A block of mass 30.0 kg is lowered by a chain. Determine the work done by the chain if the block acquires a speed of 40.0 cm/s after dropping down a distance of 2.00 m . (Take g = 9.8 m/s ^2 )

Step-by-step solution

Given m = 30.0 kg , h = 2.00 m , v = 40.0 cm/s = 0.40 m/s , and u = 0 . According to the work-energy theorem, the net work done on the block is equal to its change in kinetic energy: W_ net = K W_ gravity + W_ chain = 1 2 mv^2 - 1 2 mu^2 The work done by gravity is: W_ gravity = mgh = 30.0 9.8 2.00 = 588.0 J The change in kinetic energy is: K = 1 2 30.0 (0.40)^2 = 15.0 0.16 = 2.4 J Substituting these values into the work-energy equation: 588.0 + W_ chain = 2.4 W_ chain = 2.4 - 588.0 = -585.6 J