Rotational kinematics/dynamics problem

pppeachykeen

1. The problem statement, all variables and given/known data

A plank with mass M = 6 kg rides on top of two identical solid cylindrical rollers that have R = 0.05 m and m = 2 kg. The plank is pulled by a constant horizontal force F of magnitude 6 N applied to an endpoint of the plank and perpendicular to the axes of both cylinders. The cylinders roll without slipping on a horizontal surface and the plank does not slip on the cylinders either. Knowing that there must be rolling friction (not sliding friction) between the plank and the cylinders and between the cylinders and the surace, calculate:

(a)the linear acceleration of the plank and of the rollers
(b)the magnitudes of all friction forces that are acting.


2. Relevant equations
Not sure...

3. The attempt at a solution
I have no idea how to go about this...any help with starting would be appreciated.

OlderDan

Draw free body diagrams for each cylinder and one for the plank. Each cylinder has a horizontal frictional force acting at the top and bottom. The plank has three horizontal forces acting. All vertical forces are balanced and need not be considered (although that is an interesting problem too). Consider the relationship between the distances moved by the plank and the rollers, and the relationships between the angular and linear motion of the rollers.

You will have several equations relating the applied forces to the accelerations that can be solved simultaneously to find the forces and accelerations.