The reel shown in the figure below has radius R and moment of inertia I. One end
ID: 1453236 • Letter: T
Question
The reel shown in the figure below has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its unstretched position and the reel is then released from rest. Find the angular speed of the reel when the spring is again unstretched. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity, and .)
w = _______
Explanation / Answer
Using work energy theorem,
work done by spring + work done by gravity = change in KE
(k d^2 /2 ) + (m g d sin@) = [ m v^2 /2 + Iw^2 /2 ]
d(Kd + 2 mg sin@ ) = m (w R)^2 + I w^2
w^2 ( m R^2 + I ) = d(Kd + 2 mg sin@ )
w = sqrt[ d(Kd + 2 mg sin@ ) / ( m R^2 + I )]
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