posted by Lee .
The pulley has an inner radius of 0.35m and an outer radius of 0.65m. It has a mass of 1.8kg. A string wrapped around the inner part of the pulley is fastened to the ceiling. A second string wrapped around the outer part of the pulley is fastened to a block. Determine the mass of the block if the pulley remains at rest.
Please do show you did it and which formula did you use. Thanks very much.
The string attached to the ceiling supports the pulley and the block.
The tension of this string is T = (1.8 + m) •g,
the torque of this force is
T•r =(1.8 + m) •g•r.
The torque created by the block
is m•g•R .
The condition for equilibrium:
the net torque is zero.
(1.8 + m) •g•r = m•g•R,
m = 1.8•r/(R-r) =
= 1.8•0.35/(0.65 – 0.35) = 2.1 kg