[eric343]

The table above shows the data I collected through a series of interactions between two carts on a track (two different types of cart-cart interactions were used – collisions and explosions. In collisions, the cars collided in the center; either with both cars ‘pushing’ off from the ends of the track (collision type 1) or with the blue car starting at rest, in the middle of the track (type 2). In explosions, the two carts started in the middle with one plunger pushing against the other cart:

Initial velocity is the velocity at which the carts were traveling before they interacted, final velocity is the velocity after they interacted)

The thing is, according to the table, the two-cart system gained momentum in all cases, even though no outside forces were applied to them. Since this seems to violate the law of conservation of energy, I'm thinking I did something wrong. Any suggestions?

 

[CaptBubba]

working on it...

Isn't change in momentum (final)-(initial)?

Yeah, everything else works out fine, but I am almost positive that change in anything is the final value minus the initial value. That would account for the sign irregularity.

They probably lost momentum due to friction with the track/air. Unless you are using an air-track, in which case the numbers shouldn't be that high.

 

[eric343]

You know, I think you might be right... Since the final momentum 'should' be less than the initial momentum, we'd want the change in momentum to reflect the loss of momentum...

I guess that might do it

Though I still don't understand why in trial 5 I lost ~78g/m/s; I wasn't using an air track but the track and carts I were using had pretty good bearings... Weird. Maybe when I pushed the trigger button on the cart my finger acted as a break or something

 

[Born2bwire]

I remember these labs. Usually the data is pretty close, but I guess you've come up with a good random error for your experiment and teachers usually let slide errors when you point out what the results should have been and a possible reason for your variation. Note however, I believe that conservation of momentum applies only to elastic collisions and not to inelastic collisions, I'll need to check that when I have time, I might have some old mechanics books lying around (right now I'm doing oscillators, oh the joys of computing the model of a underdamped oscillator with sinusoidal applied force).

 

[CaptBubba]

But the carts when through the photogates after your finger stoped pressing them. I assume by the 0 measurement as the final velocity that the blue cart didn't even reach the photogate after the collision? There was probably a good deal of momentum lost to friction.

I think the most suspect trial that you had was the one where you got a loss of 1.6. That's why you are supposed to do each run multiple times.

 

[eric343]

Born2bWire: Yes, they're elastic collisions..

CaptBubba: True, for the collisions. Not so for the explosions, where the carts interacted before they went through the photogates...

And the 0 means the cart didn't move much, if at all...

 

[MacDEF]

Quote:

Originally posted by eric343 The thing is, according to the table, the two-cart system gained momentum in all cases, even though no outside forces were applied to them. Since this seems to violate the law of conservation of energy, I'm thinking I did something wrong. Any suggestions?

Eric:

Your experiments are inelastic. They may appear to be "elastic," but in reality there are few experiments available that are truly elastic. Some things that probably happened in your experiment that made it inelastic:

1) There are few substances that are 100% elastic; at the point of impact, the surfaces that came in contact absorbed a bit of energy through deformation, and there was probably a bit of friction that also absorbed energy (the two surfaces probably "scraped" a bit as they impacted).

2) When the carts hit each other in the center, at the instant of collision, the impact probably caused one or both to move to the side and/or a bit up off of the track (in other words, they didn't bounce back perfectly) -- energy is dissipated by these movements, no matter how small they are.



Plus, as you mentioned, there's going to be friction. Maybe not much, but enough to affect the outcome; remember that in addition to the friction of the wheels/bearings/axels (which you're assuming are perfectly aligned), and the wheels on the track, there's also air resistance. And I'll bet that the wheels and axels and the body of the carts aren't perfectly aligned, so you get more friction there

I guess what I'm saying is that these kinds of experiments, with the kind of equipment you're using, are demonstrations of concepts. Unless your school is spending LOTS of money on the equipment, you're not going to get frictionless, elastic trials

Oh, and you added the numbers wrong, that's why it looked like you were gaining momentum

 

[eric343]

Well, they're as close to elastic as they'll get; in the collision trials the carts used magnets to repel eachother, and theoretically magnets shouldn't dissipate energy. (the carts never touched so they couldn't "scrape")