A uniform solid cylinder and a uniform solid sphere each have mass and radius
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A uniform solid cylinder and a uniform solid sphere each have mass 1.5kg and radius 0.08m. They are released from rest side by side at the top of a 6.0m long incline that is at 15∘ to the horizontal. Both objects roll without slipping and air resistance is negligible.
(a) Determine the magnitude of the linear acceleration for each object as they move down the incline.
(b) Calculate the time it takes each object to reach the bottom and then determine by how much time one object wins the “race.”
(c) When the objects reach the bottom, they continue rolling on a horizontal surface. For each object, calculate the rotational kinetic energy as a percentage of its total kinetic energy at that instant.
(d) If both objects then roll up a second 10∘ incline without slipping and without energy losses other than conversion between translational and rotational forms, determine which object climbs to a greater vertical height before momentarily coming to rest and justify your answer quantitatively.