# Loop-the-loop marble physics

dmahmoudi
A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

I'm stumped - I'm assuming I need to use energy for this problem, but how do I factor in the loop-the-loop. Maybe with rotational kinetic energy?

Staff Emeritus
Gold Member
dmahmoudi said:
A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

I'm stumped - I'm assuming I need to use energy for this problem, but how do I factor in the loop-the-loop. Maybe with rotational kinetic energy?

There are two forces on the marble - the normal force applied by the track and the force of gravity. At the top of the track both forces point down towards the centre of the track. By Newton's second, the sum of these forces cause a centripetal acceleration. Use energy to find v and thus the centripetal acceleration at the top of the loop. Use Newton's second to find the normal force at the top. Find the height at which the normal force is zero. If released above this height, the marble goes loop-the-loop. If released below this height, the marble goes plop.

Regards,
George