How Far Will a Rolling Ball Go?

In summary, the distance a ball will stop rolling on a horizontal rough floor after being given a velocity is determined by the force and torque acting on it. Friction is not necessary to slow and stop the rotation of the ball. The main reason for torque is rolling resistance, which is caused by energy loss from deformation of the ball and the surface it is rolling on. This rolling resistance includes kinetic friction from squirming at the contact patch.
  • #1
Soumyajit6
1
0
If a ball is given a velocity, and left on horizontal rough floor then after what distance it will stop rollig (slippingis absent) ?
Explain with force and torque acting on it .
 
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  • #2
Friction isn't required to slow and stop the rotation of a ball. The main reason for the torque is related to rolling resistance, most of which is due to energy loss from deformation as the surface of the ball compresses and then expands. There's also energy loss as the surface the ball is rolling on also compresses and expands. Kinectic (sliding) friction that occurs during the deformation at the contact patch, such as squirming, is also a component of rolling resistance (and for this component the friction does matter, but not static friction).

Wiki article:

http://en.wikipedia.org/wiki/Rolling_resistance
 

1. How does the initial height of the ball affect its distance traveled?

The initial height of the ball does not have a significant effect on its distance traveled. As long as the ball has enough energy to overcome friction and other forces, it will continue to roll until it loses all of its energy.

2. What factors influence how far a rolling ball will go?

The main factors that influence how far a rolling ball will go are the initial force applied to the ball, the surface it is rolling on, and the presence of any external forces such as friction or air resistance.

3. Is there a maximum distance that a rolling ball can travel?

No, there is not a maximum distance that a rolling ball can travel. As long as the ball has enough energy, it can continue rolling indefinitely. However, external factors such as friction and air resistance will eventually slow down the ball and cause it to stop.

4. How does the shape or weight of the ball affect its distance traveled?

The shape or weight of the ball can affect its distance traveled, but it depends on the surface it is rolling on. A heavier ball may have more momentum and be able to overcome friction better, while a lighter ball may travel farther on a smoother surface due to less friction.

5. Can the distance a rolling ball travels be calculated?

Yes, the distance a rolling ball travels can be calculated using the equation d = v0t + ½at2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration. However, this calculation may not be accurate in real-world situations due to external factors such as friction and air resistance.

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