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

Answer:

$U=\pm 0.382N$

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

$U=\sqrt{u_0^2+u_T^2}$

Where

$u_0=Zero\ order\ uncertainty$

$u_0=\pm 0.5*0.25$

$u_0=\pm=0.125$

And

u_T=Total instrumental Uncertainty

$u_T=\sqrt{l_e^2+h_e^2}$

Where

l_e=Error of linearity

h_e=Error due to hysteresis

Hence

$u_T=\sqrt{0.20^2+0.30^2}$

$u_T=\pm 0.36$

Therefore

$U=\sqrt{(0.125)^2+0.36^2}$

$U=\pm 0.382N$