# Calculation of work involving unit vectors

1. Nov 2, 2013

### bakakun028

1. The problem statement, all variables and given/known data

A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force f = (30N)i - (40N)j to the cart as it undergoes a displacement s = (-9.0m)i - (3.0m)j
How much work does the force you apply do on the grocery cart?

2. Relevant equations

3. The attempt at a solution

I was assuming all I needed to do was do F*d for the i unit vector and j unit vector like so:
W = (F*d)i + (F*d)j = (30*-9)i + (-40*-3)j = (-270J)i + (120J)j

But according to the answer book, the final work has no unit vectors involved and it is the sum of those two calculated works.

-270J + 120J = -150J

How come the unit vectors are not included in the answer? Also, how come we can simply sum up the x and y W's and works like that? I know it has something to do with work being a scalar...

2. Nov 2, 2013

### consciousness

Dot product gives you a scalar quantity. Also- i.i=1 not i.

3. Nov 2, 2013

### tiny-tim

hi bakakun028! welcome to pf!

yes, work done is always a scalar quantity (an ordinary number)