15-April-2015: Impulse-Momentum activity

Part 1

Purpose:

To observe collision forces that change over time (observing the Impulse-Momentum theory).

Impulse is:

J = Force * ∆time

Impulse can therefore be represented by the area under a graph of Force versus time. 

In the Impulse-Momentum theory, impulse also equals the change in momentum so that ∆p = J.

Experiment: 

To observe this theory we set up a cart and plunger apparatus.

Pluger and Cart

1. First we clamped the dynamics cart to a rod and clamped it to the table (plunger/blue cart).

2. Then we mounted a force sensor on another dynamics cart so that the force sensor hook mounted the protruding part of the blue cart. 

3. We then set up a motion detector behind the car to measure the velocity versus position function (not shown in picture). 

4. We then made the carts collide several times to observe what happened to the spring plunger. 

5. To make sure we had good data before collecting it analyzing it, we made sure that the track was leveled so that momentum was conserved, friction was negligible, and that the force sensor was zeroed before the collision. 

Data Analysis:

Once we did the experiment, we now had the data of the position and velocity of the cart from the motion detector and the force of the collision versus time from the force sensor. 

Using the velocity, we could make a momentum column using the equation p = m*v

The momentum of the cart needs its mass, which is shown below:

mass = .684 kg

We then were able to make a column for the momentum of the cart:

Momentum of the Cart Column Equation

We then graphed the momentum versus time and put it on the same graph as the Force versus time.

We then took the integral of the force graph to find Impulse, which should equal momentum. 

Initial Momentum and Overall Impulse

Final Momentum and  Overall Impulse

Looking at the graphs, the first one shows the initial momentum and the second shows the final momentum while both graphs have the integral of the Force graph as well. 

The integral of the force graph gave us an impulse of J = 0.5170 N*s

Comparing this to the change of momentum we got:

P final - P initial = 0.224 - (-0.264) = 0.488 kg*m/s  

The percent error for this experiment is:

In this experiment, the collision is nearly elastic. In an elastic experiment, the initial momentum would be exactly equal to the final momentum, just in opposite directions. The 5. 61% error proves that although some momentum is lost, due to momentum taken by the earth's movement and other small factors such a the little bit of friction present, the change in momentum is pretty close to equalling the impulse proving the Impulse-Momentum Theory. 

Part 2

Purpose:

To observe a larger momentum change that occurs from a larger collision force.

Experiment 2:

In this next experiment, we did the same procedure but added on 500 grams of mass.

Same set up but the cart had 500 grams added

Once again, we now had the data of the position and velocity of the cart from the motion detector and the force of the collision versus time from the force sensor. 

Using the velocity, we could make a momentum column using the equation p = m*v

The momentum of the cart needed the new mass which was now 500g + 684g = 1.184 kg

The new column for momentum was created using the new mass shown below:

New Momentum of Cart Column Equation

Once again, we also graphed the momentum versus time and put it on the same graph as the Force versus time.

We then took the integral of the force graph to find Impulse, which should equal momentum. 

Initial Momentum and Overall Impulse

Final Momentum and Overall Impulse

The integral of the force graph gave us an impulse of J = 0.5820 N*s

Comparing this to the change of momentum we got:

P final - P initial = 0.260 - (-0.323) = 0.583 kg*m/s  

The percent error for this experiment is:

This time the results had a larger momentum, which makes sense because momentum is mass times velocity. The impulse was also equal to the change in momentum once again, with some error. This proves that the Impulse-Momentum Theorem applies regardless of the change in mass. 

Part 3

Purpose:

To observe the Impulse-Momentum Theorem in an Inelastic Collision.

Experiment:

1. Same set up as part 2, making sure the mass of the cart stays the same

2. This time we change the plunger into clay and add nail onto a rubber stopper that is connected to the force sensor. (The clay and nail will get stuck together, creating an inelastic collision.)

3. We then made the cart collide into the clay and observed what happened with the motion and force detector.

Data Analysis:

Same as before, we now have the data of the position and velocity versus time of the cart from the motion detector and the force versus time from the force sensor. 

The collision was proven to be inelastic since the cart stuck to the clay and the velocity was 0 in the end. 

Due to time limitations, we were unable to try the experiment several times until we got the initial velocity as the previous activity in part 2. 

We did receive graphs of the change in momentum and Impulse shown below:

Momentum final is 0 N*s

Momentum initial is -0.483 N*s

Based on the graphs the Impulse = 0.4825

P final - P initial = 0 - (-0.483) = 0.483 N*s

The percent error for this last experience is:

The Impulse-Momentum theory still holds since the momentum and impulse still equal each other with some error. The proves the rule is universal whether or not the collision is inelastic or elastic.

Error:

Due to the unequal velocity in part 2 and part 3, we could not show the difference between inelastic and elastic impulse/momentum. Since the momentum of the inelastic collision only has the initial velocity but a final velocity of zerio, it is assumed that it would be half the momentum of the cart that has an initial velocity and the same final velocity of the elastic collision. We were supposed to prove this by showing that the impulse of the elastic collision was twice that of the inelastic. In the end the theory still applies and works out successfully.

Conclusion:

The Impulse-Momentum Theory was successful in all three parts of the experiment. With little percent error, momentum equalled the Impulse whether or not mass was added or the collision was elastic versus inelastic.