# Need help with finding Work from given force and distance components

## Homework Statement

A force ~F = Fx ˆı+Fy ˆ acts on a particle that
undergoes a displacement of ~s = sx ˆı + sy ˆ
where Fx = 8 N, Fy = −4 N, sx = 5 m, and sy = 1 m.
Find the work done by the force on the
particle.

## Homework Equations

x^2 + y^2 = z^2
Work = (Force)(Distance)(cos(theta))

## The Attempt at a Solution

I found the magnitude of Force by squaring each component
F = (8)^2 + (-4)^2 = 8.9442N
I found the magnitude of Distance by squaring each component
F = (5)^2 + (1)^2 = 5.099m
I then created a triangle to find theta, using distance for my triangle sides.
tan(theta) = 1/5 so theta = inverse tan(1/5). I then got a theta of 11.310.
I plugged my force, distance and theta into the Work formula but I'm not getting the right answer.
W = (8.9442N)(5.099)(cos(11.310))
W = 44.721 Joules

## Homework Statement

Find the angle between ~F and ~s.

## The Attempt at a Solution

tiny-tim
Homework Helper
Welcome to PF!

Hi yang09! Welcome to PF! (have a theta: θ and try using the X2 and X2 tags just above the Reply box )
Work = (Force)(Distance)(cos(theta))

Work also = Force "dot" Distance, which is the easiest way to do it if you have the coordinates.

So what is (8,-4)·(5,1) ? Thanks for the tips but what do you mean by:
What is (8,-4)·(5,1) ?
Do you want me to multiply them together or what? Or are you asking me what they stand for because the 8 is the x-component of force, -4 is the y-component of force, 5 is the x-component of distance, and 1 is the y-component of distance.
I'm pretty sure my magnitude is right, but am I doing something wrong with my θ?

tiny-tim
Homework Helper
Hi yang09! Thanks for the tips but what do you mean by:
What is (8,-4)·(5,1) ?

I meant the "dot" product of two vectors (also called the "scalar product" or the "inner product"), where you multiply the components and then add.