Need help with finding Work from given force and distance components

[yang09]

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.
Answer in units of J.

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

THIS IS NOT THE RIGHT ANSWER. WHAT AM I DOING WRONG. PLEASE HELP ME.

Homework Statement

Find the angle between ~F and ~s.
Answer in units of ◦.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

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) ?

 

[yang09]

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]

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.

Have you learned about that?

… am I doing something wrong with my θ?

Yes, your θ is tan^-1(1/5), but that is the angle between (5,1) and the x-axis: you need the angle between (5,1) and (8,-4).