Question

Calculate the maximum absolute uncertainty for R if:

R = 9A / B
A = 32 +/- 2 seconds
B = 11 +/- 3 seconds

1 second


0.33 seconds


9 seconds


2 seconds


6 seconds

Answer 1

ΔR = 9 s

Step-by-step explanation:

To calculate the propagation of the uncertainty or absolute error, the variation with each parameter must be calculated and the but of the cases must be found, which is done by taking the absolute value

The given expression is R = 2A / B

the uncertainty is ΔR = |
`(dR)/(dA)` | ΔA + |
`( dR)/(dB)` | ΔB

we look for the derivatives

`(dR)/(dA)` = 9 / B

`(dR)/(dB)` = 9A (
`- (1)/(B^2 )` )

we substitute

ΔR =
`(9)/(B)` ΔA +
`(9A)/(B^2)` ΔB

the values ​​are

ΔA = 2 s

ΔB = 3 s

ΔR =
`(9)/(11)` 2 +
`(9 \ 32)/(11^2 )` 3

ΔR = 1.636 + 7.14

ΔR = 8,776 s

the absolute error must be given with a significant figure

ΔR = 9 s