An old country family uses a well as their primary water source. The bucket, when filled with water, is hand lifted by a rope from the bottom of the well to the surface. The well is 60 ft deep and the rope weighs 21 lb when extended to the bottom. The bucket weighs 70 lb when filled with water, but oh no! It leaks at a constant rate and only weighs 28 lb at the surface. Recall that water is 62.5 lb/ft^3. a) How much total work is done to lift the bucket to the surface? b) As the years pass, the family replaces the leaky bucket with a new one and has a mechanical winch installed to lift the bucket by a cable. The cable weighs 15 lb when extended to the bottom. Although the winch/cable method is far more effective, the family still keeps the rope installed as a back up. So, when the bucket is lifted to the surface only the rope's lower end, still attached to the bucket, reaches the surface. Of course, the entire cable reaches the surface along with the still full bucket of water. How much total work is done to lift the bucket now?
An old country family uses a well as their primary water source. The bucket, when filled with water, is hand lifted by a rope from the bottom of the well to the surface. The well is 60 ft deep and the rope weighs 21 lb when extended to the bottom. The bucket weighs 70 lb when filled with water, but oh no! It leaks at a constant rate and only weighs 28 lb at the surface. Recall that water is 62.5 lb/ft^3.
a) How much total work is done to lift the bucket to the surface?
b) As the years pass, the family replaces the leaky bucket with a new one and has a mechanical winch installed to lift the bucket by a cable. The cable weighs 15 lb when extended to the bottom. Although the winch/cable method is far more effective, the family still keeps the rope installed as a back up. So, when the bucket is lifted to the surface only the rope's lower end, still attached to the bucket, reaches the surface. Of course, the entire cable reaches the surface along with the still full bucket of water.
How much total work is done to lift the bucket now?
Trending now
This is a popular solution!
Step by step
Solved in 10 steps with 12 images
