A bucket begins weighing 15 pounds, including the sand it holds. The bucket is to be lifted to the top of a 35 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.3 pounds of sand each foot it is lifted. Find the work done lifting the bucket to the top of the building.

The work done lifting the bucket to the top of the building is 341.25 lbf-ft.

Explanation:

Given that bucket is part of a variable-mass system due to sand losses and such work, measured in is associated to gravitational potential energy by Work-Energy Theorem, the work done by lifting the bucket is represented by the following integral:

Where:

- Mass of the bucket as a function of height, measured in pounds.

- Gravitational constant, measured in feet per square second. ()

- lb-f to lb-m conversion factor, measured in lb-m to lb-f. ()

Since leaking is constant, the mass of the bucket can be modelled by using a first-order polynomial (linear function), that is:

Where:

- Initial mass of the bucket, measured in pounds.

- Leaking rate, measured in pounds per feet.

- Height of the bucket with respect to bottom, measured in feet.

After replacing the mass and simplifying the integral, the following expression for work is found:

If , , , and , the work done lifting the bucket to the top of the building is:

The work done lifting the bucket to the top of the building is 341.25 lbf-ft.

potential energy is directly proportional to height.

more height = more potential energy.

greatest increase in height = greatest increase in potential energy

where are the points with the greatest increase in height ?

has to be c-e or d-e .