Momentum and Collisions - Mission MC3 Detailed Help

Two balls of the same mass are thrown towards a wall and collide with it moving with a speed of 5 m/s. Ball A hits the wall and rebounds with a speed of 4 m/s. Ball B hits the wall and stops. Assume that the collisions times are the same for each ball. Compared to ball B, ball A has ____ velocity change, ____ momentum change, and ____ impact force.


 
The momentum change of an object can be calculated from knowledge of the object's mass (m) and velocity change (∆v) using the formula:

Momentum Change = m • ∆v


 
Momentum Change - Impulse Theorem:
When a force is exerted upon an object in a collision, the object is said to have encountered an impulse. The impulse is simply the mathematical product of the force exerted on the object and the amount of time over which it was exerted. The impulse changes the object's momentum and is equal to the amount of momentum change.
 
Impulse = Momentum Change
or

F•t = m•∆v


 
The essential difference between the two balls is that ball A hits the wall and bounces and ball B hits the wall and stops. For two balls such as this with the same pre-collision speed, the ball that bounces is the ball that has the greatest velocity change. After all, if ball B ball changes its velocity from +5 m/s to 0 m/s, then there is a change in velocity of -5 m/s. But if ball A ball changes its velocity from +5 m/s to -4 m/s, then there is a change in velocity of -9 m/s. Ball A has the greatest magnitude of velocity change. The ball with the greatest ∆v will also have the greatest m•∆v. And if impulse is equal to the momentum change, then the ball with the greatest m•∆v also encounters the greatest impulse.


 

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