# How much work is done on a bucket when pulling it up?

• BlueQuark
In summary: It happens sometimes.In summary, the problem involves a 6.75 kg bucket hanging in a well, with a rope passing over a frictionless pulley. The bucket is raised a distance of 4.00m by pulling on the rope horizontally. Using the equations ##W = FS## and ##ΣFy = T - mg##, the work done on the bucket is calculated to be 264.84 J. This is the correct answer, despite the answer key stating 3.60 J.
BlueQuark

## Homework Statement

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 4.00m.
A). How much work do you do on the bucket in pulling it up?

##W = FS##
##W = ΔKE##
##ΣFy = T - mg##

## The Attempt at a Solution

First, I assumed the problem was implying that the bucket was in equilibrium when it said it was moving slowly. So since the weight is ##(9.81)(6.75) = 66.21 N##, the tension force must be equal to that.

So, ##W = FS##. ##W = (66.21)(4) = 264.84 J##. This seemed like the correct answer to me, but when I look at the back of the book, it says the answer is 3.60 J.

Where did I go wrong here? Thanks!

Doc Al said:
That's what I thought too. It's from "Sears and zemansky's University Physics With Modern Physics, 12th edition".

I guess there was a mistake or something in the answer key.

BlueQuark said:
I guess there was a mistake or something in the answer key.
Yep.

## What is work done on a bucket?

Work done on a bucket refers to the amount of energy required to move a bucket from one location to another. It takes into account the weight of the bucket, the distance it is moved, and the force applied to move it.

## How is work calculated on a bucket?

Work done on a bucket can be calculated using the formula W = F x d, where W is work, F is the force applied, and d is the distance the bucket is moved. This calculation assumes that the force and distance are in the same direction.

## Does the angle of the force affect the work done on a bucket?

Yes, the angle of the force can affect the work done on a bucket. When the force is applied at an angle to the direction of movement, the calculation becomes W = F x d x cos(theta), where theta is the angle between the force and the distance. This means that the work done will be less than if the force was directly in line with the movement.

## What is the unit of measurement for work done on a bucket?

The unit of measurement for work done is joules (J). This unit is derived from the basic units of force (newtons) and distance (meters). One joule is equivalent to one newton-meter.

## Can the work done on a bucket be negative?

Yes, the work done on a bucket can be negative. This occurs when the force applied is in the opposite direction of the movement, resulting in a decrease in energy. For example, if a person lifts a bucket and then sets it back down, the work done on the bucket is negative.

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