A 30 kg block is being hoisted with a pulley that has two radii. The block is li

Question

A 30 kg block is being hoisted

with a pulley that has two radii. The block is lifted

by rope that wraps around a small hub with radius

r = 0.20 m, while someone pulls a second rope

with an applied force, Fapp, that is wrapped around

a larger pulley of radius R=0.50 m. The applied

force is Fapp =140 N, and the resulting acceleration

of the 30 kg block is 0.8 m/s/s upwards. The

pulley rotates frictionlessly about its central axis.

(a-5) What is the angular acceleration of the

pulley?

(b-3) What is the torque about the central axis provided by the applied force, Fapp ?

(c-5) Find the tension in the rope connected to the block, and use that to determine the torque

on the pulley due to that rope.

A 30 kg block is being hoisted with a pulley that has two radii. The block is lifted by rope that wraps around a small hub with radius r = 0.20 m, while someone pulls a second rope with an applied Force, Fapp, that is wrapped around a larger pulley of radius R=0.50 m. The applied force is Fapp =140 N, and the resulting acceleration of the 30 kg block is 0.8 m/s/s upwards. The pulley rotates frictionlessly about its central axis.

Explanation / Answer

1) angular acceleration = a/r= 0.8/0.2 = 4 rad/s^2

2) Torque= 140*0.5= 70 N-m

3) T=mg +ma = 30*(9.8+0.8)= 318 N

==> torque of Tension = 318*0.2 = 63.6 N-m

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