# Calculating work done

## Homework Statement

A carpenter is holding two tool boxes of mass 19kg and 21kg respectively. Calculate the work done to carry the tool boxes through a horizontal distance of 16m.

W = mgh

## The Attempt at a Solution

m = 21kg + 19kg
g = 9.81ms^-2
h = 0

W = (21 + 19)(9.81)(0)
W = 0J

Is this correct? And if this is correct, would you explain why it is 0J?

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NascentOxygen
Staff Emeritus
The formula for work involves the dot product of two vectors.

W = F . s

Does this give you a hint?

Last edited:
HallsofIvy
Homework Helper
In order to do work, you must move an object with mass in the direction of a force vector.

So if I use W = F . s, then it would be

W = (19 + 21)(9.81)(16) ?
Or is it,
W = (19 + 21)(9.81)(16) cos 90 ?

NascentOxygen
Staff Emeritus
So if I use W = F . s, then it would be

W = (19 + 21)(9.81)(16) ?
Or is it,
W = (19 + 21)(9.81)(16) cos 90 ?
this ^^^

Instead of writing the vector formula, it is often expressed as W = F s cosθ
and that's probably the best one to memorise.

NascentOxygen, would you tell me why the angle is 90? Shouldnt it be 0? And how about if I use sin 0? I will still get 0J.

NascentOxygen
Staff Emeritus