Problem 1:
Board A is placed on board B as shown. Both boards slide, without moving with respect to each other, along a frictionless horizontal surface at a speed v. Board B hits a resting board C "head-on." After the collision, boards B and C move together, and board A slides on top of board C and stops its motion relative to C in the position shown on the diagram. What is the length of each board? All three boards have the same mass, size, and shape. It is known there is no friction between boards A and B; the coefficient of kinetic friction between boards A and C is µk.
Problem 2:
A rocket has an initial mass of m0 and a constant fuel burn rate of a. What is the minimum exhaust velocity that will allow the rocket to lift off from earth immediately after firing?
Problem 3:
If two objects collide and one is initially at rest, is it possible for both to be at rest after the collision? Is it possible for one to be at rest after the collision? Explain!
Problem 4:
A particle of mass m traveling with (non-relativistic) velocity u1 makes a head-on collision with a second particle of mass M, which is at rest in the laboratory. If the collision is completely inelastic, what fraction of the original kinetic energy remains after the collision?
Problem 5:
A rocket was launched vertically upwards. When it reached the highest point, it exploded into three equal mass pieces. One piece, which fell vertically down, was observed to take time t1 to reach the ground. The other two pieces both took time t2 to reach the ground. Find the height h(t1, t2 ) at which the rocket broke into three pieces.
Problem 6:
A 15.2-g bullet hits a 0.463-kg block from below.
The initial speed of the bullet is 624 m/s and it emerges from the block at 131
m/s.
(a) How high does the block rise?
(b) If the block is 2.34-cm thick, estimate the average force on the block.
Assume that the bullet passes completely through before the block moves
appreciably.
Problem 7:
A uniform, dense rope of length b and mass per unit length m is coiled on a smooth table. You lift one end of the rope by hand vertically upward at constant speed u0. Find the force that you must apply to the rope when the end is a distance a above the table (a < b).