


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) 
Was the collision elastic? 


Explain your answer. 

b) 
Calculate the velocity of the objects after the collision. 



2. 

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. 



3. 

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. 



4. 

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. 





velocity before collision 
velocity before collision 
u_{1} = +4.0ms^{1} 
v_{1} = 1.5ms^{1} 
u_{2} = 3.0ms^{1} 
v_{2} = +5.5ms^{1} 





a) 
Calculate the ratio of the masses of the two objects, m_{1}/m_{2}. 

b) 
Was the collision elastic? 


Explain your answer. 

c) 
Calculate the total kinetic energy of the two objects before the
collision given that m_{1}=8.5kg. 



5. 

A rocket in space is initially stationary (relative to
the earth) 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. 


Explain why this is the case. 



6. 

An object, A, of mass 2kg is
moving at 5ms^{1}. 


Another object, B of mass 1.5kg
is moving at 8ms^{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. 



7. 

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. 


To state the direction of the velocity after the collision, give
the angle between the final velocity and the initial velocity of A. 



8. 

Steel balls, each of mass 0.5g
fall from a height of 1m onto a
horizontal surface. 


If 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. 



9. 

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 kinetic energy during each collision 

b) 
the average force exerted by the surface on the balls. 