Rotational motion -- Ball rolling back and forth on a U-shaped ramp

1. Apr 23, 2015

epsilon

If a ball rolls down a U-shaped ramp from a height h, why does it not reach a height h on the other side? (Frictionless ramp)

It will reach a height of (5/7)*h, but I'm not sure why. Some of the potential energy is converted to rotational and some is translational kinetic, but why do they not both re-combine to reach a height h again?

2. Apr 23, 2015

Arjun Chauhan

You see some of the energy is lost in the frictional force. You may ask where did the frictional force come in from ? The answer is quite simple. The frictional force provides a torque to the ball which causes it to 'roll' and not 'slip'. So even if we combine the the final energy of the ball (at the lowermost position), the ball cant reach the initial height 'h'. If, however, the ball had not 'rolled', it wouldve have attained the same height as initially left from. :)

3. Apr 23, 2015

Svein

First: If the ramp is frictionless, the ball won't roll - it will slide. Second: If there is friction. the ball will roll but some energy will be converted to heat.

4. Apr 23, 2015

AlephNumbers

You have that right. If a ball rolls smoothly down a ramp, some of the gravitational energy becomes translational kinetic energy, and some of it becomes rotational kinetic energy.

What do you think happens when this smoothly rolling ball hits a frictionless surface? Will it continue to rotate?

I disagree. If the ball were not to roll smoothly, and instead there was kinetic friction, then I would agree. But under the circumstances that the ball does not slip while rolling, no energy is lost due to non-conservative forces.

Once again, I disagree. The OP says the ball rolls down one ramp, but then slides up a distinctly different frictionless ramp.

5. Apr 23, 2015

AlephNumbers

Does this picture accurately represent the ramps?

6. Apr 23, 2015

nasu

Where does he say this?

7. Apr 23, 2015

Staff: Mentor

He didn't say it, but he probably meant to.

8. Apr 23, 2015

AlephNumbers

I suppose he does not. I think that I imagined that epsilon wrote it because it would make his post make sense.

I just got the impression that one side of the U-shaped ramp is frictionless and that the other is not. It would explain why the ball rolls.

9. Apr 23, 2015

Staff: Mentor

I believe your interpretation is correct and would lead to the answer provided. (This is a standard problem.)

10. Apr 23, 2015

nasu

Oh, yes. I see what you mean. :)

11. Apr 25, 2015

epsilon

Sorry, I simply did not pay enough attention to the detail of the question. It rolls down the ramp (which I didn't realise implies friction) and then "moves" (as the question says) up the other side of the ramp which is frictionless.

So thank you for both, a) Indentifying my incorrect message posting and b) helping me to understand the solution to it! :)