Inelastic Collisions Lab

The purpose of this lab is to analyze the motion of two low friction carts in an inelastic collision. We will also verify that the law of conservation of momentum is obeyed with this collision.

The materials needed for this lab are:

• Computer with Logger Pro
• Lab Pro
• Motion Detector
• Horizontal Track
• Two Carts
• 500 g masses
• Triple beam balance
• Bubble level

INTRODUCTION:

To understand what we are doing this lab we have to know what momentum is. Momentum can be described by the equation p=mv and SI units are (kg m/s). We are going to have a track set up with 2 carts with masses m1 and m2. The mass of m1 is 499.8 g or .4998 kg, m2 had a mass of 504.1 g or .5041 kg, and the mass of the bar that will be placed on the carts is 494.6 g or .4946 kg.

The picture shows m1 being pushed into a stationary m2 on the track. This is how the lab is going to be set up and performed. There will also be a point when we add a bar with nearly 500 g mass that we put on the carts to see what happens.

The law of conservation of momentum states that in a perfectly inelastic collision, which is, when two objects stick together after the collision, your initial momentum should be equal to your final momentum.

The initial momentum can be found of both objects. v2 is equal to 0 because it is not moving. The equation for momentum as pointed out before is p=mv. In the final momentum, we add the masses together because it is moving together as one unit. The V is the velocity of the two masses that are moving together.

PROCEDURE:

We set up the track with the carts and motion detector exactly as the picture shown above. We used a bubble level to make sure the track was perfectly level. We used the adjustable feet to make the track level. Once setting up the track we had 2 carts with m1=.4998 kg and m2=.5041 kg (we use our mass in kg because that is what the units are for momentum). We started Logger Pro and opened the Mechanics folder and opened the file Graphlab for our data collecting with the motion detector. 

We checked the motion detector to make sure it was working properly. Once we did that we made predictions on what our graph should look like. 

The graph shows the position vs. time graph of the cart moving by itself, colliding with the other cart, and then showing both carts moving together as time goes on. This graph shows that the cart prior to collision will have a higher velocity than the two carts together. This makes sense because according to the law of conservation of momentum, the momentum should be equal before and after the collision. Since the mass will be greater after, it should move with a lower velocity.

The process of performing the lab was:

1. One person push the Start Collecting button on the LoggerPro Software.
2. Have another person ready to push the first cart into the second cart once the motion detector starts clicking.
3. Let both of the carts move towards the end of the track and end the collection of data.

After collecting the data for the first run, we selected a small area of the graph right before the collision and made a linear fit. This is going to be the initial velocity for the initial momentum. We did the same for right after the collision. This is the final velocity for the final momentum. We performed 2 more trials for this setup.

An Extra Mass On Cart 2

Once completing this set of trials, we then added a mass onto the second mass which was 494.6 g. The total mass of the bar and the cart added up to 998.7 g or .9987 kg since we are working with masses in kilograms. We did the same thing as far as collecting data for this set of trials. We performed 3 total trials with this scenario.

We also made predictions of what the position vs. time, velocity vs. time and acceleration vs time graphs look like:

The position vs. time graph would be similar to the one at the beginning. The difference though is that this time, now that there is an extra mass on the cart2 which is going to be after the collision will cause the position to increase slower because more mass is moving at a slower rate. This makes sense because according to the law of conservation of momentum says that if you are going to add more mass to an initial mass with an initial velocity then the new velocity will be significantly less.

As the object keeps moving, the velocity will slowly decrease because there is a little bit of friction between the cart and track which is why it slows down a little compared to the initial push to the point of collision. After the collision, when both carts are attached to each other, the masses will slow down a little bit faster. This is why we are finding our velocities right before and right after collision. The starting velocity and the ending velocities are not completely accurate.

The accelerations are just describing what the velocities are doing. Since the cart slows down just a little bit before the collision, it will have a small acceleration in the negative direction. After the collision the mass is larger and the friction will be greater than before which is why the masses slow down faster having a greater acceleration in the negative direction.

Extra Mass Moved onto First Cart:

We moved the extra 494.6 g weight on the second cart onto the first cart to see what would happen with a larger mass on the initial momentum. We performed 3 trials just as the previous tests. We made a linear fit just before and just after the collision and made the following table:

Finding Average % Difference:
We next have to find the average percent difference of all 9 trials to see how well the law of conservation of momentum was obeyed in our experiment.

The average was 21.7%. According to that percent we didn't do so well in proving the law of conservation of momentum. The reason is because of the 2nd trial of Test 2. We had a 138% difference on that trial. If we don't take that trial into account and average the other 8 tests we had an average difference of 7.19%.
Based on what we found, without the second trial of the second test, our average difference is very close to verifying the law of conservation of linear momentum with our difference being less than 10%. 

% Difference of Kinetic Energy:
When looking at kinetic energy, the equation we need to know is K=(1/2)mv^2. Since we know the final and initial masses as well as velocities we can calculate what the difference is in kinetic energy from before and after the collision. We made a table of the % difference of each trial's kinetic energy.

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Next we wanted to look at theoretical problems:

1. When mass, m, collides with an identical mass, m, initially at rest.

2. When mass, 2m, collides with mass, m, initially at rest

3. When mass, m, collides with mass, 2m, initially at rest

CONCLUSIONS:
I learned that momentum will always be conserved in a perfect inelastic collision. I also learned that even though Kinetic energy uses the same values for initial and final masses and velocities, it is not conserved. We saw this with our % differences in our momentums compared to our % differences of Kinetic Energy. However, total energy will be conserved, which is the sum of initial kinetic and potential energies are equal to the sum of the final potential and kinetic energies. Therefore if momentum is conserved, kinetic energy will not be conserved. Some possible sources of error obtained in this lab could have been from not having a perfect inelastic collision occur in our 5th trial. We also are taking an average velocity at a moment just before a collision and just after so we won't necessarily be able to get "perfect" numbers giving us an error.