A solid sphere of mass and radius sits in the back of a truck
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid sphere of mass 0.80kg and radius 0.050m sits in the back of a truck. The truck’s bed is horizontal and sufficiently rough that the sphere can roll without slipping relative to the truck. The truck begins to accelerate in a straight line along the road. The moment of inertia of a solid sphere about its central axis is 52MR2. The coefficient of static friction between the sphere and the truck bed is μs=0.40.
(a) Analyze the forces acting on the sphere in an inertial reference frame fixed to Earth. Draw a free-body diagram and identify which force is responsible for the sphere’s horizontal acceleration.
(b) Using appropriate equations of motion, derive an inequality that relates the truck’s linear acceleration atruck to μs that must be satisfied to prevent slipping between the sphere and the truck bed.
(c) Determine the maximum value of atruck for which rolling without slipping can be maintained.
(d) Qualitatively discuss the subsequent motion of the sphere relative to the truck bed if the truck’s acceleration exceeds the value found in part (c).