Some nearly equivalent problems in the text:
C-7.6, 7.6, 7.11;
P-7.11, 7.15, 7.16, 7.19, 7.26, 7.29, 7.32a, 7.36, 7.39, 5.10(where did
that come from? :-))
Conceptual Questions:
1. Why is the total momentum of a system of objects always conserved, whereas the mechanical energy (potential + kinetic) might not be conserved? What happens to the kinetic energy in an inelastic collision? (C-7.11)
2. A pool table is oriented so the long direction is E-W. A player hits a ball due east into the initial triangle of 15 stationary balls. What can we say about the E-W and N-S motions of the 16 balls right after the impact? (C-7.6)
3. If a two-body collision is not head-on, then we may always assume:
a. vector momentum is conserved
b. kinetic energy is conserved
c. neither momentum nor kinetic energy are conserved
d. both momentum and kinetic energy are conserved
(C-7.6)
4. If a glass of water is on a table with a piece of paper under it, it is relatively easy to pull the paper out without disturbing the glass very much if the pull is done very quickly. This is because, with a quick pull:
a. the force on the glass will be less.
b. the momentum of the paper will be greater.
c. the impulse from the pull will be less.
d. the coefficient of kinetic friction will be less.
(C-7.5)
Numerical Problems:
1. A 75 kg swimmer dives horizontally off a 500 kg raft. If the diver's horizontal speed immediately after leaving the raft is 4 m/s, what is the corresponding raft speed? (P-7.32a)
2. A billiard ball collides in an elastic head-on collision with a second stationary identical ball. After the collision which of the following conditions applies to the first ball? (P-7.26)
a. maintains the same velocity as before
b. has one half its initial velocity
c. comes to rest
d. moves in the opposite direction
3. In a real two-body collision, if the momentum of the system is conserved, then which of the following best describes the kinetic energy after the collision? (C-7.11)
a. will be less
b. will also be conserved
c. may also be conserved
d. is doubled in value
4. The impulse experienced by a body is equivalent to its change in:
a. velocity
b. kinetic energy
c. momentum
d. None of the above choices are valid.
5. Alex throws a 0.15 kg rubber ball down onto the floor. The ball's velocity just before impact is 6.5 m/s, and just after is 3.5 m/s. If the ball is in contact with the floor for 0.025 second, what is the magnitude of the average force applied by the floor on the ball? (P-7.29)
6. A railroad freight car, mass 15,000 kg, is allowed to coast along a level track at a speed of 2 m/s. It collides and couples with a 50,000 kg loaded second car, initially at rest and with brakes released. What percentage of the initial kinetic energy in the 15,000 kg car is preserved in the two coupled cars after collision? (P-7.36)
ans: 23%
7. A model car is propelled by a cylinder of carbon dioxide gas. The cylinder emits gas at a rate of 4.5 grams/second with an exit speed of 80.0 m/s. The car has a mass of 400 grams, including the CO2 cylinder. Starting from rest, what is the car's initial acceleration? (P-7.16)
8. A helicopter stays aloft by pushing large quantities of air downward every second. What mass of air must be pushed downward at 40 m/s every second to keep a 1000 kg helicopter aloft? (P-7.15)
9. A billiard ball (Ball #1) moving at 5 m/s strikes a stationary ball (Ball #2)of the same mass. After the collision, Ball #1 moves at a velocity of 4.35 m/s at an angle of 30ø with respect to its original motion. Find the velocity and angle of Ball #2 after the collision. (P-7.39)
10. A 90 kg halfback running north with a speed of 10 m/s is tackled by a 120 kg opponent running south at 4 m/s. The collision is inelastic. Compute the velocity of the two players just after the tackle. (P-7.19)
ans: 2 m/s north
11. The moon has 1/81 the mass of the Earth and their center-to-center separation is 384,000 km. How far from the center of the Earth is the center of mass of the Earth-moon system? (P-5.10)
ans: 4,680 km