A force sensor has an input range of 0 to 10 kN and an outpu

A force sensor has an input range of 0 to 10 kN and an output range of 0 to 5V at a standard temperature of 20 °C. At 30 °C the output range is 0 to 5.5 V. Quantify this environmental effect

Solution

Input : Force and Temp
Output : Voltage

So (dV/dT)_F=10kN=(5.5-5)/(30-20)=.05 Volt/^oC
and (dV/dF)_T=20^oC=5/10=.5 mV/N
(dV/dF)_T=30^oC=5.5/10=.55 mV/N
Let dV/dF = y
So, dy/dT = (.55-.5)/(30-20)=.05/10=.005mV/N^oC
Therefore by integration it is seen y = .005T + c₁
and again integration shows V = .005TF +c₁F +c₂
at F = 0 V=0 so c₂ = 0
V = 5 at T = 20 F = 10kN . So c1 = -.0995

So V = .005TF - .0995F
Note the question can be modelled in more than one way.