Question

Question #aa46e

Answer 1

`0.6%`

Explanation:

In the classical sense , the centripetal force `F` can be measured as:

`F = (m v^2)/r`

We can take logs and say that:

`ln F = ln ((m v^2)/r)`

`= ln m + ln v^2 - ln r`

`= ln m + 2 ln v - ln r`

Using differentials:

`(dF)/F = (dm)/m + 2 (dv)/v - (dr)/r`

`= 2% + 2 * 1.3% - 4% = 0.6%`

Answer 2

`4.66%`

Explanation:

The formula for error propagation using standard deviations:

`(sigmaF)/|F|=sqrt(((sigmaa)/|a|)^2+((sigmab)/|b|)^2+((sigmac)/|c|)^2+...)`

Where a, b, c, ... are parameters used to determine the uncertainty of `F`.

`(sigmaF)/|F|` is basically a percentage in error if we multiply by 100%. Therefore,

Uncertainty in your centripetal force is `sqrt(2^2+1.3^2+4^2)=4.65725%`

Round it off to get `4.66%`.

There is a more robust way of measuring uncertainties using calculus and it is my go to formula.

Uncertainty of a quantity, `sigmaQ=sqrt((sigmaa(delQ)/(dela))^2+(sigmab(delQ)/(delb))^2+(sigmac(delQ)/(delc))^2+...)`

`(sigmaa(delQ)/(dela))` is basically `sigmaa` also known as the uncertainty to be multiplied by the derivative of `Q` with respect to parameter `a`.

Cheers.