4/15 Impulse-Momentum

Purpose: To prove the Impulse-momentum theorem in elastic and inelastic collisions.

Procedure:

Part One 

FIGURE (1)

For the first part of the lab we were observing collision forces that change with time. We connected a spring plunger to a rod (FIGURE (1)), which we were then able to clamp to our table. Next, we mounted a force sensor on a cart at the same level as the spring plunger. Once we had things all set up we collided the cart into the plunger several times and observed what happened.
QUESTIONS:
1. The net force exerted on the cart just before the collision is zero.
2. The magnitude of the force on the cart is maximum when the plunger is at its maximum compression.
3. The net force exerted on the cart after the collision is also zero.
4. The collision takes about a second.

We added a motion sensor to the opposite end of the track that the spring plunger was on. We also made sure our ramp was level. We opened the correct file from the computer and made sure all of our devices were calibrated. Then we started recording our data as we gave the cart a push toward the spring plunger and let them collide. (FIGURE (2)). We then took the integral during the time the collision took place and got a value of -0.9211. 

FIGURE (2)

The change in momentum of the cart was close to the impulse applied by the spring plunger. We calculated a value of -0.8516 (FIGURE (2.5)), which means the calculation was off by about 8%.

Part Two

In the third part of the lab we changed that mass of the cart by adding 200 g. Then we repeated the same steps as part two and took new data. (FIGURE (3)) In this trial we took the integral of the force of the collision and came up with -1.060.

FIGURE (3)

When we calculated the change in momentum (FIGURE (3.5)) we got a value of -1.006. Again, these are close- they are off by about 5%. With this outcome though, we are able to say that the impulse is equal to the change in momentum, even with a larger cart.

FIGURE (3.5)

Part Three

For the last part of the lab, we changed the set up slightly. Instead of using a spring plunger to create and elastic collision, we used a piece of clay to create an inelastic collision (FIGURE (4)). Our prediction was that the impulse would be smaller than the elastic collision and the impulse and change in momentum would still be equal to each other. 

Again we pushed the cart toward our "clay man" and collected data. (FIGURE (5)) We took the integral of the force and came up with -0.3392. This confirms one of our predictions: the impulse of the inelastic collision was smaller than the elastic collision.

We calculated the change in momentum (FIGURE (6)) and came up with a value of -.275. While this still seems close to the impulse value, it is around 23% off.

FIGURE (6)

Conclusion:
Errors in this lab could have come from having the clay spread too thin. This would cause the nail to hit the wood instead of the clay stopping it. The nail probably wouldn't have enough force to go into the wood so it would bounce back slightly.