A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass

Question

A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 4.0- 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 1.2 m to the floor. It reaches a speed of 1.1768 m/s just before striking the floor. How far apart are the masses of the dumbbell?

1.0-kg mass is attached to a string wrapped around a shaft of negligible mass and having a 5.0 cm radius. A dumbbess-shaped "flywheel" made from two 0.500kg 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 0.8 m to the floor. It reaches a speed of 1.3325 m/s just before striking the floor. How far apart are the masses of the dumbbell?

Explanation / Answer

W=V/r =1.1768/(4*10^-2)

W=29.42 rad/s

By conservation of energy

m2gh =(1/2)m2V^2 +(1/2)IW^2

where I=2m1*R^2

m2*g*h =(1/2)*m2*V^2 +(1/2)*2m1*R^2*W^2

m2*g*h =(1/2)*m2*V^2 +R^2*m1*V^2

1*9.8*1.2 =(1/2)*1*1.1768^2 +0.5*29.42^2*R^2

R=0.16 m

distance between dumbles

D=2R=0.32 m

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