19-April-2017: LAB 14: Physics 4A Impulse-Momentum activity

Purpose:

Prove that the impulse which can be calculated by the area of the force verse time plot equals to the change of momentum.

Verify the impulse-momentum theorem.

Introduction:

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. This integration equals to the change in momentum. So if we measure the area under the curve of force verse time, we can derive the integral. Compare it to the product of the cart weight and the change of the velocity. We can verify the impulse-momentum theorem by this way.

 

EXPM1:

Set the track up. Then clamp the cart to a rod clamped to the lab table. Extend the spring plunger on the dynamic cart. Mount a force sensor to another cart, with a rubber stopper replacing the hook mounted on the protruding part of the force sensor.

Collect data with logger pro and display the force verse time plot. As we can find from the plot, the force is not constant and oscillate during at short time.

As shown in the plot, the result of the integration is 0.4123 N·s.

As measured, the weight of the cart is 641 grams.

This result is close to the integral result. So the impulse-momentum theorem is verified.

EXPM2:

In the second experiment, we add 500 grams to the cart and redo the experiment by steps above. The new plots are followed.

The result of integration is 0.8575 N·s.

As we can see, the integration is close to the change in momentum. There is a little error in this experiment which may not be ignored.

EXPM3:

The last part of the experiment is the inelastic collision. Attach clay to a vertical piece of wood clamped to the lab table. Then repeat the experiment again by the above steps. The clay will ensure the cart stops and so we can calculate the momentum change of the cart and compare it to the integration.

As shown in the plot, the integration equals to 0.3154 N·s.

The results are close to each other. So we can derive the conclusion that in the inelastic collision condition, impulse-momentum theorem is still satisfied.

Conclusion:

In these experiments, we verify the impulse-momentum theorem in nearly elastic and inelastic collision. We learn to get the change of momentum and the impulse by plot. Errors may come from the friction between the cart and the tract, the imperfection of the spring and the detection error. Those errors are hard to avoid.