A piece of putty is initially located at point A on therim of a grinding wheel r

Question

A piece of putty is initially located at point A on therim of a grinding wheel rotating about a horizontal axis. The puttyis dislodged from point A when the diameter throughA is horizontal. The putty then rises vertically andreturns to A the instant the wheel completes onerevolution. (a) Find the speed of a point on the rim of thewheel in terms of the acceleration due to gravity and the radiusR of the wheel. (Use m, and g as necessary.)
v =
(b) If the mass of the putty is m, what is the magnitudeof the force that held it to the wheel? (Use m, and g asnecessary.)
F = (a) Find the speed of a point on the rim of thewheel in terms of the acceleration due to gravity and the radiusR of the wheel. (Use m, and g as necessary.)
v =

Explanation / Answer

The speed of the rim of the wheel is the same as the speed atwhich the putty is launched. The time it takes the putty to riseand return is given by: .            t = 2 v / g . And the time it takes the wheel to turn is... .           time = distance /speed           t = 2R / v . Set them equal and solve for v: .                   2R / v = 2 v /g           v2 = R g . or             v = ( R g )1/2 . The magnitude of the force is given by: .           F = m v2 / R = m   R g /R   =     m g

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