An electric motor turns a flywheel through a drive belt that joins a pulley on t

Question

An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel as shown in the figure below. The flywheel is a solid disk with a mass of 74.0 kg and a radius

R = 0.625 m. It turns on a frictionless axle. Its pulley has much smaller mass and a radius of 0.230 m. The tension Tu in the upper (taut) segment of the belt is 172 N, and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find the tension in the lower (slack) segment of the belt.

Answer: _________ N

Explanation / Answer

torque about pulley = torque about flywheel
Tensile force x radius of pulley = moment of inertia of flywheel x angular acceleration
(Tu -Tl) x radius= 0.5 x mass of flywheel x square of radius of flywheel x angular acceleration

Tu=tenssion in upper side means tight side

Tl=tension in lower side means slck side

(172-Tl )x0.23= 0.5x 74x 0.6252x 1.67

Tl= 67.0577N

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