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

[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?

 

[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 can't reach the initial height 'h'. If, however, the ball had not 'rolled', it wouldve have attained the same height as initially left from. :)

 

[Svein]

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?

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.

 

[AlephNumbers]

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?

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?

You see some of the energy is lost in the frictional force.

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.

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.

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

 

[AlephNumbers]

Does this picture accurately represent the ramps?

 

[nasu]

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

Where does he say this?

 

[Doc Al]

Where does he say this?

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

 

[AlephNumbers]

Where does he say this?

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

on the other side? (Frictionless ramp)

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.

 

[Doc Al]

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.

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

 

[nasu]

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

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

 

[epsilon]

Sorry, I simply did not pay enough attention to the detail of the question. It rolls down the ramp (which I didn't realize 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! :)