Please solve this problem...also, please explain the reasoningbehind the evaluat

Question

Please solve this problem...also, please explain the reasoningbehind the evaluation of the problem.....thanks

A block of mass 0.72 kg is suspended by a string which is wrappedso that it is at a radius of 0.057 m from the center of a pulley.The moment of inertia of the pulley is 0.0040kg·m2. There is friction as the pulley turns. Theblock starts from rest, and its speed after it has traveleddownwards a distance of D= 0.77 m, is 1.397 m/s. Calculate theamount of energy dissipated up to that point.

Explanation / Answer

m = 0.72 kg,R = 0.057 m, I = 0.0040 kg·m2. D= 0.77 m, v =1.397 m/s. Calculate the amount of energy dissipated up to thatpoint. initial energy E = mgD final energy E' = mv2/2 + I2/2 =mv2/2 + I(v/R)2/2 = mv2*(1 +I/R2)/2 the amount of energy dissipated upto that point = E - E' = mgD - [mv2*(1 +I/R2)/2] = 3.87 J

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