The average force on the force-time graph

Post date: Jan 31, 2014 9:43:41 AM

Carts A and B collide on a level track. The masses of each cart are known. Suppose that the final and initial velocities of cart B are measured, so that its momentum change is calculated. Moreover, suppose that the time interval of collision, t2 - t1, is known. However, the force history is unknown. Arnold B. Arons in his book, Teaching Introductory Physics, posts the question: What constant force acting for the same interval would have imparted the same impulse?

On the above graph, draw a rectangle with the same base (t2 - t1) and whose height has the same area as the actual, shaded area. Then, the "time average force" is:   or impulse divided by the time interval.