Percent Uncertainty Shenanigans

[dumakey1212]

Parts C and D: http://s7.postimg.org/pnq5gry63/image.png

Part D of this problem is just like Part C above it. The only difference is the presence of "sin," but that doesn't affect the calculation of percent uncertainty at all. Chapter 1 of my Physics book (Physics: Principles with Applications - Giancoli) says you calculate it by dividing the 0.5 by 71 and multiplying by 100. I used this exact approach for Parts A, B, and C and got the right answers but magically it doesn't seem to work for this last part even though it is the exact same as Parts A, B, and C. Almost seems to be a glitch in the system. The answer should be 0.7, but this doesn't work. I really don't understand what is going on. Thanks for any help with this, guys!

Edit: I just randomly punched in values since my awesome professor gives us like 30 attempts for each problem, and wound up discovering the claimed correct answer is 0.3. This makes absolutely no sense and does not equate with the method used to do this problem. I have no idea how one would arrive at 0.3 as the answer. So confused, probably Mastering Physics shenanigans, already reported to professor.

 

[gneill]

Parts C and D: http://s7.postimg.org/pnq5gry63/image.png

Part D of this problem is just like Part C above it. The only difference is the presence of "sin," but that doesn't affect the calculation of percent uncertainty at all. Chapter 1 of my Physics book (Physics: Principles with Applications - Giancoli) says you calculate it by dividing the 0.5 by 71 and multiplying by 100. I used this exact approach for Parts A, B, and C and got the right answers but magically it doesn't seem to work for this last part even though it is the exact same as Parts A, B, and C. Almost seems to be a glitch in the system. The answer should be 0.7, but this doesn't work. I really don't understand what is going on. Thanks for any help with this, guys!

Edit: I just randomly punched in values since my awesome professor gives us like 30 attempts for each problem, and wound up discovering the claimed correct answer is 0.3. This makes absolutely no sense and does not equate with the method used to do this problem. I have no idea how one would arrive at 0.3 as the answer. So confused, probably Mastering Physics shenanigans, already reported to professor.

Hi dumakey1212. Welcome to Physics Forums.

Be sure to familiarize yourself with the posting guidelines associated with the homework help sections; you should have used the posting template provided when you started the new thread.

The sin function does make a difference! It's a non-linear function so its output is not necessarily proportional to the input. That means the result can yield different percentages of error depending upon where along the sine curve the angle lies.

What methods have you been taught to deal with uncertainty propagation when such functions are involved?

 

[dumakey1212]

We haven't been taught how to do anything with trigonometric things yet but are rather expected to from previous coursework. I guess I don't understand what you would do with trigonometry in calculating this or how sine factors into this since you're given the value and the uncertainty estimate, which is all I've been taught you need.

 

[gneill]

We haven't been taught how to do anything with trigonometric things yet but are rather expected to from previous coursework. I guess I don't understand what you would do with trigonometry in calculating this or how sine factors into this since you're given the value and the uncertainty estimate, which is all I've been taught you need.

Have you learned any calculus yet? There is a general method for calculating uncertainties which involves using differentiation. Look up Uncertainties and Error Propagation on the net. In particular, have a gander at http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html, and at part (f) Other Functions: Getting formulas using partial derivatives, in particular.

Without using calculus you might estimate the error by directly calculating the results at the extremes of the uncertainty spread (sin(θ - Δθ) and sin(θ + Δθ)) to estimate the total spread of the result around the "actual" value, sin(θ).

 

[dumakey1212]

Yeah, that's all a bit over my head. I had pre-calc/trig 5 years ago and AP Calculus 3 years ago. Thank you for explaining it, though, you are very knowledgeable on this subject!