Pulley Mechanics
A small bead of mass and a rod of length and mass are initially at rest, with the bead at the lowest point of the rod, being able to move along the string. When the system is released, there is a friction between the bead and the string and both travel with constant accelerations.
If and the bead is level with the top of the rod after second, find the magnitude of the friction force (in Newtons).
Details and Assumptions:
- The masses of the pulley and the string are both negligible.
- There is no friction in the pulley.
- Take
The answer is 40.
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1 solution
The only forces acting on the right-hand piece of string are the tension T in the string and the friction force F between the string and the bead. Since the string is light, T = F .
The equation of motion for the rod is therefore M g − F = M a where a is the downwards acceleration of the rod. The equation of motion for the bead is m g − F = m b where b is the downwards acceleration of the bead. Since the downwards acceleration of the rod with respect to the bead is a − b , we also have that L = 2 1 ( a − b ) t 2 Solving these equations for F , we obtain F = t 2 ( M − m ) 2 M m L For the given values of the parameters, the magnitude of the frictional force is thus 4 0 N. Note that the value of F is independent of the value of g .