# Basic Question About A Cart Hitting another Cart

1. Jan 24, 2005

### Markd

Hi,

I am wondering if one cart is rolling down a ramp and there is another cart at the bottom. What wil happen to the bottom cart as far as energy goes(law of conservation of energy)? If I had the car at the top's velocity, displacement, etc how would I go about calculating how the far the bottom car moved when the top car hits it (formulas).

Thanks

2. Jan 24, 2005

### christinono

Use momentum conservation formulae combined with kinetic energy conservation (if Ek is conserved).

3. Jan 24, 2005

### HallsofIvy

Staff Emeritus
Of course, in calculating HOW FAR the bottom car will move, you have to be assuming that there is friction. If, for example both cars had the same mass, without friction, the first car would stop and the second car would move forever.

4. Jan 24, 2005

### christinono

Momentum will always be conserved. Conservative forces are another question. If the problem mentions friction, you must take that into consideration. It also depends on the mass of the objects. If the object that is rolling down is considerably lighter that the one at the bottom, it will probably bounce back.

5. Jan 25, 2005

### Markd

Ok sort of understand what you guys mean

So if I had a 1m long ramp and its was 15cm off the ground and car1 weighed 600g and car2 weighed 700grams and it is asking for "If car1 started at the top of the ramp and then hit car2 which is at the bottom of the ramp, how far will car2 travel until it stops?"

Thanks

6. Jan 25, 2005

### dextercioby

Compute the second cart's velocity.If it's different from zero,then,because of the lack of friction,it will move "ad infinitum"...

Daniel.

P.S.I would have said "forever",but that's the word Halls used... :tongue2:

7. Jan 25, 2005

### dekoi

Calculate angle of the ramp via sin^-1.
Calculate velocity of first cart at the bottom of the hill, via energy formulae (ma=mgsinX) (assumming no friction) to find acceleration, and kinematics (v2^2 = v1^2 + 2ad) to find v2. Then use conservation of momentum (m1v1=m1v1+m2v2) (second cart is initially still) to find the velocity of the second cart after it is hit by the first cart. If you are not given v1 then you must use another set of formulas, while assumming this is a perfectly elastic collision. These formulas are the conservation of kinetic energy and will follow something like: mv1^2 + mv2^2 = mv1^2 + mv2^2
Work with the two sets of equations to find v1 and v2`.
Once again, if there is no friction on the horizontal surface on which the second cart moves, it will move forever.