.0 with respect to the vertical. Determine the force exerted by air resistance on the bucket.A crate of weight Fg is pushed by a force P on a horizontal floor as shown in Figure P4.83. The coefficient of static friction is s, and P is directed at angle below the horizontal. (a) Show that the minimum value of P that will move the crate is given by P=sFgsec1stan (b) Find the condition on in terms of , for which motion of the crate is impossible for any value of P. Figure P4.83In Figure P1.84, the pulleys and the cord are light, all surfaces are frictionless, and the cord does not stretch. (a) How does the acceleration of block 1 compare with the acceleration of block 2? Explain your reasoning. (b) The mass of block 2 is m2 = 1.30 kg. Derive an expression for the acceleration of the block having mass m2 as a function of the mass of block 1, m1. (c) What does the result of part (b) predict if m1 is very much less than 1.30 kg? (d) What does the result of part (b) predict if m1 approaches infinity? (e) In this last case, what is the tension in the cord? (f) Could you anticipate the answers to parts (c), (d), and (e) without first doing part (b)? Explain. Figure P1.84What horizontal force must ho applied to a large block of mass M shown in Figure P4.85 so that the blocks remain stationary relative to M? Assume all surfaces and the pulley are frictionless. Notice that the force exerted by the string accelerates m2. Figure P4.85In Figure 5.5 (a)-(d), a block moves to the right in the positive x-direction through the displacement x while under the influence of a force with the same magnitude F. Which of the following is the correct order of the amount of work done by the force F, from most positive to most negative? (a) d, c, a, b (b) c, a, b, d (c) c, a, d, bThree identical halls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal, as in Figure 5.16. Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest. (a) 1, 2, 3 (b) 2, 1, 3 (c) 3, 1, 2 (d) All three balls strike the ground at the same speed. Figure 5.16 (Quick Quiz 5.3) A student throws three identical balls from the top of a building, each at the same initial speed hut at a different initial angle.Bob, of mass m, drops from a tree limb at the same time that Esther, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they reach the ground? (a) Bob's kinetic energy is greater than Esthers. (b) Esthers kinetic energy is greater than Bobs. (c) They have the same kinetic energy. (d) The answer depends on the shape of the slide.5.4QQPhysics Review A crane lifts a loud of bricks of mass 1 570 kg at an initial acceleration of 1.60 m/s2 Calculate the tension in the cable. (See Section 4.5.)Physics Review A crate of mass 20.0 kg rest on a level surface. If the coefficient of kinetic friction between the crate and surface is 0.400, (a) calculate the normal force and (b) the magnitude of the kinetic friction force when a horizontal applied force of 90.0 N moves the crate, (c) Calculate the normal force and (d) the magnitude of the kinetic friction force when the 90.0-N applied force is exerted at an angle of 35.0 above the horizontal. (See Section 4.6.)Calculate the work done by an applied force of 75.0 N on a crate if (a) the force is exerted horizontally while pushing the create 5.00 m and (b) the force is exerted at an angle of 35.0 above the horizontal. (See Section 5.1.)4WUE5WUEA 4.00-kg crate Marling at rest slides dawn a rough 6.00-m-long ramp, inclined at 30.0 below the horizontal The magnitude of the force of friction between the crate and the tamp is 8.00 N (a) How much work is done on the crate by friction? (b) What is the change in potential energy of the crate in sliding down the ramp? (c) What is the speed of the crate at the bottom of the incline? (See Sections 5.2 and 5.3.)A skier leaves a ski jump at 15.0 m/s at some angle . At what speed is he traveling at his maximum height of 4.50 m above the level of the end of the ski jump? (Neglect air friction.) (See Section 5.3.)A block of mass 3.00 kg is placed against a horizontal spring of constant k = 875 N/m and pushed so the spring compresses by 0.070 0 m. (a) What is the elastic potential energy of the block-spring system? (b) If the block is now released and the surface is frictionless, calculate the blocks speed after leaving the spring.What average mechanical power must a 70.0-kg mountain climber generate to climb to the summit of a hill of height 325 m in 45.0 min? Note: Due to inefficiencies in converting chemical energy to mechanical energy, the amount calculated here is only a fraction of the power that must be produced by the climbers body.A puck of mass 0.170 kg slides across ice in the positive x-direction with a kinetic friction coefficient between the ice and puck of 0.150. If the puck is moving at an initial speed of 12.0 m/s, (a) what is the force of kinetic friction? (b) What is the acceleration of the puck? (c) How long does it take for the puck to come to rest? (d) What distance does the puck travel during that time? (e) What total work does friction do on the puck? (f) What average power does friction generate in the puck during that time? (g) What instantaneous power does friction generate in the puck when the velocity is 6.00 m/s? (See Sections 2.5, 4.6, 5.1, and 5.6.)Consider a tug-of-war as in Figure CQ5.1, in which two teams pulling on a rope are evenly matched so that no motion takes place. Is work done on the rope? On the pullers? On the ground? Is work done on anything? Figure CQ5.1During a stress test of the cardiovascular system, a patient walks and runs on a treadmill, (a) Is the energy expended by the patient equivalent to the energy of walking and running on the ground? Explain, (b) What effect, if any, does tilting the treadmill upward have? Discuss.(a) If the height of a playground slide is kept constant, will the length of the slide or whether it has bumps make any difference in the final speed of children playing on it? Assume that the slide is slick enough to be considered frictionless. (b) Repeat part (a), assuming that the slide is not frictionless.(a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.Roads going up mountains are formed into switch-backs, with the road weaving back and forth along the face of the slope such that there is only a gentle rise on any portion of the roadway. Does this configuration require any less work to be done by an automobile climbing the mountain, compared with one traveling on a roadway that is straight up the slope? Why are switchbacks used?A bowling ball is suspended from the ceiling of a lecture hall by a strong cord. The ball is drawn away from its equilibrium position and released from rest at the tip of the demonstrators nose, as shown in Figure CQ5.6. (a) If the demonstrator remains stationary, explain why the ball does not strike her on its return swing. (b) Would this demonstrator be safe if the ball were given a push from its starting position at her nose?As a simple pendulum swings back and forth, the forces acting on the suspended object are the force of gravity, the tension in the supporting cord, and air resistance, (a) Which of these forces, if any, does no work on the pendulum? (b) Which of these forces does negative work at all times during the pendulums motion? (c) Describe the work done by the force of gravity while the pendulum is swinging.Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative: (a) a chicken scratching the ground, (b) a person studying, (c) a crane lifting a bucket of concrete, (d) the force of gravity on the bucket in part (c), (e) the leg muscles of a person in the act of sitting down.When a punter kicks a football, is he doing any work on the ball while the toe of his foot is in contact with it? Is he doing any work on the ball after it loses contact with his toe? Are any forces doing work on the ball while it is in flight?The driver of a car slams on her brakes to avoid colliding with a deer crossing the highway. What happens to the cars kinetic energy as it conies to rest?A weight is connected to a spring that is suspended vertically from the ceiling. If the weight is displaced downward from its equilibrium position and released, it will oscillate up and down. (a) If air resistance is neglected, will the total mechanical energy of the system (weight plus Earth plus spring) be conserved? (b) How many forms of potential energy are there for this situation?In most situations we have encountered in this chapter, frictional forces tend to reduce the kinetic energy of an object. However, frictional forces can sometimes increase an objects kinetic energy. Describe a few situations in which friction causes an increase in kinetic energy.Suppose you are reshelving books in a library. As you lift a book from the floor and place it on the top shelf, two forces act on the book: your upward lifting force and the downward gravity force. (a) Is the mechanical work done by your lifting force positive, zero, or negative? (b) Is the work done by the gravity force positive, zero, or negative? (c) Is the sum of the works done by both forces positive, zero, or negative?The feet of a standing person of mass m exert a force equal to mg on the floor, and the floor exerts an equal and opposite force upwards on the feet, which we call the normal force. During the extension phase of a vertical jump (see page 154), the feet exert a force on the floor that is greater than mg, so the normal force is greater than mg. As you learned in Chapter 4, we can use this result and Newtons second law to calculate the acceleration of the jumper: a = Fnet/m = (n mg)/m Using energy ideas, we know that work is performed on the juniper to give him or her kinetic energy. But the normal force cant perform any work here because the feet dont undergo any displacement. How is energy transferred to the jumper?An Earth satellite is in a circular orbit at an altitude of 500 km. Explain why the work done by the gravitational force acting on the satellite is zero. Using the work-energy theorem, what can you say about the speed of the satellite?Mark and David are loading identical cement blocks onto Davids pickup truck. Mark lifts his block straight up from the ground to the truck, whereas David slides his block up a ramp on massless, frictionless rollers. Which statement is true? (a) Mark does more work than David. (b) Mark and David do the same amount of work. (c) David does more work than Mark. (d) None of these statements is necessarily true because the angle of the incline is unknown. (e) None of these statements is necessarily true because the mass of one block is not given.If the speed of a particle is doubled, what happens to its kinetic energy? (a) It becomes four times larger. (b) It becomes two times larger. (c) It becomes 2 times larger. (d) It is unchanged. (e) It becomes half as large.A certain truck has twice the mass of a car. Both are moving at the same speed. If the kinetic energy of the truck is K, what is the kinetic energy of the car? (a) K/4 (b) K/2 (c) 0.71K (d) K (e) 2KIf the net work done on a particle is zero, which of the following statements must be true? (a) The velocity is zero. (b) The velocity is decreased. (c) The velocity is unchanged. (d) The speed is unchanged. (e) More information is needed.A car accelerates uniformly from rest. Ignoring air friction, when does the car require the greatest power? (a) When the car first accelerates from rest, (b) just as the car reaches its maximum speed, (c) when the car reaches half its maximum speed. (d) The question is misleading because the power required is constant. (e) More information is needed.A weight lifter lifts a 350-N set of weights from ground level to a position over his head, a vertical distance of 2.00 m. How much work does the weight lifter do, assuming he moves the weights at constant speed?In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth. (a) How much work did Arfeuille do on the object? (b) What magnitude force did he exert on the object during the lift, assuming the force was constant?3Pa shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25 below the horizontal. The force is just sufficient to overcome various frictional forces, so the cart moves at constant speed, (a) Find the work done by the shopper as she moves down a 50.0-m length aisle, (b) What is the net work done on the cart? Why? (c) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the work done by frictional forces doesnt change, would the shoppers applied force be larger, smaller, or the same? What about the work done on the cart by the shopper?Starting from rest, a 5.00-kg block slides 2.50 m down a rough 30.0 incline. The coefficient of kinetic friction between the block and the incline is k = 0.436. Determine (a) the work done by the force of gravity, (b) the work done by the friction force between block and incline, and (c) the work done by the normal force. (d) Qualitatively, how would the answers change if a shorter ramp at a steeper angle were used to span the same vertical height?A horizontal force of 150 N is used to push a 40.0-kg packing crate a distance of 6.00 m on a rough horizontal surface. If the crate moves at constant speed, find (a) the work done by the 150-N force and (b) the coefficient of kinetic friction between the crate and surface.A sledge loaded with bricks has a total mass of 18.0 kg and it pulled at constant speed by a rope inclined at 20.0 above the horizontal. The sledge moves a distance of 20.0 m on a horizontal surface. The confident of kinetic friction between the sledge and surface it 0.500. (a) What is the tension in the rope? (b) How much work is done by the rope on the sledge? (c) What is the mechanical energy lost due to friction?A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle = 25.0 below the horizontal as shown in Figure P5.8. Determine the work done by (a) the applied force, (b) the normal force exerted by the table, (c) the force of gravity, and (d) the net force on the block. Figure P5.8A mechanic pushes a 2.50 103-kg car from rest to a speed of v, doing 5.00 103 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, find (a) v and (b) the horizontal force excited on the car.A 7.00-kg bowling ball moves at 3.00 m/s. How fast must a 2.45-g Ping-Pong ball move so that the two balls have the same kinetic energy?A 65.0-kg runner has a speed of 5.20 m/s at one instant during a long-distance event. (a) What is the runners kinetic energy at this instant? (b) How much net work is required to double his speed?A worker pushing a 35.0-kg wooden crate at a constant speed for 12.0 m along a wood floor does 350 J of work by applying a constant horizontal force of magnitude F0 on the crate. (a) Determine the value of F0. (b) If the worker now applies a force greater than F0, describe the subsequent motion of the crate. (c) Describe what would happen to the crate if the applied force is less than F0.A 70-kg base runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. (a) How much mechanical energy is lost due to friction acting on the runner? (b) How far does he slide?A running 62-kg cheetah has a top speed of 32 m/s. (a) What is the cheetahs maximum kinetic energy? (b) Kind the cheetahs speed when its kinetic energy is one half of the value found in part (a).A 7.80-g bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming the frictional force is constant, determine how much time elapses between the moment the ballet enters the tree and the moment it stops moving.A 0.60-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 7.5 J at point B. What is (a) its kinetic energy at A? (b) Its speed at point B? (c) The total work done on the particle as it moves from A to B?A large cruise ship of mass 6.50 107 kg has a speed of 12.0 m/s at some instant. (a) What is the ships kinetic energy at this time? (b) How much work is required to stop it? (c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 2.50 km?A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.850 m/s encounters a rough horizontal surface of length l = 0.65 m as in Figure P5.18. If the coefficient of kinetic friction between the crate and rough surface is 0.558 and he exerts a constant horizontal force of 275 N on the crate, find (a) the magnitude and direction of the net force on the crate while it is on the rough surface, (b) the net work done on the crate while it is on the rough surface, and (c) the speed of the crate when it reaches the end of the rough surface. Figure P5.18A 0.20-kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone-Earth system (a) before the stone is released and (b) when it reaches the bottom of the well. (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?When a 2.50-kg object is hung vertically on a certain light spring described by Hookes law, the spring stretches 2.76 cm. (a) What is the force constant of the spring? (b) If the 2.50-kg object is removed, how far will the spring stretch if a 1.25-kg block is hung on it? (c) How much work must an external agent do to stretch the same spring 8.00 cm from its unstretched position?In a control system, an accelerometer consists of a 4.70-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 0.800g, the object should be at a location 0.500 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.A 60.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.0 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? (b) Select the height at which the athletes speed is 9.0 m/s as y = 0. What is her kinetic energy at this point? What is the gravitational potential energy associated with the athlete? (c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete? (d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. (e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer.A 2.10 103-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 5.00 m before coming into contact with the top of the beam, and it drives the beam 12.0 cm farther into the ground as it comes to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.Two blocks are connected by a light string that passes over two frictionless pulleys as in Figure P5.24. The block of mass m2 is attached to a spring of force constant k and m1 m2. If the system is released from rest, and the spring is initially not stretched or compressed, find an expression for the maximum displacement d of m2. Figure P5.24A daredevil on a motorcycle leaves the end of a ramp with a speed of 35.0 m/s as in Figure P5.25. If his speed is 33.0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance. Figure P5.25Truck suspensions often have helper springs dial engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in Figure P5.26. When the main leaf spring is compressed by distance y0, the helper spring engages and then helps to support, any additional load. Suppose the leaf spring constant is 5.25 105 N/m, the helper spring constant is 3.60 105 N/m, and y0 = 0.500 m. (a) What is the compression of the leaf spring for a load of 5.00 105 N? (b) How much work is done in compressing the springs? Figure P5.26The chin-up is one exercise that can be used to strengthen the biceps muscle. This muscle can exert a force of approximately 8.00 102 N as it contracts a distance of 7.5 cm in a 75-kg male.3 (a) How much work can the biceps muscles (one in each arm) perform in a single contraction? (b) Compare this amount of work with the energy required to lift a 75-kg person 40. cm in performing a chin-up. (c) Do you think the biceps muscle is the only muscle involved in performing a chin-up?A flea is able to jump about 0.5 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100-story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle is proportional to its cross-sectional area, and the work done by the muscle is this force times the length of contraction. If we magnified a flea by a factor of 1 000, the cross section of its muscle would increase by 1 0002 and the length of contraction would increase by 1 000. How high would this superflea be able to jump? (Dont forget that the mass of the superflea" increases as well.)A 50.0-kg projectile is fired at an angle of 30.0 above the horizontal with an initial speed of 1.20 102 m/s from the top of a cliff 142 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of the projectile? (b) Suppose the projectile is traveling 85.0 m/s at its maximum height of y = 427 m. How much work has been done on the projectile by air friction? (c) What is the speed of the projectile immediately before it hits the ground if air friction does one and a half times as much work on the projectile when it is going down as it did when it was going up?A projectile of mass m is fired horizontally with an initial speed of v0 from a height of h above a flat, desert surface. Neglecting air friction, at the instant before the projectile hits the ground, find the following in terms of m, v0, h, and g: (a) the work done by the force of gravity on the projectile, (b) the change in kinetic energy of the projectile since it was fired, and (c) the final kinetic energy of the projectile. (d) Are any of the answers changed if the initial angle is changed?A horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in Figure 5.22. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 6.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. (d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. Substitute to obtain a numerical value. (e) What is the speed at the halfway point? Why isnt it half the speed at equilibrium?A 50.-kg pole vaulter running at 10. m/s vaults over the bar. Her speed when she is above the bar is 1.0 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 m/s at the bottom, what is the height of the hill?Hookes law describes a certain light spring of unstretched length 35.0 cm. When one end is attached to the top of a door frame and a 7.50-kg object is hung from the other end, the length of the spring is 41.5 cm. (a) Find its spring constant, (b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 190 N. Find the length of the spring in this situation.A 0.250-kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light spring of force constant 4.60 N/m located at the end of the track. (a) What is the springs maximum compression if the track is frictionless? (b) If the track is not frictionless, would the springs maximum compression be greater than, less than, or equal to the value obtained in part (a)?A block of mass m = 5.00 kg is released from rest from point and slides on the frictionless track shown in Figure P5.36. Determine (a) the blocks speed at points and and (b) the net work done by the gravitational force on the block as it moves from point from to . Figure P5.36Tarzan savings on a 30.0-m-long vine initially inclined at an angle of 37.0 with the vertical. What is his speed at the bottom of the swing (a) if he starts from rest? (b) If he pushes off with a speed of 4.00 m/s?Two blocks are connected by a light string that passes over a frictionless pulley as in Figure P5.38. The system is released from rest while m2 is on the floor and m1 is a distance h above the floor. (a) Assuming m1 m2, Find an expression for the speed of m1 just as it reaches the floor. (b) Taking m1 = 6.5 kg, m2 = 4.2 kg, and h = 3.2 m, evaluate your answer to part (a), and (c) find the speed of each block when m1 has fallen a distance of 1.6 m. Figure P5.38The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.39a. If the spring is compressed a distance of 0.120 m and the gun fired vertically as shown, the gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile. Neglecting all resistive forces, (a) describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height, (b) determine the spring constant, and (c) find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure P5.39b. Figure P5.39(a) A block with a mass m is pulled along a horizontal surface for a distance x by a constant force F at an angle with respect to the horizontal. The coefficient of kinetic friction between block and table is k the force exerted by friction equal to kmg? If not, what is the force exerted by friction? (b) How much work is done by the friction force and by F? (Dont forget the signs.) (c) Identify all the forces that do no work on the block, (d) Let m = 2.00 kg, x = 4.00 m, = 37.0, F= 15.0 N, and k = 0.400, and find I the answers to parts (a) and (b). Figure P5.39(a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it. Can the equation for conservation of mechanical energy be used on the child? (b) Is the mass of the child a factor in determining his speed at the bottom of the slide? (c) The child drops straight down rather than following the curved ramp of the slide. In which case will he be traveling faster at ground level? (d) If friction is present, how would the conservation-of-energy equation be modified? (e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 12.0 m.An airplane of mass 1.50 104 kg is moving at 60.0 m/s. The pilot then increases the engines thrust to 7.50 104 N. The resistive force exerted by air on the airplane has a magnitude of 4.00 104 N. (a) Is the work done by the engine on the airplane equal to the change in the airplanes kinetic energy after it travels through some distance through the air? Is mechanical energy conserved? Explain. (b) Find the speed of the airplane after it has traveled 5.00 102 m. Assume the airplane is in level flight throughout the motion.The system shown in Figure P5.43 is used to lift an object of mass m = 76.0 kg. A constant downward force of magnitude F is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find (a) the required value of F, (b) the tensions T1, T2, and T3, and (c) the work done by the applied force in raising the object a distance of 1.80 m. Figure P5.43A 25.0-kg child on a 2.00-m-long swing is released from rest when the ropes of the swing make an angle of 30.0 with the vertical. (a) Neglecting friction, find the childs speed at the lowest position. (b) If the actual speed of the child at the lowest position is 2.00 m/s, what is the mechanical energy lost due to friction?A 2.1 103-kg car starts from rest at the top of a 5.0-m-long driveway that is inclined at 20.0 with the horizontal. If an average friction force of 4.0 103 N impedes the motion, find the speed of the car at the bottom of the driveway.A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed V0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle . (f) Would your answers be the same if the waterslide were not frictionless? Explain. Figure P5.46A skier starts from rest at the top of a hill that is inclined 10.5 with respect to the horizontal. The hillside is 2.00 102 m long, and the coefficient of friction between snow and skis is 0.075 0. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest?In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 4.0 m/s up a 20.0 inclined track. The combined mass of monkey and sled is 20. kg, and the coefficient of kinetic friction between sled and incline is 0.20. How far up the incline do the monkey and sled move?An 80.0-kg skydiver jumps out of a balloon at an altitude of 1.00 103 m and opens the parachute at an altitude of 200.0 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3.60 103 N with the parachute open, what is the speed of the diver when he lands on the ground? (b) Do you think the skydiver will get hurt? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.Q A skier of mass 70.0 kg is pulled up a slope by a motor-driven cable, (a) How much work is required to pull him 60.0 m up a 30.0 slope (assumed frictionless) at a constant speed of 2.00 m/s? (b) What power (expressed in hp) must a motor have to perform this task?A 3.50-kN piano is lilted by three workers at constant speed to an apartment 25.0 m above the street using a pulley system fastened to the roof of the building. Each worker is able to deliver 165 W of power, and the pulley system is 75% efficient (so that 25% of the mechanical energy is lost due to friction in the pulley). Neglecting the mass of the pulley, find the time required to lift the piano from the street to the apartment.While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 60.-kg person develops a power of 70. W during a race, how fast is the person running? (Assume a running step is 1.5 m long.)The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the mechanical energy loss due to frictional forces exerted on the car by the air and the road. If the power developed by an engine is 175 hp, estimate the total frictional force acting on the car when it is moving at a speed of 29 m/s. One horsepower equals 746 W.55P56PA 1.50 103-kg car starts from rest and accelerates uniformly to 18.0 m/s in 12.0 s. Assume that, air resistance remains constant at 4.00 102 N during this time. Find (a) the average power developed by the engine and (b) the instantaneous power output of the engine at t = 12.0 s, just before the car stops accelerating.A 6.50 102-kg elevator starts from rest and moves upward for 3.00 s with constant acceleration until it reaches its cruising speed, 1.75 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upward trip with constant speed?The force acting on a particle varies as in Figure P5.59. Find the work done by the force as the particle moves (a) from x = 0 to x = 8.00 m, (b) from x = 8.00m to x = 10.0 m, and (c) from x = 0 to x = 10.0 m. Figure P5.59An object of mass 3.00 kg is subject to a force Fx that varies with position as in Figure P5.60. Find the work done by the force on the object as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x = 10.0 m to x = 15.0 m. (d) If the object has a speed of 0.500 m/s at x = 0, find its speed at x = 5.00 m and its speed at x = 15.0 m. Figure P5.60The force acting on an object is given by Fx = (8x 16) N, where x is in meters, (a) Make a plot of this force vs. x from x = 0 to x = 3.00 m. (b) From your graph, find the net work done by the force as the object moves from x = 0 to x = 3.00 m.An outfielder throws a 0.150-kg baseball at a speed of 40.0 m/s and an initial angle of 30.0. What is the kinetic energy of the hall at the highest point of its motion?A person doing a chin-up weighs 700 N, exclusive of the arms. During the first 25.0 cm of the lift, each arm exerts an upward force of 355 N on the torso. If the upward movement starts from rest, what is the persons velocity at that point?A boy starts at rest and slides down a frictionless slide as in Figure P5.64. The bottom of the track is a height h above the ground. The boy then leaves the track horizontally, striking the ground a distance d as shown. Using energy methods, determine the initial height H of the boy in terms of h and d. Figure P5.64A roller-coaster car of mass 1.50 103 kg is initially at the top of a rise at point . It then moves 35.0 m at an angle of 50.0 below the horizontal to a lower point . (a) Find both the potential energy of the system when the car is at points and and the change in potential energy as the car moves from point to point , assuming y = 0 at point . (b) Repeat part (a), this time choosing y = 0 at point , which is another 15.0 m down the same slope from point .A ball of mass m = 1.80 kg is released from rest at a height h = 65.0 cm above a light vertical spring of force constant k as in Figure P5.64a. The ball strikes the top of the spring and compresses it a distance d = 9.00 cm as in Figure P5.64b. Neglecting any energy losses during the collision, find (a) the speed of the hall just as it touches the spring and (b) the force constant of the spring.An archer pulls her bowstring back 0.400 m by exerting a force that increases uniformly from zero to 230 N. (a) What is the equivalent spring constant of the bow? (b) How much work does the archer do in pulling the bow? Figure P5.64A block of mass 12.0 kg slides from rest down a frictionless 35.0 incline and is stopped by a strong spring with k = 3.00 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?(a) A 75-kg man steps out a window and falls (from rest) 1.0 m to a sidewalk. What is his speed just before his feet strike the pavement? (b) If the man falls with his knees and ankles locked, the only cushion for his fall is an approximately 0.50-cm give in the pads of his feet. Calculate the average force exerted on him by the ground during this 0.50 cm of travel. This average force is sufficient to cause damage to cartilage in the joints or to break bones.A toy gun uses a spring to project a 5.3-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of 0.032 N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.0 cm for this launch?Two objects (m1 = 5.00 kg and m2 = 3.00 kg) are connected by a light string passing over a light, frictionless pulley as in Figure P5.69. The 5.00-kg object is released from rest at a point h = 4.00 m above the table. (a) Determine the speed of each object when the two pass each oilier. (b) Determine the speed of each object at the moment the 5.00-kg object hits the table. (c) How much higher does the 3.00-kg object travel after the 5.00-kg objecthits the table? Figure P5.69In a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patients body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 375 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.60 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.20 N on it. Find (a) the maximum speed of the needle and (b) the speed at which a flange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm.A 2.00 102-g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R = 30.0 cm (Fig. P5.71). Calculate (a) its gravitational potential energy at A relative to B, (b) its kinetic energy at B, (c) its speed at B, (d) its potential energy at C relative to B, and (e) its kinetic energy at C. Figure P5.71 Problems 71 and 72.The particle described in Problem 71 (Fig. P5.71) is released from point A at rest. Its speed at B is 1.50 m/s. (a) What is its kinetic energy at B? (b) How much mechanical energy is lost as a result of friction as the particle goes from A to B? (c) Is it possible to determine from these results in a simple manner? Explain.A light spring with spring constant 1.20 103 N/m hangs from an elevated support. From its lower end hangs a second light spring, which has spring constant 1.80 103 N/m. A 1.50-kg object hangs at rest from the lower end of the second spring, (a) Find the total extension distance of the pair of springs, (b) Find the effective spring constant of the pair of springs as a system. We describe these springs as being in series. Hint: Consider the forces on each spring separately.76APIn terms of saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 10.0 mi/h, a cyclist uses food energy at a rate of about 400 kcal/h above what he would use if he were merely sitting still. (In exercise physiology, power is often measured in kcal/h rather than in watts. Here, 1 kcal = 1 nutritionists Calorie = 4 186 J.) Walking at 3.00 mi/h requires about 220 kcal/h. It is interesting to compare these values with the energy consumption required for travel by car. Gasoline yields about 1.30 108 J/gal. Find the fuel economy in equivalent miles per gallon for a person (a) walking and (b) bicycling.Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is 1 kilocalorie, which we define in Chapter 11 as 1 kcal = 4 186 J. Metabolizing 1 gram of fat can release 9.00 kcal. A student decides to try to lose weight by exercising. She plans to run up and down the stairs in a football stadium as fast as she can and as many times as necessary. Is this in itself a practical way to lose weight? To evaluate the program, suppose she runs up a flight of 80 steps, each 0.150 m high, in 65.0 s. For simplicity, ignore the energy she uses in coming down (which is small). Assume that a typical efficiency for human muscles is 20.0%. This means that when your body converts 100 J from metabolizing fat, 20 J goes into doing mechanical work (here, climbing stairs). The remainder goes into internal energy. Assume the students mass is 50.0 kg. (a) How many times must she run the flight of stairs to lose 1 pound of fat? (b) What is her average power output, in watts and in horsepower, as she is running up the stairs?A ski jumper starts from rest 50.0 m above the ground on a frictionless track and flies off the track at an angle of 45.0 above the horizontal and at a height of 10.0 m above the level ground. Neglect air resistance, (a) What is her speed when she leaves the track? (b) What is the maximum altitude she attains after leaving the track? (c) Where does she land relative to the end of the track?A 5.0-kg block is pushed 3.0 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of = 30 with the horizontal, as shown in Figure P5.76. If the coefficient of kinetic friction between block and wall is 0.30, determine the work done by (a) , (b) the force of gravity, and (c) the normal force between block and wall, (d) By how much does the gravitational potential energy increase during the blocks motion? Figure P5.76A childs pogo slick (Fig. P5.77) stores energy in a spring (k = 2.50 104 N/m). At position (x1 = 0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position (x = 0), the spring is relaxed and the child is moving upward. At position , the child is again momentarily at rest at the top of the jump. Assuming that the combined mass of child and pogo stick is 25.0 kg, (a) calculate the total energy of the system if both potential energies are zero at x = 0, (b) determine x2, (c) calculate the speed of the child at x = 0, (d) determine the value of x for which the kinetic energy of the system is a maximum, and (e) obtain the childs maximum upward speed. Figure P5.77A hummingbird is able to hover because, as the wings move downward, they exert a downward force on the air. Newtons third law tells us that the air exerts an equal and opposite force (upward) on the wings. The average of this force must be equal to the weight of the bird when it hovers. If the wings move through a distance of 3.5 cm with each stroke, and the wings beat 80 times per second, determine the work performed by the wings on the air in 1 m if the mass of the hummingbird is 3.0 g.In the dangerous sport of bungee jumping, a daring student jumps from a hot air balloon with a specially designed elastic cord attached to his waist. The unstretched length of the cord is 25.0 m, the student weighs 7.00 102 N, and the balloon is 36.0 m above the surface of a river below. Calculate the required force constant of the cord if the student is to stop safely 4.00 m above the river.The masses of the javelin, discus, and shot are 0.80 kg, 2.0 kg, and 7.2 kg, respectively, and record throws in the corresponding track events are about 98 m, 74 m, and 23 m, respectively. Neglecting air resistance, (a) calculate the minimum initial kinetic energies that would produce these throws, and (b) estimate the average force exerted on each object during the throw, assuming the force acts over a distance of 2.0 m. (c) Do your results suggest that air resistance is an important factor?A truck travels uphill with constant velocity on a highway with a 7.0 slope. A 50.-kg package sits on the floor of the back of the truck and does not slide, due to a static frictional force. During an interval in which the truck travels 340 m, (a) what is the net work done on the package? What is the work done on the package by (b) the force of gravity, (c) the normal force, and (d) the friction force?A daredevil wishes to bungee-jump from a hot-air balloon 65.0 m above a carnival midway. He will use a piece of uniform elastic cord lied to a harness around his body to stop his fall at a point 10.0 m above the ground. Model his body as a particle and the cord as having negligible mass and a tension force described by Hooke's force law. In a preliminary test, hanging at rest from a 5.00-m length of the cord, the jumper finds that his body weight stretches it by 1.50 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon. (a) What length of cord should he use? (b) What maximum acceleration will he experience?87APAn object of mass m is suspended from the top of a cart by a string of length L as in Figure P5.88a. The cart and object are initially moving to the right at a constant speed 0. The cart comes to rest after colliding and sticking to a bumper, as in Figure P5.88b, and the suspended object swings through an angle . (a) Show that the initial speed is 0=2gL(1cos). (b) If L = 1.20 m and = 35.0, find the initial speed of the cart (Hint: The force exerted by the string on the object docs no work on the object.) Figure P5.88aThree objects with masses m1 = 5.00 kg, m2 = 10.0 kg, and m3 = 15.0 kg, respectively, are attached by strings over frictionless pulleys as indicated in Figure P5.85. The horizontal surface exerts a force of friction of 30.0 N on m2. If the system is released from rest, use energy concepts to find the speed of m3 after it moves down 4.00 m. Figure P5.8590AP91APTwo blocks, A and B (with mass 50.0 kg and 1.00 102 kg, respectively), are connected by a string, as shown in Figure P5.86. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between block A and the incline is k = 0.250. Determine the change in the kinetic energy of block A as it moves from to , a distance of 20.0 m up the incline (and block B drops downward a distance of 20.0 m) if the system starts from rest. Figure P5.86Two masses m1 and m2, with m1 m2, have equal kinetic energy. How do the magnitude of their momenta compare? (a) Not enough information is given. (b) p1 p2 (c) p1 = p2 (d) p1 p2.A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft (a) remains stationary, (b) moves away from the shore, or (c) moves toward the shore. (Hint: Use conservation of momentum.)A car and a large truck traveling at the same speed collide head-on and stick together. Which vehicle undergoes the larger change in the magnitude of its momentum? (a) the car (b) the truck (c) the change in the magnitude of momentum is the same for both (d) impossible to determine without more information.An object of mass m moves to the right with a speed v. It collides head-on with an object of man 3m moving with speed v/3 in the opposite direction. If the two objects stick together, what is the speed of the combined object, of mass 4w, after the collision? (a) 0 (b) v/2 (c)v (d)2vA skater is using very low-friction rollerblades. A friend throws a Frisbee to her, on the straight line along which she is coasting. Describe each of the following events as an elastic, an inelastic, or a perfectly inelastic collision between the skater and the Frisbee. (a) She catches the Frisbee and holds it. (b) She tries to catch the Frisbee, but it bounces off her hands and falls to the ground in front of her. (c) She catches the Frisbee and immediately throws it back with the same speed (relative to the ground) to her friend.In a perfectly inelastic one-dimensional collision between two objects, what initial condition alone is necessary so that all of the original kinetic energy of the system is gone after the collision? (a) The objects must have momenta with the same magnitude but opposite directions, (b) The objects must have the same mass, (c) The objects must have the same velocity, (d) The objects must have the same speed, with velocity vectors in opposite directions.Math Review Solve the two equations mi + MVi = mf + MVf and i Vi = (f Vf) for (a) f and (b) Vf if m = 2.00 kg, i = 4.00 m/s, M = 3.00 kg, and Vi = 0. (See Section 6.3.)Math Review Given the equations 507 = 147 Vf cos and 377 = 147 Vf sin , find (a) Vf by using the identity cos2 + sin2 = 1, and (b) by using the inverse tangent function. (Note: Some may consider it easier finding the angle first, and then Vf by back substitution.) (See Section 6.4.)Math Review (a) Solve the equation 7.20 103 m/s = (4.20 103 m/s) ln (Mi/Mf) for the fraction Mi/Mf. (b) If Mi = 2.65 104 kg, calculate Mf.A soccer player runs up behind a 0.450-kg soccer ball traveling at 3.20 m/s and kicks it in the same direction as it is moving, increasing its speed to 12.8 m/s. (a) What is the change in the magnitude of the balls momentum? (b) What magnitude impulse did the soccer player deliver to the ball? (c) What magnitude impulse would be required to kick the ball in the opposite direction at 12.8 m/s, instead? (See Section 6.1.)A 57.0-g tennis ball is traveling straight at a player at 21.0 m/s. The player volleys the ball straight back at 25.0 m/s. (a) What is the magnitude of the balls change of momentum? (b) If the ball remains in contact with the racket for 0.060 0 s, what average force acts on the ball? (See Section 6.1.)An astronaut, of total mass 85.0 kg including her suit, stands on a spherical satellite of mass 375 kg, both at rest relative a nearby space station. She jumps at a speed of 2.56 m/s directly away from the satellite, as measured by an observer in the station. At what speed does that observer measure the satellite traveling in the opposite direction? (See Section 6.2.)7WUEA car of mass 750 kg traveling at a velocity of 27 m/s in the positive x-direction crashes into the rear of a truck of mass 1 500 kg that is at rest and in neutral at an intersection. If the collision is inelastic and the truck moves forward at 15.0 m/s, what is the velocity of the car after the collision? (See Section 6.3.)A car of mass 1 560 kg traveling east and a truck of equal mass traveling north collide and become entangled, moving as a unit at 15.0 m/s and 60.0 north of east. Find the speed of (a) the car, and (b) the truck prior to the collision. (See Section 6.4.)10WUE11WUEA batter bunts a pitched baseball, blocking the ball without swinging, (a) Can the baseball deliver more kinetic energy to the bat and batter than the ball carries initially? (b) Can the baseball deliver more momentum to the bat and batter than the ball carries initially? Explain each of your answers.If two objects collide and one is initially at rest, (a) is it possible for both to be at rest after the collision? (b) Is it possible for only one to be at rest after the collision? Explain.3CQAmericans will never forget the terrorist attack on September 11, 2001. One commentator remarked that the force of the explosion at the Twin Towers of the World Trade Center was strong enough to blow glass and parts of the steel structure to small fragments. Yet the television coverage showed thousands of sheets of paper floating down, many still intact. Explain how that could be.A ball of clay of mass m is thrown with a speed v against a brick wall. The clay sticks to the wall and stops. Is the principle of conservation of momentum violated in this example?A skater is standing still on a frictionless ice rink. Her friend throws a Frisbee straight to her. In which of the following cases is the largest momentum transferred to the skater? (a) The skater catches the Frisbee and holds onto it. (b) The skater catches the Frisbee momentarily, but then drops it vertically downward, (c) The skater catches the Frisbee, holds it momentarily, and throws it back to her friend.A more ordinary example of conservation of momentum than a rocket ship occurs in a kitchen dishwashing machine. In this device, water at high pressure is forced out of small holes on the spray arms. Use conservation of momentum to explain why the arms rotate, directing water to all the dishes.(a) If two automobiles collide, they usually do not stick together. Does this mean the collision is elastic? (b) Explain why a head-on collision is likely to be more dangerous than other types of collisions.Your physical education teacher throws you a tennis ball at a certain velocity, and you catch it. You are now given the following choice: The teacher can throw you a medicine ball (which is much more massive than the tennis ball) with the same velocity, the same momentum, or the same kinetic energy as the tennis ball. Which option would you choose in order to make the easiest catch, and why?A large bedsheet is held vertically by two students. A third student, who happens to be the star pitcher on the baseball team, throws a raw egg at the sheet. Explain why the egg doesnt break when it hits the sheet, regardless of its initial speed. (If you try this, make sure the pitcher hits the sheet near its center, and dont allow the egg to fall on the floor after being caught.)A sharpshooter fires a rifle while standing with the butt of the gun against his shoulder. If the forward momentum of a bullet is the same as the backward momentum of the gun, why isn't it as dangerous to be hit by the gun as by the bullet?An air bag inflates when a collision occurs, protecting a passenger (the dummy in Figure CQ6.12) from serious injury. Why does the air bag soften the blow? Discuss the physics involved in this dramatic photograph.13CQAn open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box? Explain.Does a larger net force exerted on an object always produce a larger change in the momentum of the object, compared to a smaller net force? Explain.Does a larger net force always produce a larger change in kinetic energy than a smaller net force? Explain.If two particles have equal momenta, are their kinetic energies equal? (a) yes, always (b) no, never (c) no, except when their masses are equal (d) no, except when their speeds are the same (c) yes, as long as they move along parallel lines.Two particles of different mass start from rest. The same net force acts on both of them as they move over equal distances. How do their final kinetic energies compare? (a) The particle of larger mass has more kinetic energy, (b) The particle of smaller mass has more kinetic energy, (c) The particles have equal kinetic energies, (d) Either particle might have more kinetic energy.Calculate the magnitude of the linear momentum for the following cases: (a) a proton with mass equal to 1.67 1027 kg, moving with a speed of 5.00 106 m/s; (b) a 15.0-g bullet moving with a speed of 300 m/s; (c) a 75.0-kg sprinter running with a speed of 10.0 m/s; (d) the Earth (mass = 5.98 1024 kg) moving with an orbital speed equal to 2.98 104 m/s.A high-speed photograph of a club hitting a golf ball is shown in Figure 6.3. The club was in contact with a ball, initially at rest, for about 0.002 0 s. If the ball has a mass of 55 g and leaves the head of the club with a speed of 2.0 102 ft/s, find the average force exerted on the ball by the club.A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-kg bullet moving with a speed of 1.50 103 m/s (a) What must the baseballs speed be if the pitchers claim is valid? (b) Which has greater kinetic energy, the ball or the bullet?A ball of mass m is thrown straight up into the air with an initial speed v0. (a) Find an expression for the maximum height reached by the ball in terms of v0 and g. (b) Using conservation of energy and the result of part (a), find the magnitude of the momentum of the ball at one-half its maximum height in terms of m and 0.Drops of rain fall perpendicular to the roof of a parked car during a rainstorm The drops strike the roof with a speed of 12 m/s, and the mass of rain per second striking the roof is 0.035 kg/s. (a) .Assuming the drops come to rest after striking the roof, find the average force exerted by the rain on the roof. (b) If hailstones having the same mass as the raindrops fall on the roof at the same rate and with the same speed, how would the average force on the roof compare to that found in part (a)?Show that the kinetic energy of a particle of mass m is related to the magnitude of the momentum p of that particle by KE = p2/2m. (Note: This expression is invalid for particles traveling at speeds near that of light.)An object has a kinetic energy of 275 J and a momentum of magnitude 25.0 kg m/s. Find the (a) speed and (b) mass of the objectAn estimated force vs. time curve for a baseball struck by a bat is shown in Figure P6.8. From this curve, determine (a) the impulse delivered to the ball and (b) the average force exerted on the ball.A 0.280-kg volleyball approaches a player horizontally with a speed of 15.0 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s. (a) What impulse is delivered to the ball by the player? (b) If the player's fist is in contact with the hall for 0.060 0 s, find the magnitude of the average force exerted on the players fist.A man claims he ran safely hold on to a 12.0-kg child in a head-on collision with a relative speed of 120-mi/h lasting for 0.10 s as long as he has his seat belt on. (a) Find the magnitude of the average force needed to hold onto the child, (b) Based on the result to part (a), is the mans claim valid? (c) What does the answer to this problem say about laws requiring the use of proper safely devices such as seat belts and special toddler seats?A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m. What impulse was given to the ball by the floor?A tennis player receives a shot with the ball (0.060 0 kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction. (a) What is the impulse delivered to the ball by the racket? (b) What work does the racket do on the hall?A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from 0 to 5.20 m/s in 0.832 s. What are the magnitudes of (a) the linear impulse and (b) the average total force experienced by a 70.0-kg passenger in the car during the time the car accelerates?A 65.0-kg basketball player jumps vertically and leaves the floor with a velocity of 1.80 m/s upward, (a) What impulse does the player experience? (b) What force does the floor exert on the player before the jump? (c) What is the total average force exerted by the floor on the player if the player is in contact with the floor for 0.450 s during the jump?The force shown in the force vs. time diagram in Figure P6.15 acts on a 1.5-kg object. Find (a) the impulse of the force, (b) the final velocity of the object if it is initially at rest, and (c) the final velocity of the object if it is initially moving along the x-axis with a velocity of 2.0 m/s. Figure P6.15A force of magnitude Fx acting in the x-direction on a 2.00-kg particle varies in time as shown in Figure P6.16. Find (a) the impulse of the force, (b) the final velocity of the particle if it is initially at rest, and (c) the final velocity of the particle if it is initially moving along the x-axis with a velocity of 2.00 m/s. Figure P6.16The forces shown in the force vs. time diagram in Figure P6.17 act on a 1.5-kg particle. Find (a) the impulse for the interval from t = 0 to t = 3.0 s and (b) the impulse for the interval from t = 0 to t = 5.0 s. If the forces act on a 1.5-kg particle that is initially at rest, find the particle's speed (c) at t = 3.0 s and (d) at t = 5.0 s. Figure P6.17A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of = 60.0 with the plane of the wall. It bounces off the wall with the same speed and angle (Fig. P6.18). If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball? Figure P6.18The front 1.20 m of a 1 400-kg car is designed as a crumple zone that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops uniformly in 1.20 m, (a) how long does the collision last, (b) what is the magnitude of the average force on the car, and (c) what is the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.