# Determine whether work is scalar or vector.

1. Oct 8, 2006

### alias25

right the question im finding tricky is:

by considering a body doing work against gravity, moving up a hill, determine whether work done is scalar or vector?
(2 mark question)

so i've draw like a triangle an arrow for force at an angle theta form the horizontal which has an arrow along for displacement d.
so i do d.F.cos theta = work.
but how does that justify that work is a scalar? im completly lost.

2. Oct 8, 2006

The definition of work done by a force $$\vec{F}$$ from points 1 to 2 is $$\int_{1}^2\vec{F}\cdot d\vec{r}$$, which shows that work is a scalar. (The scalar product of two vectors is a scalar.)

3. Oct 8, 2006

### alias25

should i just say...
since f and r are along same plane theta between the 2 vectors = 0
so using equation:
A.B = mod (A).mod(B) cos theta
cos theta = 1 (because theta = 0)
so u get
F.r = mod(F).mod(r) = work
so work is the product of the magnitudes of both F an r which gives a scalar product?
I draw a hill facing other direction to show that work is independant of direction?

4. Oct 8, 2006

### arildno

Look at the DEFINITION, for God's sake!
there isn't anything more to the answer to the question than that you know the difference between vectors and scalars, along with the definition of work.

5. Oct 8, 2006

### Office_Shredder

Staff Emeritus
alias, define scalar and vector. Then we'll be in business