# Work of force not working out

• Jan 14th 2011, 11:45 AM
Work of force not working out
I have a question about work done by force:

If a 10N (newton) force acting in the direction of vector (1,1) moves an object from P =(-2,1) to Q=(5,6) calculate the work done. Distance measured in metres.

I did vector PQ
Q-P = (5,6) - (-2,1) = (7,5)
Absolute value PQ = sqrt7^2 + 5^2 = sqrt74

vector (1,1) is a 45 degree angle or 1/sqrt2

next, work = (force)(QP)(1/sqrt2)
10sqrt74(1/sqrt2)

Im getting 5sqrt148 but the correct answer is 60sqrt2
• Jan 14th 2011, 11:53 AM
Ackbeet
The problem is that work is actually equal to the dot product of force with displacement. That is,

$\displaystyle W=\mathbf{F}\cdot\mathbf{d}=\left(\dfrac{10}{\sqrt {2}}\langle 1,1\rangle\right)\cdot\langle 7,5\rangle=\dots$

What do you get when you do that?
• Jan 14th 2011, 12:00 PM
so i'd do the dot product of (10/sqrt2,10/sqrt2).(7,5)?

I got the answer doing that.
• Jan 14th 2011, 12:10 PM
Ackbeet
That'd work, too (pun intended).