A wheel of radius R = 25.4 cm, mass M = 2.77 kg, and moment of inertia I is moun

Question

A wheel of radius R = 25.4 cm, mass M = 2.77 kg, and moment of inertia I is mounted on a frictionless, horizontal axle as in the figure. A light cord wrapped around the wheel supports an object of mass m = 0.636 kg. Calculate the angular acceleration of the wheel, the linear acceleration of the object, and the tension in the cord.

Solved and got these values right.

Tension= 4.27 N

a= 3.09 m/s^2

Angular acc. = 12.2 rad/s^2

Suppose the wheel is rotated at a constant rate so that the mass has an upward speed of 4.07 m/s when it reaches a point P. At that moment, the wheel is released to rotate on its own. It starts slowing down and eventually reverses its direction due to the downward tension of the cord. What is the maximum height, h, the mass will rise above the point P?
h = m ???

Explanation / Answer

total accleration of the bloack downwards = 3.09 m/s^2

=> total force downwards = 0.636*3.09 = 1.96524 N

work done by this force = change in KE

=> -h*1.96524 = 0 - 0.5*0.636*(4.07)^2

=> h = 0.5*0.636*4.07*4.07/1.96524

=> h = 2.68 m

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