In a collision
of two objects
, for an example a foot about to kick a football- the velocity
of one or both objects is abruptly changed. It is known, from Newton's laws of motion
, that such a change means a force
has been applied. The strong but short-duration force associated with a collision is called an impulsive force
. Alhtough the gravitational force
also acts on the ball, during the collision the impulsvie force is overwhelmingly dominant.
The impulsive force is related to the change in an object's momentum through Newton's second law:
*Bold face denotes the letter as a vector quantity.
F = dp/dt
Multiplying this equation by dt and integrating from some time t1 before the collision to a time t2 after the collision, it is seen that:
∫(t1, t2) F dt = ∫(t1, t2) dp
The right-hand integral is just the change ΔP that occurs during the collision. The integral on the left is known as the impulse, I, associated with the collision. The result then shows that the change in an object's momentum is equal to the impulse.
I = ∫(t1, t2) F dt = Δp
The units of impulse are the same as those of momentum. kg · m/s, or, equivalently, N · s. Since the difinite integral corresponds to the area under a curve, the impulse eqatuion is given geometrically by the area under the force v. time curve. It does not matter whether the force curve includes any nonimpulsive forces that may be present, for that definition of a collision ensures that the change in momentum associated with nonimpulsive forces is negligible during the time of the collision.