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An object has a mass of 88.60 kg ± 0.09 kg. I calculated the weight to be 869 N but now I need to calculate the absolute uncertainty in weight.

My thinking was that the absolute uncertainty would be .09/869 = 0.0001. Then multiply that by the weight, so .0001 by 869. So 0.09 but however this is not correct Looking for some help

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The weight is given by:

$$ W = mg $$

where $m$ is your mass and $g$ is the acceleration due to gravity. If we have some error in the mass we can write the mass as $m \pm \sigma_m$ where $\sigma_m$ is the error (0.09 kg in this case) so we get:

$$\begin{align} W &= (m \pm \sigma_m)g \\ &= mg \pm \sigma_mg \end{align}$$

So the weight we get is $mg$ with an error of $\pm \sigma_mg$.

(This is assuming we can ignore any errors in the value of $g$.)

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  • $\begingroup$ so how do I calculate +- Og sorry didn't know how to do the symbol $\endgroup$
    – jh123
    Commented Sep 25, 2016 at 15:48
  • $\begingroup$ so .09 * 9.8 ???? $\endgroup$
    – jh123
    Commented Sep 25, 2016 at 15:49
  • $\begingroup$ and would the unit be Newtons then? $\endgroup$
    – jh123
    Commented Sep 25, 2016 at 15:49
  • $\begingroup$ @javahelper123: you can see the code used to generate symbols by right clicking on the symbol and choosing Show math as then TeX commands on the popup menu. $\endgroup$
    – John Rennie
    Commented Sep 25, 2016 at 16:00
  • $\begingroup$ thanks for that so would .09 * 9.8 = .9N be the correct answer? $\endgroup$
    – jh123
    Commented Sep 25, 2016 at 16:05

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