a 1.5 kg block is hanging from the left side of a pulley from a rope that goes o

Question

a 1.5 kg block is hanging from the left side of a pulley from a rope that goes over the pulley. the pulley has a radius of 25 cm and is 2.5 kg. the pulley has no friction 15.5 N tension is applied to the other end of the rope. someone is holding the pulley from rotating once they let go of the pulley: A: what direction does the pulley rotate? towards the 15 kg block or the opposite direction? B;what is the angular acceleration of the pulley? C;what is the acceleration of the mass? D;How long does it take the mass to move 30 cm?

Explanation / Answer

part(a)

In the opposite direction

part B

for hanging mass

T1 - m*g = m*a

T1 = mg + ma

T1 = mg + mR*alpha

for the pulley

net torque = I*alpha

(T2 - T1 )*R = (1/2)*M*R^2*alpha

T2 - mg - mR*alpha = (1/2)*M*R*alpha

15.5 - 1.5*9.8 - 1.5*0.25*alpha = (1/2)*2.5*0.25*alpha

alpha = 1.164 rad/s^2   <<<<----------ANSWER

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(C)

acceleration a = R*alpha = 0.25*1.164 = 0.291 m/s^2

=====================

D)

along vertical

y = voy *t + (1/2)8ay*t^2

0.3 = 0 + (1/2)*0.291*t^2

tiem t = 1.44 s <<<-------ANSWER

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