A wheel of radius R = 27.9 cm, mass M = 2.47 kg, and moment of inertia I is moun

Question

A wheel of radius R = 27.9 cm, mass M = 2.47 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 = 0.651 kg. 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?

Explanation / Answer

process can be as with values as   R = 25.2 cm, mass M = 2.27 kg,  A light cord wrapped around the wheel supporting an object of mass m = 0.798 kg.

Tension = T

Torque = 0.252T

Moment of inertia = MR^2/2 = 2.27 x 0.252^2 / 2 = 0.07208 kgm^2

Angular acceleration, alpha = torque/ moment of inertia= 0.252T/0.07208 = 3.496T

First 'trick'

If w = angular velocity, speed of rim = v = wr.

Linear acceleration, a, of a point on the rim = dv/dt = (dw/dt)r = alpha.r

Linear acceleration of a point on the rim a = 3.496T x 0.252 = 0.881T

_______________________________________...

Second 'trick':

The linear acceleration of the hanging mass = linear acceleration of the rim (as cord doesn

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