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- a) What is the mechanical advantage of a wheelbarrow, such as the one in Figure 9.24, if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is 55.0 kg? (c) What force does the wheel exert on the ground? Figure 9.24 (a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot IS the wheel's axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel's load) is less than the input force (from the hand nearest the load), because the Input is exerted closer to the pivot than is the outputA uniform beam of length L and mass m shown in Figure P12.8 is inclined at an angle to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is s. Assume the angle is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and . (c) Using the condition of translational equilibrium, find a second expression for T in terms of s, m, and g. (d) Using the results from parts (a) through (c), obtain an expression for s involving only the angle . (e) What happens if the ladder is lifted upward and its base is placed back on the ground slightly to the left of its position in Figure P12.8? Explain. Figure P12.8A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = = 4.00 m. A painter of mass m = 70.0 kg stands on the ladder d = 3.00 m from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.
- Two children of mass 15 kg and 26 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw.If the children are separated by a distance of 3.0 m, at what distance, in meters, from the pivot point is the smaller child sitting in order to maintain the balance? r1 =A 55.0 kg child sits 1.80 m to the left of center on a seesaw of length, L=7.00 m, and mass 16.0 kg if a second child sits at the end of the opposite side, and the system is balanced, (a) what is the mass of the child person? (b) determine the normal force exerted at the pivot point.An object that weighs 1180 N rests on a lever at a point 0.390 m from a support. On the same side of the support, at a distance of 3.00 m from it, an upward force with magnitude F is applied. Ignore the weight of the board itself. If the system is in equilibrium, what is F? Express your answer in Newtons. where P = 1180 and x = 0.390. _____N
- A uniform beam of length L and mass m shown in the figure below is inclined at an angle ? to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is ?s. Assume the angle ? is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and ?. (c) Using the condition of translational equilibrium, find a second expression for T in terms of ?s, m, and g. (d) Using the results from parts (a) through (c), obtain an expression for ?s involving only the angle ?. (e) What happens if the beam is lifted upward and its base is placed back on the ground slightly to the left of its position in the figure above? Explain4) a) Two children are sat on a see-saw. Shelia is 35kg and is sat at the end, 2.0 m from the pivot. Michael is 45kg and sits on the opposite side of the pivot. Calculate at what distance (x) must he sit to balance the see-saw.You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 7 kg, length L = 7 m) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset = 29 cm from the end of the board when seated as shown.You have selected a child of mass m = 23 kg (shown on the right), and an adult of mass n =5 times the mass of the child (shown on the left) to test out your prototype. a)Determine the distance d in m. b)Determine the magnitude of the force exerted on the pivot point by the see-saw in N.
- Two children of mass 17 kg and 32 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 5 m, at what distance from the pivot point is the small child sitting in order to maintain the balance? _______ mYou have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 14 kg, length L = 9 m) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset = 9 cm from the end of the board when seated as shown.You have selected a child of mass m = 23 kg (shown on the right), and an adult of mass n =4 times the mass of the child (shown on the left) to test out your prototype. Determine the distance d in m.You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 7 kg, length L = 7 m) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset = 11 cm from the end of the board when seated as shown.You have selected a child of mass m = 29 kg (shown on the right), and an adult of mass n =3 times the mass of the child (shown on the left) to test out your prototype.