# Sphere in a potential well

• ShayanJ
In summary, Walter Lewin's MIT video lecture showed that a sphere rolling on a track will have a shorter period than if it slides. He hypothesized that friction was not the reason for the difference, but it turned out that air resistance was. Additionally, because the process of accelerating the ball takes more time, it stops sooner than if it slid.

#### ShayanJ

Gold Member
Imagine you put a sphere on a track which is part of a vertical circle.You expect the sphere to roll in a path like a pendulum.it should do it like a mass on an almost frictionless surface because the friction of the surface is rolling the sphere not stopping it and the air drag isn't very high.
But in one of the Walter Lewin's MIT video lectures,He did such a thing but the period was less than what he predicted with conservation of energy and the sphere stopped rolling in a short time that I didn't expect.He didn't explain why that happens and the problem is I can't explain it and its killing me.really need some help.
thanks

It has to be some kind of dissipation of energy... you cannot make a perfectly frictionless surface..

This is because of air resistance even if it is not very high .Also the surface is almost frictionless but not completely without friction

Yes I could think of that.But at first he asks students what's the reason and when they say friction,he says no.friction is not that much.

if ball was sliding without rolling (this means that friction is trully zero since the torque from friction is what makes the ball rotate) then with simple conservation of energy the ball would continue forever. But due to the torque from friction some energy is converted to heat.

Delta² said:
if ball was sliding without rolling...
I think you meant:
If ball was rolling without sliding.

...But due to the torque from friction some energy is converted to heat.
this is in contrast to your first sentence.

In fact here we have two retarding forces:
1)Air drag
2)Because you can't have perfect rolling,there is just a little sliding and that intoduces a little friction.
But as I said,Lewin said that friction is not the reason.
The difference between Lewin's prediction of period and the real period was higher than an amount that could be possible due to such small frictions.

I have not seen the video but I am fairly sure I know what he was trying to get the students to understand.

If the sphere slides on the track you get one answer for the period, if it rolls you get a different period. The key is the conservation of energy. A sliding sphere just exchanges energy between gravitational potential energy and kinetic energy. A rolling sphere has to share the potential energy between kinetic energy and the energy of its own rotation due to its moment of inertia.

The friction and hence the damping is also different between the sliding and rolling scenarios.

Hope this helps.

Regards

Sam

Ok seems i was wrong, only possible losses seem due to not perfect rolling as you said. Probably there is some other factor in the experiment which eludes our attention.

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The point is the period formula differs by a factor of sqrt(10/7).
also because the process of accelerating the ball takes more time because of rolling,I think in that time there is some sliding and so it stops sooner than an object sliding on an almost frictionless surface.

## What is a sphere in a potential well?

A sphere in a potential well is a physical system in which a spherical object is placed in a region of space where there is a potential energy minimum at the center. This creates a well-like shape for the potential energy, with the sphere being able to move freely within the well.

## How does the potential energy affect the sphere in a potential well?

The potential energy affects the motion of the sphere in the well by determining the equilibrium position and the stability of the system. The sphere will tend to stay at the bottom of the well, where the potential energy is at a minimum.

## What is the relationship between the size of the potential well and the sphere?

The size of the potential well and the size of the sphere are important factors in determining the behavior of the system. A larger potential well will result in a larger range of motion for the sphere, while a smaller potential well will restrict the sphere's motion to a smaller area. The size of the sphere also affects the potential energy, with a larger sphere having a greater potential energy than a smaller one.

## How does the shape of the potential well affect the motion of the sphere?

The shape of the potential well can greatly influence the motion of the sphere. A spherical potential well will allow the sphere to move equally in all directions, while a more elongated well will restrict the motion to certain directions. The shape of the potential well can also affect the stability of the system, with a deeper and narrower well providing more stability than a shallower and wider one.

## What are some real-world examples of a sphere in a potential well?

A common example of a sphere in a potential well is a marble rolling in a bowl. The bowl represents the potential well, and the marble is the sphere moving freely within it. Another example is a planet orbiting around a star, with the gravitational force acting as the potential well. Other examples include a pendulum swinging back and forth, a ball rolling in a concave track, and a charged particle in an electric potential well.