A man pushes a plank of mass m₂ resting on a cylinder of mass m₁ as shown. There is no slipping at either contact and the horizontal applied force is F. Which option gives the correct complete set for cylinder-centre acceleration a꜀, plank acceleration aₚ, and the top/bottom friction forces?

Question

G1 Physics · Accepted Answer

Write translation for the cylinder and plank and rotation of the cylinder about its centre. The no-slip constraints at the upper and lower contacts relate acceleration of cylinder, acceleration of plank and α. Solving gives acceleration of cylinder=4F/(3m₁+8m₂), acceleration of plank=2acceleration of cylinder. The upper-contact friction is 3m₁F/(3m₁+8m₂) to the right and the lower-contact friction is m₁F/(3m₁+8m₂) to the right. Hence option D.