# A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 8.0- cm radius. A dumbbell-shaped "flywheel" made from two 0.500- kg masses is attached to one end of the shaft and perpendicular to its axis (see the figure). The mass is released from rest and allowed to fall 0.9 m to the floor. It reaches a speed of 1.4361 m/s just before striking the floor. How far apart are the masses of the dumbbell?

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A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 8.0- cm radius. A dumbbell-shaped "flywheel" made from two 0.500- kg masses is attached to one end of the shaft and perpendicular to its axis (see the figure). The mass is released from rest and allowed to fall 0.9 m to the floor. It reaches a speed of 1.4361 m/s just before striking the floor. How far apart are the masses of the dumbbell?

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Step 1

The total energy of the sytem must be conserved. The initial energy of the sytem is equal to the potential energy of the mass attached to the string. The final energy of the sytem is equal to the sum of the translational kinetic energy and the rotational kinetic energy of the system.The equation for the conservaton of energy can be written as,

Step 2

Put the expressions for moment of inertia and angular veloc...

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