Percent Uncertainty Problem -NEED HELP

In summary, the question asks for the percent uncertainty of a measurement given as 1.57 m^2. The formula for percent uncertainty is the ratio of the uncertainty to the measured value, multiplied by 100. After several attempts, the correct answer is found to be 1%, using the equation A=X^2 and considering error propagation. The final measurement of 1.57 m^2 is thought of as an area, and the percent uncertainty is related to the differential or dy.
  • #1
soccerdude010
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Percent Uncertainty Problem -NEED URGENT HELP!

Homework Statement


The question is: What, approximately, is the percent uncertainty for the measurement given as 1.57 m^2.


Homework Equations


I know the formula that this textbook: 6th edition: Physics - Giancoli gave. It is simply, the ratio of the uncertainty to the measured value, multiplied by 100.


The Attempt at a Solution


I have tried numerous attempts and for some reason, I couldn't seem to come up with the right answer the book gives in the back. I'm really not sure what other way to do it.

I tried, simply to put:
(.01)/1.57 * 100 = .64%

(.01)/(1.57^2) * 100 = .41%

(1.58-1.57)/1.57 *100 = .64%

...the correct answer in the back of the book is 1%. I kept using .01 because the measured value they gave me 1.57m^2. I am not sure whether I messed up there, I was hoping someone could help me. Thanks
 
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  • #2


I'm very new to both calculus and physics but I am having trouble understanding how any value is to be found with such little information.

The final measurement 1.57 is in m^2 and maybe is thought of as an area?

I think the percent uncertantity is related to the differential or dy.

dy is equal to f'(x)dx.

So I guess the equation f(x) could be A=X^2 and A' would be 2X. A' could be thought of as delta A because if there is error in the measurements (delta X or Y) it would be propagated into the calculation of the area. For small values of error, delta X=dX and delta Y=dy and dx*dy=dA ( I wonder if this thinking is correct).

Anyway then you would need to be given the estimated deviation of any measurement taken. For instance X is found to be correct to within dX m.

So with this I did

A=x^2
1.57=X^2
X=1.25

dA=2Xdx
=2(1.25)(dX)
=2.5dX m^2 propagated error

to find the percent error the ratio of the change to the actual areas multiplied by 100 should be preformed...

dA/A
= (2Xdx/X^2) 100
= (2dx/x) 100
=[2(dX)/1.25] 100
=160 dX% error.

...thats all I think after having taken calculus one...
 
  • #3


Hello,

It seems like you are on the right track with using the formula for percent uncertainty. However, there may be a small error in your calculations. The correct formula for percent uncertainty is (uncertainty/measured value) * 100. So for this problem, it would be (0.01/1.57) * 100 = 0.64%. The book may have rounded up to 1%, so it could also be possible that your answer is correct. It's always important to check your calculations and make sure you are using the correct formula. I hope this helps! If you are still having trouble, I recommend seeking help from a tutor or your teacher.
 

1. What is percent uncertainty?

Percent uncertainty is a measure of the potential error or variation in a measurement or calculation. It is typically expressed as a percentage, and it represents the range of values within which the true value is likely to fall.

2. How is percent uncertainty calculated?

Percent uncertainty is calculated by taking the absolute uncertainty (the smallest possible value that a measurement or calculation could have) and dividing it by the measured or calculated value, then multiplying by 100 to convert to a percentage.

3. Why is percent uncertainty important?

Percent uncertainty is important because it allows us to understand the potential error or variability in our measurements and calculations. It helps us determine the reliability and accuracy of our data and can guide us in making decisions based on that data.

4. How can I reduce percent uncertainty?

There are several ways to reduce percent uncertainty, including using more precise instruments, taking multiple measurements, and minimizing sources of error. It is also important to properly estimate and record the uncertainties associated with each measurement or calculation.

5. Can percent uncertainty be negative?

No, percent uncertainty cannot be negative. It is always expressed as a positive value, as it represents the range of values above and below the measured or calculated value. A negative value would indicate that the uncertainty is smaller than the actual value, which is not possible.

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