### Introduction

The impulse-momentum theorem relates impulse, the average force applied to an object times the length of time the force is applied, and the change in momentum of the object:

$\overline F \Delta t = m{v_f} - m{v_i}$

Here, we will only consider motion and forces along a single line. The average force, F, is the net force on the object, but in the case where one force dominates all others, it is sufficient to use only the large force in calculations and analysis.

For this experiment, a Motion Encoder Cart will roll along a level track. Its momentum will change as it collides with a hoop spring. The hoop will compress and apply an increasing force until the cart stops. The cart then changes direction and the hoop expands back to its original shape. The force applied by the spring is measured by a Dual-Range Force Sensor. The cart velocity throughout the motion is measured with a Motion Encoder. You will then use data-collection software to find the impulse to test the impulse-momentum theorem.

### Objectives

• Measure a cart’s momentum change and compare it to the impulse it receives.
• Compare average and peak forces in impulses.