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bawbag
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Homework Statement
A force of 500N is measured with a possible error of 1N. Its component in a direction 60° away from its line of action is required, where the angle is subject to an error of 0.5°. What (approximately) is the largest possible error in the component?
Homework Equations
The Attempt at a Solution
The component force is [tex] F_x = F cos \theta [/tex]
so [tex] lnF_x~=~lnF~+~lncos\theta[/tex]
applying differentials: [tex]\frac{dF_x}{F_x} = \frac{dF}{F} + \frac{d~cos\theta}{cos\theta} (-sin\theta) [/tex][tex] =\frac{dF}{F} + \frac{sin^{2} \theta}{cos\theta}d\theta[/tex]
plugging in values [tex] \frac{dF_x}{F_x} = \frac{1}{500} + \frac{3}{4} \frac{2}{1} \frac{1}{2} \frac{\pi}{180} = 0.002 + 0.013 = 0.015[/tex]
so the error is [itex] (0.015)(500)cos(60) = 3.75N[/itex]
The solution says 4.28N, however, which I confirmed by checking each error combination. Where am I going wrong here?
Thanks in advance.