#6 #12 #24 #26 #28 #346. Which has the greater momentum, a supertanker docked at a pier or a motorboat pulling a water skier?
The motorboat will have the greater momentum. Since the supertanker's velocity is zero, its momentum is zero too.
12. Why is skiing into a wall of deep powder less hazardous to your health than skiing into a wall of bricks? Assume in both cases that you have the same initial speed and come to a complete stop.
The time to slow down is greater when you ski into the pile of deep powder than it is when skiing into a pile of bricks. Since force is the change in momentum divided by the change in time, the force is smaller when the time is longer. Thus, the force you feel is smaller when skiing into the pile of snow.
24. If the force exerted on the rocket by the expelled gases from its engine is constant, does the momentum of the rocket increase at a constant rate? What happens to the momentum of the entire system?
Since the impulse is constant the rate at which the momentum changes is constant. The momentum of the complete system remains constant since the momentum of a closed system is conserved. (A closed system is a system in which there are no external forces.)
26. The momentum of a freely falling ball is not conserved. Why is this not a violation of the law of conservation of momentum?
Momentum is conserved when there are no outside forces acting on a system. In the case of the falling ball, gravity is an outside force acting on the falling ball. Note that if we had included the SOURCE of the gravity, that is the earth, momentum would be conserved in the earth-ball system.
28. A friend is standing on a giant skateboard that is initially at rest. If you ignore frictional effects with the floor, what is the momentum of the skateboard if your friend walks to the right with a momentum of 150 kilogram-meters per second?
The system was initially at rest, so the system's initial momentum is zero. Since momentum is conserved, the final momentum is equal to the initial momentum of zero. Thus, the momentum of the skateboard must be 150 kilogram-meters per second to the left.
34. During a 4th of July celebration, a rocket is launched from the ground and explodes at the top of its arc. If we ignore air resistance, what happens to the total momentum of all of the rocket's fragments?
The total momentum of the pieces changes just like the unexploded rocket's momentum would have changed if it had not exploded at all. At the instant the rocket is exploded its velocity is horizontal, so its momentum is horizontal - exploded or not. The momentum of the fragments a second later is the same as what the rocket's momentum would have been if it had not been exploded (assuming that the ground has not intervened and stopped any of the pieces).