1. Centripital force: mass (m) frequency (n) raidus (r) I do not know if I did t

Question

1. Centripital force: mass (m) frequency (n) raidus (r)

I do not know if I did this right, but I wrote

Can someone please show me how to write the expression for uncertainty of the original equation using standard deviation?

2. A researcher is using Hooke's law (F=-kx) to determine the spring constant of a spring. The spring is stretched by a force of 2+,-.05N and the length the spring changes is measured to be 25cm. Write an expression for the uncertainty of the spring constant by propagation of errors using standard deviation.

I know that the constant will be k=8+,-.2N/m but I do not know how to write the work using standard deviation.

Explanation / Answer

ANSWER 1

Let ?n, ?m, and ?r be the uncertainties of n, m, and r, respectively. Then the error propagation law tells us that the relative uncertainty of the product F=4?2n2mr is

?F/F = 2 ?n/n + ?m/m + ?r/r,

from which you can find ?F.

Note: a constant factor (4?2) does not contribute to the relative uncertainty, whereas the exponent 2 in n

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