(a) Use energy methods to predict the speed ofthe block after it has moved to a

Question

(a) Use energy methods to predict the speed ofthe block after it has moved to a second photogate 0.700 maway.
1 m/s

(b) Find the angular speed of the pulley at the same moment.
2 rad/s
The answers I am getting are incorrect by 10-100%, pleasehelp In the figure below, the sliding block has a mass of 0.850 kg, thecounterweight has a mass of 0.420 kg, and the pulley is a uniformsolid cylinder with a mass of 0.350 kg and an outer radius of0.0320 m. The coefficient of kineticfriction between the block and the horizontal surface is0.290. The pulley turns withoutfriction on its axle. The light cord does not stretch and does notslip on the pulley. The block has a velocity of 0.835 m/s toward the pulley when it passes througha photo-gate. (a) Use energy methods to predict the speed ofthe block after it has moved to a second photogate 0.700 maway. 1 m/s (b) Find the angular speed of the pulley at the same moment. 2 rad/s The answers I am getting are incorrect by 10-100%, pleasehelp

Explanation / Answer

M = 0.850 kg, M' = 0.420 kg, m = 0.350 kg, r = 0.0320 m. = 0.290. v = 0.835 m/s,d = 0.700 m a) find v' initial energy = (M + M')v2/2 + I2/2 +M'gd = (M + M')v2/2 +(mr2/2)(v/r)2/2 + M'gd = (M + M' + m/2)v2/2 + M'gd final energy = (M + M' + m/2)v'2/2 work done by friction W = -Mgd so -Mgd = (M + M' + m/2)v'2/2 - [(M + M' +m/2)v2/2 + M'gd] v' = [v2 + 2gd(M' - M)/(M + M' +m/2)] = 1.53 m/s b) = v'/r = 47.85 rad/s

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