Percentage Uncertanty and youngs modulus

[pandit bandit]

Homework Statement

hi there! I am new to this forum and was just wondering if anyone could help with this question on percentage uncertainty. I am supposed to find the percentage uncertainty in d^3

the info given is
mass attached to the end of a strip= 0.1 (+-0.001)kg
the width of the strip = 12.6 (+- 0.1)mm
the thickness of the strip= 0.66(+- 0.01)mm

Homework Equations

I am also given the equation for youngs modulus

E= 16pi^2 K^2 M/bd^3

The Attempt at a Solution

I worked out the percentage uncertainty of the thickness of the strip which was approx. 1.52% but am for completely lost

Thank You!

 

[Mapes]

Looks like a http://en.wikipedia.org/wiki/Propagation_of_uncertainty#Partial_derivatives" problem to me.

 

[pandit bandit]

so would i just simply multiply the percentage uncertainty by 3 as its d^3?

 

[Mapes]

Sure, I'd buy that.

 

[rwisz]

I can provide some guidance on how to approach this question on percentage uncertainty and Young's modulus. First, let's define what percentage uncertainty means. It is a measure of the possible error or deviation in a measurement, expressed as a percentage of the measured value. In other words, it tells us how accurate or precise our measurement is.

In this case, you are asked to find the percentage uncertainty in d^3, where d is the thickness of the strip. To do this, you need to first calculate the uncertainty in d, which is given as +- 0.01 mm. This means that the actual value of d could be anywhere between 0.65 mm and 0.67 mm. To find the percentage uncertainty, we can use the formula (uncertainty/actual value) x 100%. In this case, it would be (0.01/0.66) x 100%, which gives us a percentage uncertainty of approximately 1.52%.

Now, let's look at the equation for Young's modulus, E= 16pi^2 K^2 M/bd^3. We can see that it depends on the values of K, M, b, and d^3. Since we have already calculated the percentage uncertainty in d^3, we can use this to find the overall percentage uncertainty in E. To do this, we need to find the partial derivatives of E with respect to each variable (K, M, b, and d^3), and then multiply them by their respective percentage uncertainties. Finally, we add these values together to get the overall percentage uncertainty in E.

It is important to note that this method assumes that the uncertainties in each variable are independent and random. If this is not the case, then the calculation of percentage uncertainty may be more complex. Additionally, depending on the level of precision required, you may need to consider higher order terms in the partial derivatives.

I hope this helps in solving your homework question. Good luck!