Calculating Tension in a Flywheel Drive Belt

[chevyboy86]

An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley of the flywheel. The flywheel has a mass of 80 kg and a diameter of 1.25m. Its pulley has a much smaller mass and a radius of .230m. the tension in the upper (taut) part of the belt is 135N and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find tension in lower belt.

The answer is 21.5N but I can't figure out the equations to get the answer.

 

[berkeman]

The difference in tension between the upper and lower belts will provide the net torque that causes the clockwis angular acceleration. Draw a drawing of the forces and radii, etc., and see where you get to...

 

[kyle8921]

I can confirm that the answer of 21.5N is correct. To calculate the tension in the lower belt, we can use the equation T = Iα/r, where T is the tension, I is the moment of inertia, α is the angular acceleration, and r is the radius of the pulley.

First, we need to calculate the moment of inertia of the flywheel, which is given by the equation I = 1/2mr^2. Plugging in the values, we get I = 1/2 * 80 kg * (1.25m)^2 = 62.5 kgm^2.

Next, we can use the given angular acceleration of 1.67 rad/s^2 and the radius of the pulley of 0.230m to calculate the tension in the upper belt. Using the equation T = Iα/r, we get T = (62.5 kgm^2) * (1.67 rad/s^2) / (0.230m) = 454.3 N.

Since the upper part of the belt has a tension of 135N, we can use the equation T = Tupper + Tlower to find the tension in the lower belt. Rearranging the equation, we get Tlower = T - Tupper. Plugging in the values, we get Tlower = 454.3 N - 135 N = 319.3 N.

Therefore, the tension in the lower belt is 319.3 N, which is equivalent to 21.5 N.