Force vector - Value and uncertainty for components

[mybrohshi5]

Homework Statement

A force in polar coordinates is given by F1 = 50±2 N at the angle 30±2 degrees.

Find the value and uncertainty for F_x and F_y

Since force is a vector, there will be an error in both its magnitude and direction...

angle calculations must be in RADIANS...

$30\frac{+}{}2 degrees = \frac{\pi}{6} \frac{+}{} \frac{\pi}{90}<br />$

Homework Equations

F_x = F cos(θ)
F_y = F sin(θ)

The Attempt at a Solution

F_x is a function of both F and θ so i took the derivative of F_x = F cos(θ) using the chain rule.

$<br /> F_{x-error} = cos(\theta)\frac{dF_x}{dF} - F(sin(\theta))\frac{dF_x}{d\theta}<br />$

I did the same for F_y

$<br /> F_{y-error}= sin(\theta)\frac{dF_y}{dF} + F(cos(\theta))\frac{dF_y}{d\theta}<br />$Can i please get some help with what to do next. I am a little lost and confused :(

Thanks for any help :)

 

[mybrohshi5]

Can anyone suggest anything for this?

I know it deals with partial derivatives and everything, I am just not exactly sure about all that stuff and what to do for this question and my professor sure as heck doesn't explain it at all :(