A wheel of radius R = 29.1 cm, mass M = 2.72 kg, and moment of inertia I is moun

Question

A wheel of radius R = 29.1 cm, mass M = 2.72 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 = 0.774 kg.

HINTS GETTING STARTED I M STUCK MASTER IT Suppose the wheel is rotated at a constant rate so that the mass has an upward speed of 4.52 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

Torque acting on wheel due to tension is T = R*F = I*alpha

R = 29.1 cm = 0.291 m

F is the tension in the string

I is the moment of inertia = (M*R^2) = (2.72*0.291^2) = 0.23 Kg-m^2

alpha is the angular accelaration = a/R

using kinematic equations

intial speed is Vo = 0 m/sec

Final speed is V = 4.52

accelaration is a = ?

using V^2 = 2*a*S

a = V^2/(2*S) = 4.52^2/(2*h)

then I*alpha = R*T

0.23*(a/R) = R*(mg+ma)

0.23*(a/0.291) = 0.291*0.774*(a+9.8)

a = 3.9 m/s^2

then

a = 4.52^2/(2*h) = 3.9

h = 2.62 m

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