Percent Uncertainty Problem -NEED HELP

[soccerdude010]

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

 

[brusier]

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...

 

[nlightner]

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.