Rolling Motion of a bowling ball

[m2003]

How do I do this Problem?:

A bowling ball is given an initial speed of 5m/s on an alley such that it slides initially without rolling. The coefficient of friction between the ball and the alley is 0.12. How far must the ball travel until pure rolling motion sets in?

Any help would be greatly appreciated.

 

[ehild]

How do I do this Problem?:

A bowling ball is given an initial speed of 5m/s on an alley such that it slides initially without rolling. The coefficient of friction between the ball and the alley is 0.12. How far must the ball travel until pure rolling motion sets in?

Any help would be greatly appreciated.

The motion of the ball consist of a translation of its centre of mass and a rotation around the axis through the centre of mass. The friction decelerates translation and accelerates rotation till the condition of pure rolling would fulfill, that is the speed of the CM is equal to Rw, radius times angular speed.

ehild

 

[wais]

Thank you!

To solve this problem, we need to use the concept of rolling motion and the equations of motion. Rolling motion is a combination of translational motion (movement in a straight line) and rotational motion (spinning around an axis). In order to transition from sliding to rolling, the ball needs to have enough torque to overcome the friction force and start rotating.

First, we need to find the torque acting on the ball. Torque is calculated by multiplying the force applied (friction force) by the distance from the axis of rotation (radius of the ball). In this case, the torque is equal to the friction force multiplied by the radius of the ball.

Next, we can use the equation for torque (Torque = Moment of Inertia * Angular Acceleration) to find the angular acceleration of the ball. The moment of inertia for a solid sphere (like a bowling ball) is 2/5 * mass * radius^2.

Once we have the angular acceleration, we can use the equation for rotational motion (Angular Velocity = Initial Angular Velocity + Angular Acceleration * Time) to find the time it takes for the ball to start rolling.

Finally, we can use the equation for translational motion (Distance = Initial Velocity * Time + 1/2 * Acceleration * Time^2) to find the distance traveled by the ball until it starts rolling.

Plugging in the given values and solving for time and distance, we get a distance of approximately 8.3 meters. This means that the ball must travel 8.3 meters before pure rolling motion sets in.

I hope this explanation helps you solve the problem. If you have any further questions or need clarification, please don't hesitate to ask. Good luck!