Impulse versus Momentum

Purpose:
The purpose of this experiment was to experimentally show that impulse is equal to the change in momentum to the objected which has the force acted on it.

Equipment Used:

The cart was set with a a force sensor on top. First the cart was ran into a spring and sent back. The motion sensor recorded the position and velocity relative to time. Then a nail was attached to the force sensor and the spring was replaced and a piece of clay.









Data Collection:
For the first portion of the experiment, the cart was sent into the spring and the force sensor recorded the amount of force it took to send the cart back. The motion sensor recorded the velocity of the cart before and after the collision. The change in the momentum of the system should be equal to the integral of the force that was applied to the cart.
mass of cart + force sensor = .449 kg
integral of force = -.8135
initial velocity = 1.153m/s
final velocity = -.911m/s
Then more mass, specifically .5 kg, was added to the cart and the procedure was repeated.
mass of cart + force sensor + additional mass = .949kg
integral of force = -.8336
initial velocity = .524m/s
final velocity = -.390m/s
Then a nail was attached to the force sensor and the nail was sent into a piece of clay. The collision is considered to be completely elastic.
mass of cart + force sensor = .449kg
integral of force = -.2214
initial velocity = .760m/s
final velocity = 0m/s

Calculations:
Calculating the change in momentum is done by multiplying the change in velocity by the mass of the object. Change in momentum = m(Vf - Vo)
For the first part of the experiment the change in momentum was -.9267 and the integral of the force was -.8315. % error = 10.27%
The second portion of the experiment where more mass was added the change in momentum was -.8674 and the integral of the force was -.8336. % error = 4.05%
The final portion of the experiment where the nail stuck to the clay the change in momentum was -.3412 and the integral of force was -.2214. % error = 35%

Conclusion:
The percent error for the first portion of the experiment was fairly high. There are several reasons that could contribute to the high amount of percent error. The force sensor could have ran into the spring at an angle so the force sensor would not be able to read the entire force of the spring and only managed to read a portion of the force. The more likely reason for the error was that the cart was moving at a high velocity and it returned at a high velocity as well. This hypothesis has some validity since the second portion of the experiment, which was essentially the same except more mass was added to the cart, the cart was sent into the spring at a smaller velocity and returned at a small velocity as well. The final portion of the experiment had an extremely high percent error at 35%. The most likely source of error is that the force sensor didn't read all of the force that was being applied to the nail since the nail was taped to the force sensor.

Sincerely,

Swaggy C