Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 8, Problem 8.56AP

(a)

To determine

The height covered by the projectile above the point B.

(b)

To determine

To draw: Draw four energy bar charts for this situation.

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A ball of mass  m = 1.75 kg  is released from rest at a height  h = 68.0 cm  above a light vertical spring of force constant k as in Figure [a] shown below. The ball strikes the top of the spring and compresses it a distance  d = 8.50 cm  as in Figure [b] shown below. Neglecting any energy losses during the collision, find the following. Figures a and b show a ball of mass m above a spring of force constant k that is vertically aligned such that its lower end is attached to the ground and its upper end is unattached.   (a) Find the speed of the ball just as it touches the spring.  m/s(b) Find the force constant of the spring.

Chapter 8 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 8 - In a laboratory model of cars skidding to a stop,...Ch. 8 - What average power is generated by a 70.0-kg...Ch. 8 - A ball of clay falls freely to the hard floor. It...Ch. 8 - A pile driver drives posts into the ground by...Ch. 8 - One person drops a ball from the top of a building...Ch. 8 - A car salesperson claims that a 300-hp engine is a...Ch. 8 - Prob. 8.3CQCh. 8 - Prob. 8.4CQCh. 8 - Prob. 8.5CQCh. 8 - Prob. 8.6CQCh. 8 - In the general conservation of energy equation,...Ch. 8 - Consider the energy transfers and transformations...Ch. 8 - A block is connected to a spring that is suspended...Ch. 8 - In Chapter 7, the work-kinetic energy theorem, W =...Ch. 8 - For each of the following systems and time...Ch. 8 - Prob. 8.2PCh. 8 - A block of mass 0.250 kg is placed on top of a...Ch. 8 - A 20.0-kg cannonball is fired from a cannon with...Ch. 8 - cal energy of the ballEarth sys-tem at the maximum...Ch. 8 - A block of mass m = 5.00 kg is released from point...Ch. 8 - Two objects are connected by a light string...Ch. 8 - Prob. 8.8PCh. 8 - A light, rigid rod is 77.0 cm long. Its top end is...Ch. 8 - At 11:00 a.m, on September 7, 2001, more than one...Ch. 8 - Prob. 8.11PCh. 8 - A sled of mass m is given a kick on a frozen pond....Ch. 8 - A sled of mass m is given a kick on a frozen pond....Ch. 8 - A crate of mass 10.0 kg is pulled up a rough...Ch. 8 - A block of mass m = 2.(K) kg is attached to a...Ch. 8 - A 40.0-kg box initially at rest is pushed 5.00 m...Ch. 8 - A smooth circular hoop with a radius of 0.500 m is...Ch. 8 - At time ti, the kinetic energy of a particle is...Ch. 8 - A boy in a wheelchair (total mass 47.0 kg) has...Ch. 8 - As shown in Figure P8.10, a green bead of mass 25...Ch. 8 - A toy cannon uses a spring to project a 5.30-g...Ch. 8 - The coefficient of friction between the block of...Ch. 8 - A 5.00-kg block is set into motion up an inclined...Ch. 8 - A 1.50-kg object is held 1.20 m above a relaxed...Ch. 8 - A 200-g block is pressed against a spring of force...Ch. 8 - An 80.0-kg skydiver jumps out of a balloon at an...Ch. 8 - Prob. 8.27PCh. 8 - Sewage at a certain pumping station is raised...Ch. 8 - An 820-N Marine in basic training climbs a 12.0-m...Ch. 8 - The electric motor of a model train accelerates...Ch. 8 - When an automobile moves with constant speed down...Ch. 8 - Prob. 8.32PCh. 8 - An energy-efficient lightbulb, taking in 28.0 W of...Ch. 8 - An electric scooter has a battery capable of...Ch. 8 - Make an order-of-magnitude estimate of the power a...Ch. 8 - An older-model car accelerates from 0 to speed v...Ch. 8 - For saving energy, bicycling and walking are far...Ch. 8 - A 650-kg elevator starts from rest. It moves...Ch. 8 - Prob. 8.39PCh. 8 - Energy is conventionally measured in Calories as...Ch. 8 - A loaded ore car has a mass of 950 kg and rolls on...Ch. 8 - Make an order-of-magnitude estimate of your power...Ch. 8 - A small block of mass m = 200 g is released from...Ch. 8 - Prob. 8.44APCh. 8 - Review. A boy starts at rest and slides down a...Ch. 8 - Review. As shown in Figure P8.26, a light string...Ch. 8 - A 4.00-kg particle moves along the x axis. Its...Ch. 8 - Why is the following situation impossible? A...Ch. 8 - A skateboarder with his board can be modeled as a...Ch. 8 - Heedless of danger, a child leaps onto a pile of...Ch. 8 - Jonathan is riding a bicycle and encounters a hill...Ch. 8 - Jonathan is riding a bicycle and encounters a hill...Ch. 8 - Consider the blockspringsurface system in part (B)...Ch. 8 - As it plows a parking lot, a snowplow pushes an...Ch. 8 - Prob. 8.55APCh. 8 - Prob. 8.56APCh. 8 - As the driver steps on the gas pedal, a car of...Ch. 8 - Review. Why is the following situation impossible?...Ch. 8 - A horizontal spring attached to a wall has a force...Ch. 8 - More than 2 300 years ago, the Greek teacher...Ch. 8 - A child's pogo stick (Fig. P8.61) stores energy in...Ch. 8 - A 1.00-kg object slides to the right on a surface...Ch. 8 - A 10.0-kg block is released from rest at point in...Ch. 8 - Prob. 8.64APCh. 8 - A block of mass 0.500 kg is pushed against a...Ch. 8 - Review. As a prank, someone has balanced a pumpkin...Ch. 8 - Review. The mass of a car is 1 500 kg. The shape...Ch. 8 - A pendulum, comprising a light string of length L...Ch. 8 - A block of mass M rests on a table. It is fastened...Ch. 8 - Review. Why is the following situation impossible?...Ch. 8 - While running, a person transforms about 0.600 J...Ch. 8 - A roller-coaster car shown in Figure P8.72 is...Ch. 8 - A ball whirls around in a vertical circle at the...Ch. 8 - An airplane of mass 1.50 104 kg is in level...Ch. 8 - Prob. 8.75APCh. 8 - In bicycling for aerobic exercise, a woman wants...Ch. 8 - Review. In 1887 in Bridgeport, Connecticut, C. J....Ch. 8 - Prob. 8.78APCh. 8 - Review. A uniform board of length L is sliding...Ch. 8 - Starting from rest, a 64.0-kg person bungee jumps...Ch. 8 - Prob. 8.81CPCh. 8 - Prob. 8.82CPCh. 8 - What If? Consider the roller coaster described in...Ch. 8 - A uniform chain of length 8.00 m initially lies...Ch. 8 - Prob. 8.85CP
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  • An inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?
    A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P7.79). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point , the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The blocks speed at the bottom of the track is = 12.0 m/s, and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?
    Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x=0 , is moving with speed v in the x-direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)
  • Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F, on a vine having length L and initially making an angle with the vertical (Fig. P7.81). Take D = 50.0 m, F = 110 N, L = 40.0 m, and = 50.0. (a) With what minimum speed must Jane begin her swing to just make it to the other side? (b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80.0 kg.
    A small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P7.45). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point , (c) its speed at point , and (d) its kinetic energy and the potential energy when the block is at point . Figure P7.45 Problems 45 and 46.
    A 5.00-kg block is set into motion up an inclined plane with an initial speed of i = 8.00 m/s (Fig. P8.23). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of = 30.0 to the horizontal. For this motion, determine (a) the change in the blocks kinetic energy, (b) the change in the potential energy of the block-Earth system, and (c) the friction force exerted on the block (assumed to be constant). (d) What is the coefficient of kinetic friction?
  • A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P7.55. (a) The block is pulled to a position xi = 6.00 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through equilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position xi/2 = 3.00 cm? (d) Why isnt the answer to part (c) half the answer to part (b)? Figure P7.55
    A childs pogo stick (Fig. P7.69) stores energy in a spring with a force constant of 2.50 104 N/m. At position (x = 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. The combined mass of child and pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so lets assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the childstickEarth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine x. (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. (e) Calculate the childs maximum upward speed. Figure P7.69
    A 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P6.27 (page 188). Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2, = 3 400 N/m. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the cars initial speed.
  • The Flybar high-tech pogo stick is advertised as being capable of launching jumpers up to 6 ft. The ad says that the minimum weight of a jumper is 120 lb and the maximum weight is 250 lb. It also says that the pogo stick uses a patented system of elastometric rubber springs that provides up to 1200 lbs of thrust, something common helical spring sticks simply cannot achieve (rubber has 10 times the energy storing capability of steel). a. Use Figure P8.32 to estimate the maximum compression of the pogo sticks spring. Include the uncertainty in your estimate. b. What is the effective spring constant of the elastometric rubber springs? Comment on the claim that rubber has 10 times the energy-storing capability of steel. c. Check the ads claim that the maximum height a jumper can achieve is 6 ft.
    Check Your Understanding There is a second solution to the system of equations solved in this example (because the energy equation is quadratic): v1.f=-2.5m/s , v2.f=0 . This solution is unacceptable on physical grounds; what’s with it?
    An inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P7.47. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest? Figure P7.47 Problems 47 and 48.
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