an 8 kg weight is attached to a 6kg weight over a pulley. the pulley is a uniform disk with a moment of inertia I= 2Kg m^2 and a radius R=.4m. the block starts from rest, and after the 8kg block has fallen a distance h, it is observed to be traveling at 3m/s.
what is the mass of the pulley?
what is the mass of the pulley?
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By I = 1/2mr^2
=>2 = 1/2 x m x (0.4)^2
=>m = 25 kg
=>By the law of enerrgy conservation:-
=>PE(loss) in 8 kg mass = KE(gain) by pully + PE(gain) by 6 kg
=>Mgh = 1/2Iω^2 + mgh
=>1/2Iω^2 = (M-m)gh
=>1/2 x 2 x (v/r)^2 = (8-6) x 9.8 x h
=>1/2 x 2 x (3/0.4)^2 = 2 x 9.8 x h
=>h = 2.87 m
=>2 = 1/2 x m x (0.4)^2
=>m = 25 kg
=>By the law of enerrgy conservation:-
=>PE(loss) in 8 kg mass = KE(gain) by pully + PE(gain) by 6 kg
=>Mgh = 1/2Iω^2 + mgh
=>1/2Iω^2 = (M-m)gh
=>1/2 x 2 x (v/r)^2 = (8-6) x 9.8 x h
=>1/2 x 2 x (3/0.4)^2 = 2 x 9.8 x h
=>h = 2.87 m