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Momentum, Energy, and Velocity Questions

1. (a) What is the momentum of a 1.20 x 10^4 kg garbage truck moving at 30.0 m/s? (b) At what speed would an 8.00 kg trash can have the same momentum?

2. One hazard of space travel is debris left by previous missions. There are several thousand masses large enough to detect by radar orbiting the earth, but there are far greater numbers of very small masses, such as flakes of paint. Calculate the force exerted by a 0.100 mg chip of paint that strikes a space shuttle window at a relative speed of 4000 m/s, given the collision lasts 6.00 x 10^(-8) s. Such a collision chipped the window of the ill-fated Challenger in June 1983, causing $50,000 of damage.

3. A 0.450 kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving it 1.00 cm into a board. (a) Calculate the duration of the impact. (b) What was the average force exerted on the nail?
Note: There are (at least) two strategies here. One is to assume constant acceleration over the 1-cm distance and determine the time using the equations for constant acceleration. From that, you can find the average force. However, a more "relevant" strategy, in terms of what we have been learning, is to first use the work-energy principle to find the average force. Then use the impulse-momentum principle to find the duration of impact.

4. It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. When that is the case, the gas velocity and momentum are in the same direction as the rocket's. How does the rocket still obtain thrust by ejecting the gases?

5. Water from a fire hose is directed horizontally against a wall at a rate of 50.0 kg/s and a speed of 42.0 m/s. Calculate the force exerted on the wall, assuming the water's horizontal momentum is reduced to zero.

6. Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 150,000 kg and a velocity of 0.300 m/s, and the second having a mass of 110,000 kg and a velocity of -0.120 m/s. What is their final velocity?

7. A 0.240 kg billiard ball moving at 3.00 m/s strikes the bumper and bounces straight back at 2.40 m/s (80% of the original speed.) The collision lasts 0.0150 s. (a) Calculate the average force exerted on the ball by the bumper. (b) How much kinetic energy in joules is lost during the collision? (c) What percent of the original energy is left?

8. Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and was approaching at 8.00 m/s due south. The second car has a mass of 850 kg and was approaching at 17.0 m/s due west. (a) Draw arrows representing the momentum vector of each car, and draw an arrow representing the resultant (vector sum) of these two. Label each arrow with its magnitude in kg-m/s. (Make this a clear diagram, with arrows at least 3 inches long. Make the relative length of the arrows accurate.) (b) Calculate the final velocity of the cars. (Magnitude and direction.) (c) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.)

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Solution Summary

The solution has the eight solutions to the momentum, energy and velocity questions. These are standard classical mechanics problems pertaining to work.