A bucket of water with total mass 23 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder,with crank,at the top of a well.The moment of inertia of the cylinder and crank is 0.12 kg*m².The bucket is raised to the top of the well and released to fall back into the well.What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s? A)2.1 x 10³J B)1.5 x 10³J C)0.70 x 10³J D)0.40 x 10³J

Question

Quizplus · Accepted Answer

The kinetic energy of the cylinder and crank can be calculated using the rotational kinetic energy formula: $ KE = \frac{1}{2} I \omega^2 $. The angular velocity $ \omega $ is related to the linear speed $ v $ by $ \omega = \frac{v}{r} $. Substituting the given values, $ I = 0.12 \, \text{kg} \cdot \text{m}^2 $, $ v = 8.0 \, \text{m/s} $, and $ r = 0.050 \, \text{m} $, we find $ \omega = \frac{8.0}{0.050} = 160 \, \text{rad/s} $. Thus, $ KE = \frac{1}{2} \times 0.12 \times (160)^2 = 1.5 \times 10^3 \, \text{J} $.

A Bucket of Water with Total Mass 23 Kg Is