How Do You Prove the Law of Conservation of Momentum in Collisions?

[ally baker]

Homework Statement

This lab I have the mass and change in distance measurements for inelastic collisions; and then we did an elastic collision one where we determined the mass and measured the times three of them simultaneously where we measured it as it bumped the car. So I am supposed to prove the law of conservation of momentum, but i have no clue which equation I am supposed to start with. For the measurements on the inelastic collisions I got a mass of 66.3 for change in distance of 3 feet, and 266.3 for 2.12 feet, and 366.3 for 1.88 feet. For the elastic mass of 66.3 or .0663 kg and the times we got as it bumped each car, simultaneously were 1.17 sec, .13 sec, and 1.32 sec. I believe that we are supposed to compare the ratio to determine the ratio of distances is equal to the ratio of masses and therefore show that momentum is conserved. We also are supposed to use KE somehow, but not in the inelastic collision. How would I get V? Or how would I start? I don't have any time measurements for the first one tho. I feel like I am over thinking this. Thanks beforehand if you can help me.

Homework Equations

I was thinking I need to use mVa+mVa=mVb+mVb and then mVa+mVb=0 So mVa= -mVb but I don't have V So would I use Va*t=Da and Va*t=Db so Va/Vb=Da/Db and then Ma*Da= -Ma*Db or use this MA*VA+ MB*VB =(MA+MB)*Vf. But where would I get V?

 

[Simon Bridge]

The law of conservation of momentum is where you start... which you have done.
You need masses and speeds before and after the collision... which you get from distances and times.

It would help to have a careful description of the experiment. It is not clear what distances and times etc have been measured for instance.
Remember that none of us know what you did so you have to tell us carefully and precisely or we will get it wrong.

 

[ally baker]

Two carts were pushed away with each other. The masses were changed and distance traveled was measured and compared for each one.
There are different kinds of collisions with their different masses, and the motion was studied. I am supposed to
prove the ratio of distances is equal to the ratio of masses; therefore, momentum is conserved. I don't have the speed for the inelastic I only have the change in distance and the mass; and for the elastic collision the time which the car started and right before it hit the other car, and that car starting and when it end, and where it stopped at the end; so basically three time measurements. We measured these all at the same time and the mass.

 

[ally baker]

OR Would I just use X1/X2=M1/M2?

 

[gneill]

Two carts were pushed away with each other. The masses were changed and distance traveled was measured and compared for each one.
There are different kinds of collisions with their different masses, and the motion was studied. I am supposed to
prove the ratio of distances is equal to the ratio of masses; therefore, momentum is conserved. I don't have the speed for the inelastic I only have the change in distance and the mass; and for the elastic collision the time which the car started and right before it hit the other car, and that car starting and when it end, and where it stopped at the end; so basically three time measurements. We measured these all at the same time and the mass.

Can you describe the experimental setup a bit more? What type of carts are involved? Are they moving on a track of some sort? Is there friction involved in their motions, or are you to ignore friction? How were times measured?

It would be excellent if you could pick one of the experimental trials and provide a diagram of the setup and what measurements were taken and how. As it stands I'm finding it hard to picture what your "change in distance" represents as a measured quantity related to a collision experiment. If you have a written lab description perhaps you could upload a picture of it?

 

[Simon Bridge]

A common momentum demo is to set up two dynamics carts with different loads, lock the spring on one and put the carts so the locked plunger touches the back of the other. Release the spring and the carts spring apart ... then roll to a stop over different distances (if you have room) or travel a measured distance in different times.
You can then compare distances to stop, or times, with the masses.

I suspectr a variation on that ... but we need the details.

 

[ally baker]

I think its like you mentioned only, we used carts. The first one has a spring on it. The other trial doesn't.

 

[Simon Bridge]

I think its like you mentioned only, we used carts. The first one has a spring on it. The other trial doesn't.

... you "think it's like"? Don't you know? You were there after all - please tell us specifically what was done.
Don't get creative or arty with the language - just spell it out as if we are totally ignorant of the experiment.
Without this information, nobody can help you.

 

[ally baker]

Just I said before. The first car had a spring on it, and we got the time ratios and the distance the cars bounced off each other which would be the distance between them. We also did a second trial without the spring where one car bumped into the other car. This trial we got where these each of the cars started and ended, and got 3 measurements. We had to basically create the experiment to compare the ratio of distances and masses right?

 

[haruspex]

Just I said before. The first car had a spring on it, and we got the time ratios and the distance the cars bounced off each other which would be the distance between them. We also did a second trial without the spring where one car bumped into the other car. This trial we got where these each of the cars started and ended, and got 3 measurements. We had to basically create the experiment to compare the ratio of distances and masses right?

Ally, please try to understand that we are not mind readers and did not witness the experiment. Describe the equipment (carts, track, configuration), what you did (pushed a cart, both carts, released a spring...), the subsequent interaction (a moving cart hit a stationary cart, two moving carts collided, moved together or separately after impact, ...) and what you measured (distance each moved from point of impact, finishing distances from some fixed reference, times to come to rest after initial push, times to come to rest after impact,...).

Depending on exactly what times and distances you measured, by assuming constant acceleration you might be able to deduce speeds just after collision. (I would have thought you would not need to know the times, though, since you only care about the ratios of the speeds.)

 

[Simon Bridge]

Just I said before. The first car had a spring on it, ...

OK, but there are lots of ways a car may have a spring on it.

...and we got the time ratios and the distance the cars bounced off each other which would be the distance between them.

... would it be? It either is or it isn't. Don't you know? You were there, we weren't. You need to describe things carefully. We don't know what you mean by "time ratios" etc because you have not defined your terms. Presumably you take the time for something to happen and the time for something else to happen and divide one by the other... but what things, what times? Its the same problem with the other measurements you talk about.

We also did a second trial without the spring where one car bumped into the other car. This trial we got where these each of the cars started and ended, and got 3 measurements. We had to basically create the experiment to compare the ratio of distances and masses right?

I dunno, did you? You read the instructions - don't you know?

It is important to make sure you understand the practical exercises you do before you do them.
I think the biggest problem showing up here is communication.
As an exercize, get a freind, both of you get a pad and pen and sit so you cannot see each others pad. You draw a picture and describe what you are drawing to you freind. Your friend must make a drawing following your instructions... and you cannot draw on common knowledge between you. After, compare drawings.