2. A uniform solid sphere ($r_s = 11.9$ cm, $m_s = 0.130$ kg) and loop ($R_L = 1.96$ 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)
(b) If the loop was frictionless, would $k_{min}$ 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.