The pipe bender consists of two grooved pulleys mounted and free to turn on a fixed frame. The pipe is bent into the shape shown by a force P=300N.Calculate the forces supported by the bearings of the pulleys.[/B]
The force equilibrium equations in two mutually perpendicular directions x- and y, i.e, ∑Fx=0 and ∑Fy=0 (treating the problem as two-
The moment equilibrium equation about any point O on or off the body i.e,[/B] ∑MO=0.
3. The Attempt at a Solution
My confusion is whether to neglect the frictional forces on the pipe by the two pulleys which is essential to drive the pipe between the pulleys.If we consider the frictional forces between the pulleys A and B and the pipe surface then the problem becomes statically indeterminate as we would have four unknowns which are,NA and NB - the normal reactions by pulleys A and B on the pipe and FA and FB - the frictional forces exerted by the pulleys A and B on the pipe with only three independent equations of equilibrium in hand.
On the other hand if we neglect the frictional forces assuming the pipe and pulley surfaces to be perfectly smooth we would have only two unknowns and the problem can be solved theoretically.But again we need to resolve the force P into components along and perpendicular to the pipe axis(the portion of pipe between the pulleys) for writing the force equilibrium equations.So I need to calculate the angle between the line of action of P and the pipe axis which I am unable to do with the given data in hand.
Can someone help?