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

In summary, the ball will reach a height of (5/7)*h on the other side of the U-shaped ramp due to the conversion of potential energy to both translational and rotational kinetic energy. However, if there is friction present, some of the energy will be lost as heat and the ball will not reach a height of h again. Additionally, if the ramp is frictionless, the ball will slide instead of roll, affecting its trajectory.
  • #1
epsilon
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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?
 
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  • #2
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. :)
 
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  • #3
epsilon said:
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.
 
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  • #4
epsilon said:
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?

Arjun Chauhan said:
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.

Svein said:
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.
 
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  • #5
SnapshotU-shapedramp.jpg
Does this picture accurately represent the ramps?
 
  • #6
AlephNumbers said:
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?
 
  • #7
nasu said:
Where does he say this?
He didn't say it, but he probably meant to. :smile:
 
  • #8
nasu said:
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.

epsilon said:
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.
 
  • #9
AlephNumbers said:
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.)
 
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  • #10
Doc Al said:
He didn't say it, but he probably meant to. :smile:
Oh, yes. I see what you mean. :)
 
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  • #11
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! :)
 

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

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. It involves both linear and angular motion and is commonly seen in objects like wheels, gears, and planets.

2. How is rotational motion different from linear motion?

Linear motion involves movement in a straight line, while rotational motion involves movement around an axis. In linear motion, an object's velocity and acceleration are in the same direction, while in rotational motion, they are perpendicular to each other.

3. What factors affect the speed of a ball rolling back and forth on a U-shaped ramp?

The speed of a ball rolling back and forth on a U-shaped ramp is affected by the angle of the ramp, the mass and size of the ball, and the surface of the ramp. Friction also plays a role in the speed of the ball.

4. How does the shape of the ramp affect the ball's motion?

The shape of the ramp affects the ball's motion by changing the direction and speed of the ball. A U-shaped ramp will cause the ball to roll back and forth in a curved motion, while a straight ramp will cause the ball to roll in a straight line.

5. How can rotational motion be calculated and measured?

Rotational motion can be calculated and measured using various equations and tools, such as the moment of inertia, angular velocity, and torque. Experiments can also be conducted using sensors and data collection technology to measure the motion of rotating objects.

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