Lab 14 Impulse-Momentum activity

Purpose: The purpose of this laboratory is to test the idea that impulse is equal to the change in momentum of an object in a collision.

The apparatus used in this experiment was used to measure the velocity and the force of the cart over a certain period of time.

The impulse momentum theorem states that the amount of momentum change for the moving cart is equal to the amount of the net impulse acting on the cart. This is shown by the relationship:

To test this idea. We are going to measure the are under the curve of the Force vs. time graph for the collision. Also, we are going to calculate the change in momentum of the cart by knowing the mass of the cart and its velocity before and after the collision. And the two values should be equal to show that this theorem to be true.

The impulse momentum theorem can also be written as:

Where J represents the impulse, m represents the mass of the cart, Vf represents the final velocity, and Vi represents the initial velocity.
The equation to find impulse using Force is :

Where the integral of the force over the time interval that the force is acting on the cart will give the impulse J.

In experiment 1 we saw if the impulse momentum theorem was true for a nearly elastic collision.
Where the incoming cart collides with the still cart (that is clamped and has its spring extended), and bounces back after the collision.

The graphs for this collision are:

Using the velocity vs time graph we chose a point on the graph right before the collision to get the initial velocity and a point right after the collision to get the final velocity. On the force and time graph we integrated the graph when the collision is happening to get the impulse (J).

Velocity initial : .183 m/s
Velocity final : -.160 m/s
mass of the cart : .715 kg

plugging into the right equations:

For the second experiment we added 500g to the cart and repeated the experiment.

The graphs that we got are as follows:

The information that we got from these graphs:

Velocity initial : .334 m/s
Velocity final : -.319 m/s

Measured mass of the cart: 1.215 kg

Plugging into the proper equations like above:

Taking the integral we get the impulse to be -.827 and the change in momentum is -.793.

For the third experiment we examined the impulse momentum in an inelastic collision. where we attach a nail to the moving cart, and making the cart with the nail collide into a wooden block with clay attached to it. and seeing if the impulse momentum thermo works for this kind of collision. We left the same mass on the cart so that the mass of the cart was the same as in experiment 2.

We did the experiment and the graphs that we got for the experiment were:

The information that we collected from the graph:

Initial velocity: .301 m/s
Final velocity: 0 m/s

measured mass of the cart: 1.233kg

Plugging the information in the proper equations gives us the following:

The impulse given from taking the integral of the collision is -.408. The change in momentum calculated is -.371.

The data tells us that the impulse momentum theorem is true. The impulse in experiment 1 was -.2268 while the change in momentum was -.2542. In experiment 2 the impulse was -.827 while the change in momentum was -.793. In experiment 3 the impulse was -.408 and the change in momentum was -.371. The values are really close but not exact due to the fact that there are friction forces and air resistance that could have caused error in the data. But the information supports the idea that impulse is equal to the change in momentum of a collision.