Kevin Tran
Lab Partners: Kevin Nguyen, Jose Rodriguez
22 April, 2017

Impulse- Momentum 

Purpose: To test the impulse- momentum theory with inelastic and elastic collision activities.

Introduction: We performed 3 EXPT: Observing Collision Forces that change with time, A larger momentum change, and impulse momentum theorem in an inelastic collision.

First, we performed EXPT 1: Observing collision forces that change with time.

First we set up a track with one end having the motion detector and the other end with a cart with its stringy bit extended. The cart is clamped to a rod clamped to the table. We will be setting our main cart around the middle of the track where the motion detector can accurately collect data. First we calibrated the motion sensor, which is attached to the main cart. We mounted the force probe onto the cart with a rubber stopper to replace the hook mounted on the protruding part of the force sensor. We collided the cart with the plunger few times and observed what happens to the spring plunger.

First, I like to say that the mass of the cart + motion probe= 0.692 kg

During the collision, the force is not constant since the impulse-moment theorem states that the amount of momentum change for the moving cart is equal to the amount of the net impulse acting on the act, which is J=delta P

Now, we pushed our cart and collided with the clamped cart with a stringy bit extended. As a result with have an elastic collision between a cart and the clamped cart with a stringy bit extended.

Above, we have two graphs: a velocity/time graph and a Force/time graph of the cart before and after the elastic collision. 

In the Force/time graph (2nd graph), we highlighted a portion of the graph from one time to another during the time frame of the collision, and we took the integration of it. Since we know that Impulse= Force*time, we can take the integration to find our impulse. As a result, we got an impulse of 0.7347 N*s. Now we want to test if the momentum is similar to the result of impulse. In order to find out, we have to use the formula of momentum:

delta p= mvf - mvi

From our graph, we have an initial velocity of -0.542m/s before the collision and a final velocity of 0.503m/s after the collision.

Since our mass of the cart is 0.692kg, we can solve for momentum.

m(vf-vi) = 0.692kg(0.503m/s-(-0.542m/s)) = 0.7251 kgm/s.

If we compare 0.7347 N*s to 0.7251 kgm/s, the results are relatively the same, which proves the impulse-momentum theorem for this case.

EXPT 2: A Larger Momentum Change.

For this experiment, we performed the same exact task as EXPT 1, but the only difference is increasing the mass of the cart.

We added 500 grams onto our cart and got a total mass of 1.192kg

In performed the same ritual as EXPT 1. We highlighted a portion of the Force/time graph from one time to another during the time frame of the collision, and we took the integration of it . As a result, we got an impulse of 0.9055 N*s. We will be using the same formula to test that J=delta p

Delta p =mvf - mvi

From our graph, we have an initial velocity of -0.448m/s before the collision and a final velocity of 0.323m/s after the collision.

Since now our mass of the cart is 1.192kg, we can solve for momentum.

m(vf-vi) = 1.192kg(0.323m/s-(-0.448m/s)) = 0.89996kgm/s

If we compare 0.9055 N*s to 0.89996 kgm/s, the results are relatively the same, which also proves the impulse-momentum theorem for this case.

EXPT 3: Impulse-Momentum Theorem in an Inelastic Collision.

First, I like to say that we will be using the same mass of the cart from EXPT 2 of 1.192 kg. Now we have a case when we have an inelastic collision. In other words, after the collisions, they will stick to each other instead of bouncing off each other.

Below is the picture of our set up. We will be replacing the rubber stopper with a nail. Also, we removed the dynamics cart from its clamp and replaced it with a wooden wall and attached a blob of clay to the wall at the height of nail. Now we have created an elastic collision set up. 

Next, we made sure we zeroed our force probe and then collide the cart with the clay.

Above is our velocity/ time graph and Force/time graph. We realized during the graph we have an initial velocity, but our final velocity becomes zero since the collision was inelastic. Similarly to the other two EXPT, we highlighted a portion of the Force/ time graph and took the integration to find impulse. As a result, our impulse is 0.5045 N*s. Again, we proved that J=delta P in this case.

Delta P= mvf -mvi

From our graph, we have an initial velocity of -0.408m/s before the collision and a final velocity of 0m/s after the collision.

Since the mass of the cart is 1.192kg,

m(vf-vi) = 1.192kg(0m/s-(-0.408m/s))= 0.486kgm/s

If we compare 0.5045 N*s to 0.486 kgm/s, they are relatively the same, which proves the impulse-momentum theorem.

Conclusion:

After performing three experiments, we were able to prove the impulse-momentum theorem that J=delta P. During an elastic collision, we know that there will be an initial an a final velocity since both carts will bounce off of each other. While in an inelastic collision, we know that there will be an initial velocity but no final velocity since the cart and the clay will stick to each other; therefore there will be no final velocity.