Question 1
The diagram below shows two objects, A of mass 3kg and B of mass 2kg, which are about to collide.  
There are no external forces acting during the collision. After the collision, A and B stick together.  
a)  Is the collision elastic? Explain your answer. 
b)  Calculate the velocity of the objects after the collision. 
A gun of mass M = 5kg fires a bullet at 320ms^{1}. If the gun recoils with a speed of 24ms^{1}, calculate the mass m of the bullet. 
A ball is thrown against a fixed wall where it bounces elastically. The mass of the ball is m and its velocity just before it hits the wall is u.  
For simplicity, ignore the force of gravity in this question.  
a)  Does the principle of conservation of momentum apply to this situation? 
b)  Obtain an expression for the change in momentum of the ball in terms of m and u. 
Two objects collide. No external forces act during the collision. The velocities of the objects before and after the collision are given in the table below.  
 
a)  Calculate the ratio of the masses of the two objects, m_{1}/m_{2}.  
b)  Was the collision elastic? Explain.  
c)  Calculate the total kinetic energy of the two objects before the collision given that m_{1} = 8·5kg. 
A rocket in space is initially stationary and has a total mass of 5000kg. The motors are started and exhaust gases are ejected at the rate of 1250kg per minute with a velocity of 600ms^{1}.  
a)  Calculate the magnitude of the force which the rocket motor produces. 
b)  Calculate the initial acceleration of the rocket. 
c)  Assuming that the motors continue to operate, the acceleration of the rocket will increase with time. Why? 
An object, A, of mass 2kg is moving at 5ms^{1}. Another object, B of mass 1·5kg is moving at 8 ms^{1}in a direction at 90° to the direction of motion of A. The two objects collide and stick together. Find the magnitude and direction of their velocity after the collision. (To state the direction of the velocity after the collision, give the angle between the final velocity and the initial velocity of A.)

An object of mass 10kg explodes into three separate pieces. Piece A, of mass 2kg, moves away from the explosion at 60ms^{1}. Piece B, of mass 5kg, moves away at 20ms^{1} in a direction at 60° to the direction of motion of A. Find the magnitude and direction of the velocity of the third piece, C. (State the direction as in the previous question.)

Steel balls, each of mass 0·5g fall from a height of 1m onto a horizontal surface. In balls hit the surface at the rate of 200 per minute. Assuming that the collisions between the balls and the surface are elastic, calculate the average force exerted by the balls on the surface.

Consider again the situation described in the previous question but now the balls only rebound to a height of 0·4m. Calculate  
a)  the loss of k.e. during each collision 
b)  the average force exerted by the surface on the balls. 