A block of mass 0.84 kg issuspended by a string which is wrapped so that it is a

Question

A block of mass 0.84 kg issuspended by a string which is wrapped so that it is at a radius of0.060 m from the center of a pulley. The moment of inertia of thepulley is 0.0040 kg·m2. There is friction as thepulley turns. The block starts from rest, and its speed after ithas traveled downwards a distance of D= 0.75 m, is 1.592 m/s.Calculate the amount of energy dissipated up to thatpoint. A block of mass 0.84 kg issuspended by a string which is wrapped so that it is at a radius of0.060 m from the center of a pulley. The moment of inertia of thepulley is 0.0040 kg·m2. There is friction as thepulley turns. The block starts from rest, and its speed after ithas traveled downwards a distance of D= 0.75 m, is 1.592 m/s.Calculate the amount of energy dissipated up to thatpoint.

Explanation / Answer

m = 0.84kg, R = 0.06 m, I = 0.0040 kg·m2. D= 0.75 m, v = 1.592 m/s. initial energy E = mgD final energy E' = mv2/2 + I2/2                  = mv2/2 + I(v/R)2/2                = mv2*(1 + I/R2)/2 amount of energy dissipated up tothat point = E - E' = ___ J

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