Question

The magnitudes of two forces are measured to be 120 ± 5 N and 60 ± 3 N. Find the sum and difference of the two magnitudes, giving the uncertainty in each case.

Answer 1

sum of forces = (180 ± 8) N

difference of force = (60 ± 8) N

two forces are measured as,

F1 = (120 ± 5) N

F2 = (60 ± 3) N

we have to find sum and difference of F1 and F2 and also have to uncertainty in each case.

sum of F1 and F2 , F = F1 + F2

= (120 ± 5) + (60 ± 3)

= (120 + 60) ± (5 + 3)

= (180 ± 8) N

so, sum of forces is 180 N and uncertainty on it is 8 N .

similarly, difference of F1 and F2, F' = F1 - F2

= (120 ± 5) - (60 ± 3)

= (120 - 60) ± (5 + 3) [error should be considered as maximum . that's why we considered positive in place of negative sign ]

= (60 ± 8) N

hence, difference of forces is 60N and uncertainty on it is 8N

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Answer 2

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