A bead is released at the top of a long ramp, slides down to the bottom and ascends a vertical loop of radius R on the inside. It must have enough speed to complete the loop, but just barely. Using energy and centripetal force, find the height of the ramp H compared to the radius of the loop, R. (Hint: You could assume a mass for the bead as well as a translational speed for the bead at the top of the loop. These are “straw quantities” which will disappear as you work out the problem.) This bead is sliding, not rolling, and all surfaces are assumed frictionless.

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Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.