Calculating Work: 6.75kg Bucket Raised 4m

[zrbecker]

Homework Statement

An old oaken buck 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 4.00m. (a) How much work do you do on the bucket in pulling it up? (b) How much work does gravity do on the bucket? (c) What is the total work done on the bucket?

Homework Equations

W = Fscos(phi)

The Attempt at a Solution

For (b) my solution was

F = mg = 6.75 * 9.81
s = 4.00
phi = 180 degrees (gravity pulls down, bucket moves up)

So W = 6.75 * 9.81 * 4.00 * -1 = -265 J

The book says it is -0.900 J

EDIT: Figured it out. Book is wrong. Found a solutions manual.

 

[anathema]

I can confirm that your solution for part (b) is correct. The work done by gravity on the bucket is indeed -265 J. It is important to note that the negative sign indicates that the work is done against gravity, as the bucket is moving in the opposite direction of the force of gravity.

I would recommend double checking the solutions manual you referenced to see if there may have been a mistake or typo in their answer. It is always important to double check and verify information, especially in the scientific community. Keep up the good work!