# Two boxes with same initial velocity on a 2d track but one is at top of a hill

1. Feb 9, 2012

### JPHL

I'm trying to understand a problem someone gave me recently. there is a frictionless track that initially starts flat then there is an incline of 20 degrees then it levels out again at the bottom of the incline. you have two masses, 1 is .4 kg and is located at the top of the hill and has an initial speed of 1 m/s towards the end of the track. The second mass is 0.2 kg and is located on the flat section at the bottom of the hill and also has an initial speed of 1 m/s in the direction of the track. Will these two masses collide? I'm thinking they won't since while the first box is on the ramp the speed will increase but only in the y-component and when the box gets to the bottom of the hill the track would exert a force canceling that gained momentum out entirely leaving it with its initial velocity and since they both have the same velocity they won't ever actually collide will they?

2. Feb 10, 2012

### gsal

Hhhhmmm....so, if you have a mass with zero initial horizontal velocity at the top of the hill and you let go of it...will it stop on its tracks as soon as it gets to the bottom of the hill? or will it shot out of there?

I think you need a free body diagram of the body in the middle of the hill, see how the pull of gravity against an inclined plane will results into components normal and parallel to it, effectively increasing the speed of the mass along the track...then, at the bottom of the hill, you again have the mass coming in at an angle and so the flat of the track can only cancel the vertical component of it, but there should be a horizontal remaining.