Consider the cantilever-beam Wheatstone bridge system that has four strain gages (two in compression and two in tension). Which of the following statements is not true: (a) the change in resistance in each gage is proportional to the applied force, (b) temperature and torsional effects are automatically compensated for by the bridge, (c) the longitudinal (axial) strain in the beam is proportional to the output voltage of the bridge, (d) a downward force on the beam causes an increase in the resistance of a strain gage placed on its lower (under) side. Final Ans: (d) Compression on a lower side gage causes an increase in its resistance.

 (b) temperature and torsional effects are automatically compensated for by the bridge,

Explanation:

As can be seen, strain gages 1 and 4 are on top of the beam and strain gages 2 and 3 are on the bottom of

the beam. Therefore strain gages 1 and 4 experience a tensile strain (are stretched) and strain gages 2

and 3 experience a compressive strain. If the relationship between strain and resistance is linear, then

under some load F the changes in resistance will be

R1= R1 + dR1

R4= R4 + dR4

tensile(4)and

R ¢2= R2 -dR2

R ¢3= R3 -dR3

compressive. (5)

when the four strain gages have an equal nominal

resistance (i.e., R1 = R2 = R3 = R4 = R) then the deflection method Wheatstone bridge equation reduces to the linear equation

Using known weights, a calibration curve can be established that relates the weight W to the output

voltage on a digital meter Eo,

Eo= a0 + a1W , (4)

where a0 and a1 are some constants. Once an unknown weight is known, an unknown mass or density

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.