A bucket of water with total mass 24.0 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 0.35 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 the cylinder turns on frictionless bearings,and that g = 9.8 m/s². ) A)1 600 N B)3.4 N C)34 N D)670 N E)4.1 N

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Quizplus · Accepted Answer

The minimum force required can be calculated using the principle of moments, where the force exerted by the weight of the bucket (mass times gravity) is balanced by the force applied at the end of the crank. The torque (moment of force) due to the weight of the bucket is the product of the weight (mass times gravity) and the radius of the cylinder, while the torque due to the applied force is the product of this force and the radius of the crank. Setting these two torques equal gives us the equation: $F_{applied} \times r_{crank} = m_{bucket} \times g \times r_{cylinder}$. Plugging in the given values: $F_{applied} \times 0.35 = 24 \times 9.8 \times 0.05$, solving for $F_{applied}$ gives approximately 34 N.

A Bucket of Water with Total Mass 24