# GRE Test Problem (elementary)

1. Jul 29, 2013

### Sam_Hawkins

1. The problem statement, all variables and given/known data

2. Relevant equations
Conservation of energy?!!

3. The attempt at a solution
Well what I think is that if there is no friction, whenever the initial velocity is >0, the particle will just keep sliding over all the bumps, right? The potential energy will just be transformed into kinetical and vice versa ...or am I terribly missing something? The explanation is here:
but it seems really twisted to me.

2. Jul 29, 2013

### voko

Conservation of energy has very little to do with this.

The motion is curvilinear, and that means the particle must experience varying acceleration as it follows the curved path. This acceleration is produced by the force of gravity and the reaction of the rippled surface, and there are certain limits to that. So the condition for staying on the surface is that the acceleration required for that must be within the imposed limits.

3. Jul 29, 2013

### Sam_Hawkins

allright, but why does the conservation of energy not apply here?

4. Jul 29, 2013

### voko

This is not what I said.

5. Jul 29, 2013

### Sam_Hawkins

Okay, but I do think you know exactly what I meant.

I will play your game then. Why can't I use the conservation of energy?

For every initial speed u>0 it holds that at the bottom of the sinusoid the speed will be v+u where v=sqrt(4gd) which is by itself enough to overcome the gravitational force and climb up at the top of the sinusoid plus it will of course still have the initial velocity. So what is the reason why it does not perform infinite motion? If I imagine the sinusoid as a potential for a particle moving in 1D, the only chance with the particle initially being at the top to perform a finite motion is staying at the spot, is that right?

6. Jul 29, 2013

### voko

The problem does not state that, either. Nor is this what the problem is about.

Because the surface is frictionless, conservation of energy holds and motion continues infinitely, you are quire correct about this.

However, as the initial speed exceeds a certain value, the particle will not just slide at the surface, it will fly without any support. The problem is about finding the max speed at which the particle can move along the surface without flying.

7. Jul 29, 2013

### Sam_Hawkins

ah alright my bad lol :D
well that is just retarded, I thought the problem is asking whether the point will slide all the way to the end of the sinusoid (where the line ends on the picture lol :D ).

Ok now it is clear. thanks.

8. Jul 30, 2013

### Sam_Hawkins

9. Jul 30, 2013