What is the work done on the bucket in a frictionless pulley problem?

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In a frictionless pulley scenario, the work done on the bucket is calculated by considering the force applied and the distance moved. The mass of the bucket is 6.75 kg, and it is raised a distance of 4.00 m. The gravitational force acting on the bucket is 66.15 N (6.75 kg multiplied by 9.81 m/s²). The work done is the product of this force and the distance, resulting in 264.6 joules. Therefore, the work done on the bucket in pulling it up is 264.6 joules.
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An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise the bucket slowly a distance of 4.00 m.

How much work do you do on the bucket in pulling it up?
 
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