A rope is wrapped around a wheel of diameter, 50cm. The wheelis mounted with a f

Question

A rope is wrapped around a wheel of diameter, 50cm. The wheelis mounted with a frictionless bearing on an axle through itscenter. A block of 15kg is suspended from the end of the rope. Whenthe system is released from rest the block falls 5.0m in2.0s. A. What is the linear acceleration of the falling block? B. What is the angular acceleration of the wheel, assuming therope doesn't slip on the wheel. C. What is the tension in the rope? D. What is the moment of inertia of the wheel? Note, thisshould be calculated from data in the problem and not from theformula for I of a disk or a hoop. A rope is wrapped around a wheel of diameter, 50cm. The wheelis mounted with a frictionless bearing on an axle through itscenter. A block of 15kg is suspended from the end of the rope. Whenthe system is released from rest the block falls 5.0m in2.0s. A. What is the linear acceleration of the falling block? B. What is the angular acceleration of the wheel, assuming therope doesn't slip on the wheel. C. What is the tension in the rope? D. What is the moment of inertia of the wheel? Note, thisshould be calculated from data in the problem and not from theformula for I of a disk or a hoop.

Explanation / Answer

A rope is wrapped around a wheel of diameter, 50cm. The wheelis mounted with a frictionless bearing on an axle through itscenter. A block of 15kg is suspended from the end of the rope. Whenthe system is released from rest the block falls 5.0m in2.0s. A. What is the linear acceleration of the falling block?
a=2g/3=19.6/3=6.5333m/sec2
B. What is the angular acceleration of the wheel, assuming therope doesn't slip on the wheel.
angularacceleration=a/r=6.533/.25=26.13rad/sec2
C. What is the tension in the rope?
T=mg/3=15*9.8/3=49N
D. What is the moment of inertia of the wheel? Note, thisshould be calculated from data in the problem and not from theformula for I of a disk or a hoop.
I=2Tr/=2*49*0.25/6.533=3.7501kgm2

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