Question

(1) A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. Find the minimum value of h (in terms of R) such that the sphere completes the loop. Solid sphere of mass m and radius $r << R$.

          (1) A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. Find the minimum value of h (in terms of R) such that the sphere completes the loop.
Solid sphere of mass m and radius $r << R$.

(1) A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. Find the minimum value of h (in terms of R) such that the sphere completes the loop.
Solid sphere of mass m and radius r << R.

Added by Dustin G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

04/14/2022

Step 1

The forces acting on the sphere are gravity (mg) and the normal force (N) from the track. At the top of the loop, the normal force will be pointing downwards, and at the bottom of the loop, the normal force will be pointing upwards. Show more…

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(1) A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts higher than r. Find the minimum value of A (in terms of A) such that the sphere completes the loop, with the lowest point of the sphere at height h above the bottom of the loop of radius R much larger than r. Find the minimum value of A in terms of R such that the sphere completes the loop. Solid sphere of mass m and radius << R.