A system of two objects has $\Delta K_{tot}=7J$ and $\Delta U=-5J$. How much work is done by interaction forces?

A system consists of interacting objects A and B, each exerting a constant 3.0 N pull on the other. What is ∆U for the system if A moves 1.0 m toward B while B moves 2.0 m toward A?

The free-fall acceleration on a large asteroid, in the vacuum of space, is 0.15 m/s². A spacecraft hovering 500 m above the surface drops a 25 kg payload wrapped in a padded jacket. What is the payload's impact speed?

A 55 kg skateboarder wants to just make it to the upper edge of a 'quarter pipe,' a track that is one-quarter of a circle with a radius of 3.0 m. What speed does he need at the bottom?

A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45° angle?

A pendulum is made by tying a 500 g ball to a 75-cm-long string. The pendulum is pulled 30° to one side, then released. What is the ball's speed at the lowest point of its trajectory?

A 1500 kg car traveling at 10 m/s suddenly runs out of gas while approaching the valley shown in FIGURE EX10.11. The alert driver immediately puts the car in neutral so that it will roll. What will be the car's speed as it coasts into the gas station on the other side of the valley? Ignore rolling friction.

The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that a leg bone of a healthy, 60 kg human can absorb about 200 J. From what maximum height could a 60 kg person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed by the leg bones in a rigid landing.

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. What is $\Delta U_G$ of 1.0 kg of water?

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.

A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far?

As a 15,000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60,000 N/m. If the spring stretches 30 m to stop the plane, what was the plane's landing speed?

The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 41 mm while those of nonathletes stretch only 33 mm. The spring constant of the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathletes?

FIGURE EX10.24 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particle's speeds at B, C, and D?

FIGURE EX10.25 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0 m. What is the particle's maximum speed? At what position does it have this speed?

In FIGURE EX10.26, What minimum speed does a 100 g particle need at point B to reach point A?

In FIGURE EX10.27, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm

FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. Where are the particle's turning points?

In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m?