Eric Murray, Spring 2006
The impulse-momentum theorem states that an impulse on an object changes the object's momentum. In one dimension,
Jx = ∫Fxdt = Δpx
Your object will be a cart and force sensor on a horizontal track. A force will be applied by a mass on a hanger attached to a string that passes over a pulley. You will measure the impulse directly as the area under an Fx vs. t graph. You will also calculate the momentum of the object from its measured mass and velocity at various times as it accelerates along the track. Since the expectation is that the impulse will be the same as the change in momentum, the impulse-momentum theorem may be tested by checking
Jx - Δpx = 0
By making multiple measurements, both at various times as the cart accelerates along the track, and with different forces applied to the object, you will be able to find the average difference between the impulse and the change in momentum, along with its experimental uncertainty. If you find that this difference is not zero, within your measure of experimental error, then you will have to consider systematic errors. One likely source of systematic error is a frictional force acting on the object. Note that as greater forces are applied to the object, a frictional force will be of decreasing significance, so agreement with theory will improve with greater applied force. If agreement with theory does not improve with greater applied force, then a source of systematic error other than friction must be considered.