Conservation of Momentum: Crash Lessons

Purpose:

To show and prove the conservation of momentum:  For a collision occurring between two objects, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by one object is equal to the momentum gained by the other object.

Background:

Momentum is a physical quantity that determines the motion of a moving object. In effect, momentum measures how hard it is to stop a particular object’s motion. For example, it is easier to stop a fly moving at 6 m/h than a car moving at the same speed. However, it is easier to stop a car moving at 6 m/h than a car moving at 60 m/h. These examples illustrate momentum and the factors upon which it depends, that is velocity and mass. The momentum of an object at any given time is equal to:

p=mv

In addition to the above, momentum is a vector quantity, which means it has a direction (right, left, up, down, etc).

What we have said so far , though, applies for one object only. As we have been taught from countless movies and T.V. shows is that objects are meant to collide. Following a similar trace of thinking Physicists found the so-called law of conservation of momentum. This law states that in a given system, the total momentum of the system remains the same unless a force is applied in the system. For instance, let’s say we have two cars on two ends of a road and the one is moving at a speed of 10 m/h towards the other car, which is stationary (v=0 m/h). Before the collision takes place we can calculate the total momentum of the system, which will be equal to the sum of the two momenta of the cars. If both cars weigh 1000 pounds, then

p_a=m_av_a=1000*10=10000 kg*m*h^-1 and

p_b=m_bv_b=1000*0=0kg*m*h^-1

So the total momentum of the system before the collision is

Totalp_i=p_a+p_b =10000+0=10000 kg*m*h^-1.

Let’s say that when the two cars collide, both of them are moving with a velocity of 5m/h. If we repeat the calculations for the system then we will see that

p_a=m_av_a =1000*5=5000 kg*m*h^-1 and

p_b=m_bv_b =1000*5=5000 kg*m*h^-1 . Then the total momentum of the system after the collision is

Totalp_f=p_a+p_b =5000 +5000=10000.

 

Therefore, we can see that the momentum of the system did not change after the collision. From the above formula we can derive the velocity of an object after a collision, or the mass of an object, or anything that is relevant for that matter. In our experiments we tried to prove the law of the conservation of momentum when two carts are colliding. We calculated the total momentum of a system before a collision and after it and determined whether the momentum of the system remained the same or not, thus (hopefully)proving or disproving the law of conservation of momentum.

Procedure:

Setup: For this experiment you will need the following materials: Horizontal car ramp, two toy cars, masses, nxt processor, and motion sensors.

Data collection: Set up the horizontal car ramp and motion sensors (there should be two sensors on each end of the ramp). Measure the mass of each cart. Each sensor should record the velocity of a cart. Place a cart in the middle of the ramp and place a cart at the end of the ramp. One person should be in charge of pushing the cars for the collision and the other two should be responsible for starting and stopping the motion sensors. Once everyone is ready, push the cart at the beginning of the ramp towards the stationary cart in the middle of the ramp (it doesn’t matter how hard you push it but it is better not to push it very hard because the cars could fly off the track and injure a fellow group member!). When you push it, the member controlling the motion sensor of that end should start recording and right before the carts collide they should stop recording. Then, the second member of the group should initiate the second motion sensor . The computer should have recorded the data and placed it onto an excel file for your group. Repeat the process two more times and then find the average of the velocity measurements. From that you can derive the momenta of the carts before and after the collision. Finally add some masses on one of the carts and do the experiments again. You should do the process with 3 different mass setups and each mass setup should be repeated thrice, adding up to a total of 9 experiments.

Theoretical: Using the NXT software find the momentum of the system before the collision. The momentum of the system after the collision should be equal to the one before the collision, so use that as a measuring device.

Data:

When we carried out the experiment we collected the data below:

Sensor at the End					Sensor at the Start
Mass1=500 Mass2= 900					Mass1=500 Mass2= 900
	Velocity	Momentum	Experiment Number			Velocity	Momentum	Experiment Number
	-6.349206	-8.518517933	1			24.25107	11.303302	1
	-5.494505					23.206751
	-6.410256					20.361991
average	-6.084655667				Average	22.606604
Mass1=500 and Mass2=500					Mass1=500 and Mass2=500
	Velocity	Momentum	Experiment Number			Velocity	Momentum	Experiment Number
	-10.50175	-13.1795	2			17.507	13.8303165	2
	-12.820513					27.431421
	-16.216216					38.043478
average	-13.179493				Average	27.660633
Mass1=900 Mass2=500					Mass1=900 Mass2=500
	Velocity	Momentum	Experiment Number			Velocity	Momentum	Experiment Number
	-11.71459	-20.84826567	3			22.072937	26.1902565	3
	-15.011547					28.53067
	-17.948718					36.697248
average	-14.89161833				Average	29.100285

 

 

 

 

 

 

 

 

 

 

 

 

Then we calculated the absolute momentum for both motion sensor measurements and for all experiments to produce the table below. Three columns make up the chart; the first column, is meant to represent the results of the absolute momentum after the carts collisions. The second column’s data represents the absolute momentum before the collisions. And the last column, connotes what experiment was repeated (1,2 or 3):

After obtaining our data, the group decided to graph the numbers in order to get a visual representation of the absolute momentum collisions. The graph below  shows both data collisions in the same graph, and it’s easier to grasp the similarity of the curves that are given. This similarity in the curves tell us that momentum was conserved but the existence of errors made it impossible to produce identical curves.

Analysis:

Does the experiment prove the conservation of momentum theory?

From our data we can see that the momentum of the two sides is almost the same, which points to the fact that momentum is conserved.

What variables could have skewed the results collected?

In our case friction was the primary source of error. due to the fact that we used a track, when the cars collide they have twice the amount of fiction they have when they are on their own. Therefore, there is an external force acting on the system which is why momentum is not conserved.

How does mass affect the results?

When the two carts collide, they stick together. When that happens their masses are added. As a result the force of gravity, which is the product of mass and acceleration increases. Therefore, the force acting on the system is greater than before, thus skewing our results.

Can you suggest things that might improve the experiment or the accuracy of the results?

If we used a frictionless track, there would be no external force acting on the system, so we would get the results we expected.

 

Conclusion:

In our hypothesis we expected momentum to be conserved. The experiments we conducted showed a pattern that indicates to the fact that momentum is conserved. Even though the existence of friction skews our results, we can still see why and how momentum is conserved.

Experiences:

Anestis Luarasis:

I believe that the experiments we conducted were successful, and they showed that momentum was conserved. The team cooperated adequately and were highly productive. If there was one thing i would  change it would be the track. Otherwise everything was fine.

Nurta Ibrahim:

I loved all my team members they all took the time to put this wonderful experiment together. They even took their own time out to work on the blogs and doing the whole experiment. I couldn’t have asked for better members than the ones i have worked with. The only issue was that the data was skewed due to the existence of friction from the track.

Darwin Huang:

Overall this project was a great experience for me. I made new friends and even learned something new. The members in the group were never mean and we had lots of fun when we were devising our outline and plan. One thing i would change about the project is get a frictionless track because it complicated our project results by a pretty big factor. Otherwise it was great.

Cristian Koch :

This project was a great opportunity for working as a team. Over the last few weeks the members and I worked hard and managed to accomplish a successful experiment. The experiment had me learn about the physical quantity that determines the motion of a moving object, momentum. I can conclude that the experiment was a success and not only had it taught me new things but also improved my work ethics with others.

Ramon Morales Pozo:

This was a very interesting experiment. We proved the conservation of momentum, and we found a way to prove it which I find was very creative and informative at the same time. Overall, I enjoyed the project, and I was glad to have such good teammates.