QUESTION 1:

Figure 1 shows a 20 mm diameter rod that is subjected to a tensile load of 20 kN. The initial length of the rod is 400 mm. The Young's modulus of the rod material is 5.2 GPa. A resistance strain gage is attached to the surface of the rod to measure the strain undergone by the rod.

a) Calculate the strain undergone by the rod.

b) The strain gage used to measure strain in the rod has a gage factor (GF) of 2 and a resistance of 500 W. Determine the change in resistance resulting from the strain caused by the load.

c) With the aid of a diagram, explain how the change in resistance calculated in Part (b) can be measured.

QUESTION 2:

The Prony brake shown in Figure 2 is commonly used in torque measurement. The rope is wound round the brake drum mounted onto the shaft. One end of the rope carries a dead load of weight W and the other end is attached to a spring balance

a) The force exerted by the rope on the drum is F_r and the force exerted on the spring balance is F_s. Write down the relationship between F_r, F_s and W.

b) Derive the expression for the torque on the shaft using the relationship between F_r, F_s and W in Part (a).

c) The Prony brake was used to measure the output torque of an engine. The following data is given:

Drum diameter = 400 mm

Spring force, F_r = 0.2 kN

Dead weight, W = 0.5 kN

Determine the torque output by the engine. If the shaft rotates at 2000 rpm, calculate the power output of the engine.

What is the main limitation of the Prony brake method? How is this limitation overcome in practice?