A hemisphere of radius R and mass M, curved side down, is pulled along a plane at a constant velocity by
means of a horizontal force F. The coefficient of sliding friction is mu. Find the the angle at which the hemisphere
is inclined as it is pulled. C.M. of the hemisphere is at a distance 3R/8 from it's flat surface. The force applied is
at the equator of the hemisphere.
Sum of the forces = ma =0
Sum of the Torques = Iw =0 (possibly)
The Attempt at a Solution
I determined a force diagram with the standard normal force equal to weight and Ff equal to the force applied.
Then we determined to use sum of the torques being equal to zero. Problem is is that we have all but the applied force
at the axis of rotation so it is equal to zero and we have the rotational normal force and rotational force of gravity canceling out with the
friction force being equal to zero if you set the axis of rotation at point of applied force.
Are the sum of the torques equal to zero?
Are the torques placed in the right position?
Should we use torques at all?
Any suggestions would help immensely.