5. A 16 kg block is attached to a cord that is wrapped aroundthe rim of a flywhe

Question

5. A 16 kg block is attached to a cord that is wrapped aroundthe rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertiaof the flywheel is 0.50 kg m2. When the block is released and the cord unwinds, theacceleration of the block is: A) 0.15 g B) 0.56 g C) 0.84 g D) g E) 1.3 g 5. A 16 kg block is attached to a cord that is wrapped aroundthe rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertiaof the flywheel is 0.50 kg m2. When the block is released and the cord unwinds, theacceleration of the block is: A) 0.15 g B) 0.56 g C) 0.84 g D) g E) 1.3 g

Explanation / Answer

the kinetic energy is equal to the rotational kinetic energyof the flywheel therefore (1/2) * m * v^2 = (1/2) * I * w^2 or w^2 = (m * v^2/I) or w^2 = [m * (2g * r)/(m * r^2)] = (2g/r) the acceleration of the block is a = (v^2/r) = (r^2 * w^2/r) = r * w^2 = r * (2g/r) = 2g

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