Question

Conservation of Momentum questions

1. A marble is going down a ramp and collides with some marbles at the end of the ramp. What would happen to the momentum if the angle of the inclined ramp increased or decreased?

2. What can you conclude about the momentum of the released marble(s) just before the impact and the momentum of the marble(s) knocked away after the impact?​

3. What type of collision(s) do you observe when the marble(s) going down the ramp collide with the marbles at the end of the ramp? Do you expect kinetic energy to be conserved? Explain your answer.  

4. A ball is moving at 4 m/s and has a momentum of 48 kg m/s. What is the mass of the ball? Show your work.

5. A ball with a mass of 3 kg moving at 5 m/s collides with a 9 kg ball at rest. After the collision, the impacting (3 kg) ball bounces back at a speed of 2.5 m/s. How fast does the 9 kg ball move and in what direction? (Show all steps in your work.)

6. A ball bouncing against the ground and rebounding is an example of an elastic collision. Describe two different methods of evaluating this interaction, one for which momentum is conserved, and one for which momentum is not conserved. Fully explain your answer.   

Answer 1

1. Downward acceleration of marble on ramp is gSin . So if angle is small acceleration is small and hence momentum (velocity) acquired by marble will be less. If is large momentum acquired will be more.

2. The initial and final momentum of both particles combined will be same. Initially second marble has momrntum 0 and first marble has momentum along positive x direction and negative y direction. After colision marble 2 will have some momentum along the positive x direction and first marble will also have momentum along positive x direction but momentum will be little less as it gets transfeered to marble 2.

3 Marbles are approximately rigid bodie. So coliision will be elastic. So kinetic energy and momentum both will be conserved. However in practical situations we except some loss of kinetic energy since collisions are not perfectly elastic

4. momentum = mass * velocity , mass = momentum/ velocity = 48/4 = 12Kg

5. m₁ = 3Kg U₁ = 5m/s m₂ = 9Kg U₂ = 0   

after collision , V₁= -2.5m/s V₂ = ?

conserving momentum, m₁U₁+m₂U₂ = m₁V₁+m2V₂

15 + 0 = -7.5 + 9V₂

V₂=2.5m/s

6. If no dissipiative force is present like air resistance and only gravity acts. Than momentum is conserved. We can conserve momentum. The Body will come back to same height after bouncing from which it was dropped. However is some dissipiative forces are present momentum will not be conserved. The body will loss some momentum after each bounce and ultimately comes to rest.