A uniform solid sphere (rs = 13.9 cm, ms = 0.190 kg) and loop (RL = 1.99 m) are illustrated, below. The loop has a launching mechanism attached to one side that will launch a solid sphere
into the loop allowing the sphere to roll without slipping along the loop, in the direction shown.
The launching mechanism uses a spring to launch the ball, with the change in length of the
compressed spring as shown. When the spring reaches its unstretched length, the sphere will
no longer be interacting with the launcher.
(a) Determine the minimum spring constant, kmin, that the spring must have in
order for the sphere to negotiate the loop. Assume that ∆L = 4 cm and the launch point
is exactly one RL above the bottom of the loop.
(b) If the loop was frictionless, would kmin be a larger or smaller number. Justify
using POCOE.
(c) Identify and calculate the force that is acting as the centripetal force on the sphere,
at the top of the loop.