Example 1 - The Average Force of a Collision

Problem: The magnitude of the force of a certain collision between two bodies can be approximated by the equation

a) When is the force zero?

b) What is the time interval of the collision?

c) What is the magnitude of the average force on each body?

d) What is the magnitude of the change in the momentum of each body?

Solution: A graph helps to visualize this function:

a) The force is zero at t = 0 and t = 2 seconds.

b) The time interval of the collision is 2.00 seconds.

c) By looking at the graph, you might be tempted to call the average the "half-height" of 0.75 N. Let's see... Using the integral to find the area (which is the impulse) under the curve,

Since impulse is equal the change in the momentum for one of the bodies, it has the same units as momentum. Dividing by the time interval of 2 seconds, the magnitude of the average force is 1.00 N.

Comment: The "half-height" would be valid if the force rose linearly.

d) The magnitude of the change in the momentum is the impulse = 2.00 kg m/s.