Propagation of errors addition numbers without uncertainty

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SUMMARY

The discussion focuses on calculating uncertainty when adding numbers with uncertainty, specifically in the context of physics problems involving mass, acceleration, and friction. The example provided uses a mass (M) of 350g, an acceleration (a) of 0.624 ± 0.001 m/s², a coefficient of friction (µk) of 0.07, and gravitational acceleration (g) of 9.80 m/s². The total force (T) is calculated as 458.5 N, with the uncertainty derived solely from the acceleration term, resulting in an uncertainty of 0.35 N. Constants such as M, g, and µk are treated as having no uncertainty.

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Silvestor
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Homework Statement


I am having trouble calculating uncertainty when a number is added to a value with uncertainty.

M = 350g
a = 0.624 [itex]\pm[/itex] 0.001
µk = 0.07
g = 9.80 m/s2

Homework Equations


T = M*a + µk*M*g


The Attempt at a Solution


T = (350g)*(0.624 m/s2) + (0.07)*(350g)*(9.80m/s2)
T= 458.5 N
D[itex]_{}t[/itex] = M*(D[itex]_{}a[/itex]) + ...
D[itex]_{}t[/itex] = (350g)*(0.001 m/s2) + ...
D[itex]_{}t[/itex] = 0.35 N + ...
 
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If you're given that there is no uncertainty in M, g, or µk then you treat them as constants that are 100% accurate. The uncertainty in the result, then, only depends upon the uncertainty in a, as you've written. The uncertainty in the µk*M*g term is zero.
 
thanks
 

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