A person pulls a bucket of water up from a well with a rope. Assume the initial

Question

A person pulls a bucket of water up from a well with a rope. Assume the initial and final speeds of the bucket are zero (v_i=v_f=0), and that the person lifted the bucket a vertical distance h. By looking at energy changes in the bucket-Earth physical system, we can make sense of the force the person must exert to pull the bucket up and the amount of work the person does. Think about whether this is an open or closed system. What energy systems undergo a change in energy during the process? Construct a particular energy-system diagram for this process and include the algebric expression of energy conservation (in terms of Delta E's and if open, any Heat or Work). Substitute the algebric expression we use for the change in gravitational potential energy and solve for the work done by the person on the rope/bucket. Use the definition of work in terms of force and distance (refer to the Energy-Interaction Model Summary) to find the average force exerted by the person on the rope and bucket while they are lifting it up.

Explanation / Answer

We look at the initial and ending energy states:
Initial energy of the bucket and water = 0
Final energy of the bucket and water =
Potential energy = mass * height * g
= massOfBucketWater * h * 9.81 N/kg

That increase in energy is the amount of work done by the person (Wp). Average force can be calculated as follows:

Work = F * distance
Wp = Favg * height
Favg = Wp/h = massofBucketWater * 9.81 N/kg or rather simply, the weight of the bucket.

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