Problem

A solid ball of mass m and radius r rolls without slipping through a loop of radius R, as...

A solid ball of mass m and radius r rolls without slipping through a loop of radius R, as shown in the figure. From what height h should the ball be launched in order to make it through the loop without falling off the track?

Step-by-Step Solution

Solution 1

Step #1 of 5

THINK:

Determine the height should the ball be launched in order to make it through the loop without falling off the track.

SKETCH:

The figure shows a solid ball of massand radiusis rolling without slipping through a loop of radius.

Step #2 of 5

RESEARCH:

Energy is conserved because there is no friction and slipping. The only force acting on the ball at the top of the loop is the centripetal force, and is given by