11/14/2017 Name Section TEST 3 AU\'17 PHYSICS 4A 5. (22 POINTS) A 1.000-kg block

Question

11/14/2017 Name Section TEST 3 AU'17 PHYSICS 4A 5. (22 POINTS) A 1.000-kg block hangs vertically at the end of a string wrapped around a pulley of radius R 0.250 m and mass M = 2.000-kg shaped in the form of a solid cylinder. Thus, the pulley has l = ½MR2 about the stationary axis of rotation through the center. The vertically hanging block and pulley are shown at the start of the motion when they are released from rest. The block is released from a height h above the ground and reaches the ground with linear speed v = 3.00 m/s. What is the height h of the block when the motion begins? 4.5 1 kg

Explanation / Answer

Using law of conservation of energy

Energy at height h = energy at the ground

m*g*h = (0.5*m*v^2)+(0.5*I*w^2)

I is the moemnt of inertia of the pulley = 0.5*M*R^2

w is the angular speed of the pulley = V/R

but given that V = 3 m/s

then

m*g*h =(0.5*m*V^2)+(0.5*0.5*M*R^2*(V/R)^2)

1*9.8*h = (0.5*1*3^2)+(0.5*0.5*2*3^2)

9.8*h =9

h = 9/9.8 = 0.92 m

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