Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information.... 
Home Conservation Laws Conservation of Momentum The ForceTime Graph  
Search the VIAS Library  Index  
The ForceTime GraphFew real collisions involve a constant force. For example, when a tennis ball hits a racquet, the strings stretch and the ball flattens dramatically. They are both acting like springs that obey Hooke's law, which says that the force is proportional to the amount of stretching or flattening. The force is therefore small at first, ramps up to a maximum when the ball is about to reverse directions, and ramps back down again as the ball is on its way back out. The equation F = Δp/Δt, derived under the assumption of constant acceleration, does not apply here, and the force does not even have a single welldefined numerical value that could be plugged in to the equation.
As with similarlooking equations such as v = Δp/Δt, the equation F = Δp/Δt is correctly generalized by saying that the force is the slope of the p  t graph. Conversely, if we wish to find Δp from a graph such as the one in figure m, one approach would be to divide the force by the mass of the ball, rescaling the F axis to create a graph of acceleration versus time. The area under the accelerationversustime graph gives the change in velocity, which can then be multiplied by the mass to find the change in momentum. An unnecessary complication was introduced, however, because we began by dividing by the mass and ended by multiplying by it. It would have made just as much sense to find the area under the original F  t graph, which would have given us the momentum change directly. Discussion Question


Home Conservation Laws Conservation of Momentum The ForceTime Graph 