Question

A force measuring instrument comes with a certificate of calibration that identifies two instrument errors and assigns each an uncertainty at 95% confidence over its range. Provide an estimate of the instrument design-stage uncertainty.

Resolution: 0.25 N
Range: 0 to 100 N
Linearity error: within 0.20 N over range
Hysteresis error: within 0.30 N over range

Answer 1

`U=\pm 0.382N`

Step-by-step explanation:

From the question we are told that:

Resolution: 0.25 N

Range: 0 to 100 N

Linearity error: within 0.20 N over range

Hysteresis error: within 0.30 N over range

Generally the equation for Stage Uncertainty is mathematically given by

`U=√(u_0^2+u_T^2)`

Where

`u_0=Zero\ order\ uncertainty`

`u_0=\pm 0.5*0.25`

`u_0=\pm=0.125`

And

u_T=Total instrumental Uncertainty

`u_T=√(l_e^2+h_e^2)`

Where

l_e=Error of linearity

h_e=Error due to hysteresis

Hence

`u_T=√(0.20^2+0.30^2)`

`u_T=\pm 0.36`

Therefore

`U=√((0.125)^2+0.36^2)`

`U=\pm 0.382N`