Coefficient of Static Friction error (Lab)

[mlostrac]

Homework Statement

Need to calculate the error of coefficient of static friction in a lab where: µs = tan(theta)s They say to use the general theory of errors?

Homework Equations

delta[tan(theta)] = [1/cos(theta)]^2 (delta)(theta)

The Attempt at a Solution

Do I just plug in my angle value of 26 into the theta's to get the answer? I tried that and I got a value of 0.40, which doesn't make sense because my coefficient of static friction is 0.50?

 

[kuruman]

You are on the right track, but not there yet. Your fractional error is d(tanθ)/tanθ. To get the percent error multiply by 100. Be sure to do all calculations and express all angles in radians.

 

[mlostrac]

You are on the right track, but not there yet. Your fractional error is d(tanθ)/tanθ. To get the percent error multiply by 100. Be sure to do all calculations and express all angles in radians.

Ok so I adjusted my angle from 26.5 degrees to 0.46 rad, and then plugged that into each theta for the above equation giving me:
d(tan(theta)) = 1 x d(theta)

kinda confused on what I do after this

 

[kuruman]

Ok so I adjusted my angle from 26.5 degrees to 0.46 rad, and then plugged that into each theta for the above equation giving me:
d(tan(theta)) = 1 x d(theta)

kinda confused on what I do after this

I am not sure what you have done here. The fractional error in tanθ is given by the ratio

$$\frac{d(tan(\theta))}{tan\theta}=\frac{d \theta}{tan\theta*cos^2(\theta)}$$

 

[mlostrac]

I am not sure what you have done here. The fractional error in tanθ is given by the ratio

$$\frac{d(tan(\theta))}{tan\theta}=\frac{d \theta}{tan\theta*cos^2(\theta)}$$

d tan(theta)/tan(theta) = d (0.462)/ [tan(0.462) x cos (0.462)^2)]
= 0.46/0.00806
= 57.32 rad

I think my answer is way off, what am I doing wrong and why does something as simple as error calculation seem so complicated?

 

[kuruman]

d tan(theta)/tan(theta) = d (0.462)/ [tan(0.462) x cos (0.462)^2)]
= 0.46/0.00806
= 57.32 rad

I think my answer is way off, what am I doing wrong and why does something as simple as error calculation seem so complicated?

You seem not to understand the meaning of the symbols in the expression you are plugging in. Here θ is 0.46 radians, true enough. However, dθ is not also 0.46 rad; it represents the uncertainty in the angle. To what accuracy did you measure that angle in radians? That's your dθ. Only you, who did the experiment, can make an educated guess about the size of dθ.

 

[mlostrac]

You seem not to understand the meaning of the symbols in the expression you are plugging in. Here θ is 0.46 radians, true enough. However, dθ is not also 0.46 rad; it represents the uncertainty in the angle. To what accuracy did you measure that angle in radians? That's your dθ. Only you, who did the experiment, can make an educated guess about the size of dθ.

Oops, haha. Ok I think I got it right this time. I put my accuracy at .001, and then my answer ended up being 0.12.

So that kinda makes sense. A coefficient of static friction = 0.500 +/- .001.

Thanks for your help kuruman!