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 at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible,that cylinder turns on frictionless bearings,and that g = 9.8 m/s². ) A)45 N B)68 N C)90 N D)135 N

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Quizplus · Accepted Answer

The torque required to raise the bucket is equal to the weight of the bucket times the radius of the cylinder. The force required to turn the crank is equal to the torque divided by the turning radius of the crank.$$	au = Fr$$$$F = \frac{	au}{r} = \frac{mgr}{r_c}$$$$F = \frac{(23 	ext{ kg})(9.8 	ext{ m/s}^2)(0.050 	ext{ m})}{0.25 	ext{ m}} = 45 	ext{ N}$$

A Bucket of Water with Total Mass 23 Kg Is