Momentum and Collisions - Mission MC3 Detailed Help

A soccer ball is at rest on the field when it suddenly encounters a collision with a moving foot. The force causes the soccer ball to change its momentum. If the contact time between the foot and the ball were to increase (OR decrease) by a factor of 2 (with no change in the force), then the impulse would ____ and the resulting momentum change would ____.


 
The impulse (I) encountered by an object can be calculated from the force (F) that is exerted on it and the time (t) over which the force is exerted. The formula is
 
Impulse = F • t


 
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

F • t = m • ∆v


 
The impulse encountered by an object depends on both the contact force and the time of contact (see Formula Frenzy section). If the same force endures for a longer the time, then the impulse is increased. The factor by which the time is increased is equal to the factor by which the impulse is increased. The impulse results in and is equal to the momentum change of the object. Thus, the increasing of the time not only increases the impulse, it also serves to increase the momentum change of the object by the same factor.