Chapter 5

If a person does \(50 \mathrm{~J}\) of work in moving a \(30-\mathrm{kg}\) box over a \(10-\mathrm{m}\) distance on a horizontal surface, what is the minimum force required?

A \(5.0-\mathrm{kg}\) box slides a 10 -m distance on ice. If the coefficient of kinetic friction is 0.20 , what is the work done by the friction force?

A passenger at an airport pulls a rolling suitcase by its handle. If the force used is \(10 \mathrm{~N}\) and the handle makes an angle of \(25^{\circ}\) to the horizontal, what is the work done by the pulling force while the passenger walks \(200 \mathrm{~m} ?\)

A 3.00 -kg block slides down a frictionless plane inclined \(20^{\circ}\) to the horizontal. If the length of the plane's surface is \(1.50 \mathrm{~m}\), how much work is done, and by what force?

A 0.50 -kg shuffleboard puck slides a distance of \(3.0 \mathrm{~m}\) on the board. If the coefficient of kinetic friction between the puck and the board is \(0.15,\) what work is done by the force of friction?

A crate is dragged \(3.0 \mathrm{~m}\) along a rough floor with a constant velocity by a worker applying a force of \(500 \mathrm{~N}\) to a rope at an angle of \(30^{\circ}\) to the horizontal. (a) How many forces are acting on the crate? (b) How much work does each of these forces do? (c) What is the total work done on the crate?

A hot-air balloon ascends at a constant rate. (a) The weight of the balloon does (1) positive work, (2) negative work, (3) no work. Why? (b) A hot-air balloon with a mass of \(500 \mathrm{~kg}\) ascends at a constant rate of \(1.50 \mathrm{~m} / \mathrm{s}\) for \(20.0 \mathrm{~s}\). How much work is done by the upward buoyant force? (Neglect air resistance.)

A change in gravitational potential energy (a) is always positive, (b) depends on the reference point, (c) depends on the path, (d) depends only on the initial and final positions.

A hockey puck with a mass of \(200 \mathrm{~g}\) and an initial speed of \(25.0 \mathrm{~m} / \mathrm{s}\) slides freely to rest in the space of \(100 \mathrm{~m}\) on a sheet of horizontal ice. How many forces do nonzero work on it as it slows: (a) (1) none, (2) one, (3) two, or (4) three? Explain. (b) Determine the work done by all the individual forces on the puck as it slows.

The change in gravitational potential energy can be found by calculating \(m g \Delta h\) and subtracting the reference point potential energy: (a) true, (b) false.

The reference point for gravitational potential energy may be (a) zero,= (b) negative, (c) positive, (d) all of the preceding.

\(\mathrm{A} 500-\mathrm{kg}\), light-weight helicopter ascends from the ground with an acceleration of \(2.00 \mathrm{~m} / \mathrm{s}^{2}\). Over a \(5.00-\mathrm{s}\) interval, what is (a) the work done by the lifting force, (b) the work done by the gravitational force, and (c) the net work done on the helicopter?

A man pushes horizontally on a desk that rests on a rough wooden floor. The coefficient of static friction between the desk and floor is 0.750 and the coefficient of kinetic friction is \(0.600 .\) The desk's mass is \(100 \mathrm{~kg} .\) He pushes just hard enough to get the desk moving and continues pushing with that force for \(5.00 \mathrm{~s} .\) How much work does he do on the desk?

If a nonconservative force acts on an object, and does work, then (a) the object's kinetic energy is conserved, (b) the object's potential energy is conserved, (c) the mechanical energy is conserved, (d) the mechanical energy is not conserved.

A student could either pull or push, at an angle of \(30^{\circ}\) from the horizontal, a \(50-\mathrm{kg}\) crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is \(0.20 .\) The crate is to be moved a horizontal distance of \(15 \mathrm{~m}\). (a) Compared with pushing, pulling requires the student to do (1) less, (2) the same, or (3) more work. (b) Calculate the minimum work required for both pulling and pushing.

The speed of a pendulum is greatest (a) when the pendulum's kinetic energy is a minimum, (b) when the pendulum's acceleration is a maximum, (c) when the pendulum's potential energy is a minimum, (d) none of the preceding.

To measure the spring constant of a certain spring, a student applies a 4.0 - \(\mathrm{N}\) force, and the spring stretches by \(5.0 \mathrm{~cm} .\) What is the spring constant?

Two springs are identical except for their force constants, \(k_{2}>k_{1}\). If the same force is used to stretch the springs, (a) spring 1 will be stretched farther than spring 2 (b) spring 2 will be stretched farther than spring 1 , (c) both will be stretched the same distance.

A spring has a spring constant of \(30 \mathrm{~N} / \mathrm{m}\). How much work is required to stretch the spring \(2.0 \mathrm{~cm}\) from its equilibrium position?

If it takes \(400 \mathrm{~J}\) of work to stretch a spring \(8.00 \mathrm{~cm}\) what is the spring constant?

Two identical stones are thrown from the top of a tall building. Stone 1 is thrown vertically downward with an initial speed \(v\), and stone 2 is thrown vertically upward with the same initial speed. Neglecting air resistance, which stone hits the ground with a greater speed: \((\) a) stone \(1,(\) b) stone \(2,\) or \((\mathrm{c})\) both have the same speed?

If a \(10-\mathrm{N}\) force is used to compress a spring with a spring constant of \(4.0 \times 10^{2} \mathrm{~N} / \mathrm{m},\) what is the resulting spring compression?

A certain amount of work is required to stretch a spring from its equilibrium position. (a) If twice the work is performed on the spring, the spring will stretch more by a factor of \((1) \sqrt{2}(2) 2,(3) 1 / \sqrt{2}(4) \frac{1}{2} .\) Why? (b) If \(100 \mathrm{~J}\) of work is done to pull a spring \(1.0 \mathrm{~cm},\) what work is required to stretch it \(3.0 \mathrm{~cm} ?\)

Which of the following is not a unit of power: (a) \(\mathrm{J} / \mathrm{s}\) (b) \(\mathrm{W} \cdot \mathrm{s},(\mathrm{c}) \mathrm{W},\) or (d) hp?

Consider a 2.0 -hp motor and a 1.0 -hp motor. Compared to the 2.0 -hp motor, for a given amount of work, the1.0-hp motor can (a) do twice as much work in half the time, (b) half the work in the same time, (c) one quarter of the work in three quarters of the time, (d) none of the preceding.

A spring with a force constant of \(50 \mathrm{~N} / \mathrm{m}\) is to be stretched from 0 to \(20 \mathrm{~cm}\). (a) The work required to stretch the spring from \(10 \mathrm{~cm}\) to \(20 \mathrm{~cm}\) is (1) more than (2) the same as, (3) less than that required to stretch it from 0 to \(10 \mathrm{~cm}\). (b) Compare the two work values to prove your answer to part (a).

A particular spring has a force constant of \(2.5 \times 10^{3} \mathrm{~N} / \mathrm{m}\). (a) How much work is done in stretching the relaxed spring by \(6.0 \mathrm{~cm} ?\) (b) How much more work is done in stretching the spring an additional \(2.0 \mathrm{~cm} ?\)

A spring (spring 1 ) with a spring constant of \(500 \mathrm{~N} / \mathrm{m}\) is attached to a wall and connected to another weaker spring (spring 2) with a spring constant of \(250 \mathrm{~N} / \mathrm{m}\) on a horizontal surface. Then an external force of \(100 \mathrm{~N}\) is applied to the end of the weaker spring \((\\# 2) .\) How much potential energy is stored in each spring?

A 0.20 -kg object with a horizontal speed of \(10 \mathrm{~m} / \mathrm{s}\) hits a wall and bounces directly back with only half the original speed. (a) What percentage of the object's initial kinetic energy is lost: \((1) 25 \%,(2) 50 \%,\) or (3) \(75 \% ?\) (b) How much kinetic energy is lost in the ball's collision with the wall?

A \(1200-\mathrm{kg}\) automobile travels at \(90 \mathrm{~km} / \mathrm{h}\). (a) What is its kinetic energy? (b) What net work would be required to bring it to a stop?

A 1200 -kg automobile travels at \(90 \mathrm{~km} / \mathrm{h}\). (a) What is its kinetic energy? (b) What net work would be required to bring it to a stop?

A \(2.00-\mathrm{kg}\) mass is attached to a vertical spring with a spring constant of \(250 \mathrm{~N} / \mathrm{m}\). A student pushes on the mass vertically upward with her hand while slowly lowering it to its equilibrium position. (a) How many forces do nonzero work on the object: (1) one, (2) two, or (3) three? Explain your reasoning. (b) Calculate the work done on the object by each of the forces acting on it as it is lowered into position.

The stopping distance of a vehicle is an important safety factor. Assuming a constant braking force, use the work-energy theorem to show that a vehicle's stopping distance is proportional to the square of its initial speed. If an automobile traveling at \(45 \mathrm{~km} / \mathrm{h}\) is brought to a stop in \(50 \mathrm{~m}\), what would be the stopping distance for an initial speed of \(90 \mathrm{~km} / \mathrm{h} ?\)

A large car of mass \(2 m\) travels at speed \(v\). A small car of mass \(m\) travels with a speed \(2 v\). Both skid to a stop with the same coefficient of friction. (a) The small car will have (1) a longer, (2) the same, (3) a shorter stopping distance. (b) Calculate the ratio of the stopping distance of the small car to that of the large car. (Use the work-energy theorem, not Newton's laws.)

An out-of-control truck with a mass of \(5000 \mathrm{~kg}\) is traveling at \(35.0 \mathrm{~m} / \mathrm{s}\) (about \(80 \mathrm{mi} / \mathrm{h}\) ) when it starts descending a steep \(\left(15^{\circ}\right)\) incline. The incline is icy, so the coefficient of friction is only \(0.30 .\) Use the work-energy theorem to determine how far the truck will skid (assuming it locks its brakes and skids the whole way) before it comes to rest.

If the work required to speed up a car from \(10 \mathrm{~km} / \mathrm{h}\) to \(20 \mathrm{~km} / \mathrm{h}\) is \(5.0 \times 10^{3} \mathrm{~J},\) what would be the work required to increase the car's speed from \(20 \mathrm{~km} / \mathrm{h}\) to \(30 \mathrm{~km} / \mathrm{h} ?\)

How much more gravitational potential energy does a 1.0-kg hammer have when it is on a shelf \(1.2 \mathrm{~m}\) high than when it is on a shelf \(0.90 \mathrm{~m}\) high?

You are told that the gravitational potential energy of a \(2.0-\mathrm{kg}\) object has decreased by \(10 \mathrm{~J} .\) (a) With this information, you can determine (1) the object's initial height, (2) the object's final height, (3) both the initial and the final height, (4) only the difference between the two heights. Why? (b) What can you say has physically happened to the object?

Six identical books, \(4.0 \mathrm{~cm}\) thick and each with a mass of \(0.80 \mathrm{~kg}\), lie individually on a flat table. How much work would be needed to stack the books one on top of the other?

The floor of the basement of a house is \(3.0 \mathrm{~m}\) below ground level, and the floor of the attic is \(4.5 \mathrm{~m}\) above ground level. (a) If an object in the attic were brought to the basement, the change in potential energy will be greatest relative to which floor: (1) attic, (2) ground, (3) basement, or (4) all the same? Why? (b) What are the respective potential energies of \(1.5-\mathrm{kg}\) objects in the basement and attic, relative to ground level? (c) What is the change in potential energy if the object in the attic is brought to the basement?

A} 0.50-\mathrm{kg}\( mass is placed on the end of a vertical spring that has a spring constant of \)75 \mathrm{~N} / \mathrm{m}$ and eased down into its equilibrium position. (a) Determine the change in spring (elastic) potential energy of the system. (b) Determine the system's change in gravitational potential energy.

A horizontal spring, resting on a frictionless tabletop, is stretched \(15 \mathrm{~cm}\) from its unstretched configuration and a \(1.00-\mathrm{kg}\) mass is attached to it. The system is released from rest. A fraction of a second later, the spring finds itself compressed \(3.0 \mathrm{~cm}\) from its unstretched configuration. How does its final potential energy compare to its initial potential energy? (Give your answer as a ratio, final to initial.)

A student has six textbooks, each with a thickness of \(4.0 \mathrm{~cm}\) and a weight of \(30 \mathrm{~N}\). What is the minimum work the student would have to do to place all the books in a single vertical stack, starting with all the books on the surface of the table?

A \(0.300-\mathrm{kg}\) ball is thrown vertically upward with an initial speed of \(10.0 \mathrm{~m} / \mathrm{s}\). If the initial potential energy is taken as zero, find the ball's kinetic, potential, and mechanical energies (a) at its initial position, (b) at \(2.50 \mathrm{~m}\) above the initial position, and (c) at its maximum height.

A girl swings back and forth on a swing with ropes that are \(4.00 \mathrm{~m}\) long. The maximum height she reaches is \(2.00 \mathrm{~m}\) above the ground. At the lowest point of the swing, she is \(0.500 \mathrm{~m}\) above the ground. (a) The girl attains the maximum speed (1) at the top, (2) in the middle, (3) at the bottom of the swing. Why? (b) What is the girl's maximum speed?

A \(1.00-\) kg block \((M)\) is on a flat frictionless surface (vFig. 5.32). This block is attached to a spring initially at its relaxed length (spring constant is \(50.0 \mathrm{~N} / \mathrm{m}\) ). A light string is attached to the block and runs over a frictionless pulley to a \(450-\mathrm{g}\) dangling mass \((m)\). If the dangling mass is released from rest, how far does it fall before stopping?

A \(500-g\) (small) mass on the end of a 1.50 -m-long string is pulled aside \(15^{\circ}\) from the vertical and shoved downward (toward the bottom of its motion) with a speed of \(2.00 \mathrm{~m} / \mathrm{s}\). (a) Is the angle on the other side (1) greater than, (2) less than, or (3) the same as the angle on the initial side \(\left(15^{\circ}\right)\) ? Explain in terms of energy. (b) Calculate the angle it goes to on the other side, neglecting air resistance.

A 0.20 -kg rubber ball is dropped from a height of \(1.0 \mathrm{~m}\) above the floor and it bounces back to a height of \(0.70 \mathrm{~m} .\) (a) What is the ball's speed just before hitting the floor? (b) What is the speed of the ball just as it leaves the ground? (c) How much energy was lost and where did it go?

A \(1.5-\mathrm{kg}\) box that is sliding on a frictionless surface with a speed of \(12 \mathrm{~m} / \mathrm{s}\) approaches a horizontal spring. (See Fig. 5.19.) The spring has a spring constant of \(2000 \mathrm{~N} / \mathrm{m}\). If one end of the spring is fixed and the other end changes its position, (a) how far will the spring be compressed in stopping the box? (b) How far will the spring be compressed when the box's speed is reduced to half of its initial speed?

\(0.50-\mathrm{kg}\) mass is suspended on a spring that stretches \(3.0 \mathrm{~cm}\). (a) What is the spring constant? (b) What added mass would stretch the spring an additional \(2.0 \mathrm{~cm} ?\) (c) What is the change in potential energy when the mass is added?