The thin hoop of negligible mass and radius r contains a homogeneous semicylinder of mass m which is rigidly attached to the hoop and positioned such that its diametral face is vertical. The assembly is centered on the top of a cart of mass M which rolls freely on the horizontal surface. If the system is released from rest, what x-directed force P must be applied to the cart to keep the hoop and semicylinder stationary with respect to the cart, and what is the resulting acceleration a of the cart? Motion takes place in the x-y plane. Neglect the mass of the cart wheels and any friction in the wheel bearings. What is the requirement on the coefficient of static friction between the hoop and cart?

Transcribed Image Text:

y m M P