Question

Calculate the increase in energy of a brass bar of length 0.2 m and cross sectional area 1 cm^2 when compressed with a load of 5 kg weight along its length. y = 1.0*10^11N/m^2 and g = 10m/s^2.

Answer 1

The energy increase on application of force along the length of the rod is 0.000025 J or 2.5 x 10^(-5) J.

Energy of a rod undergoing compression when we are aware of its young's modulus can be given by the formula:

Energy (E) = 0.5 x (stress)^2 x (Volume / Young's modulus)

Stress is defined as the existing pressure of a body, i.e., ration of force and pressure. Hence, stress for the rod is:

Stress = (m x g) / A

Stress = (5 x 10) / (0.0001) = 5 x 10^(5)

Hence, energy is calculated as:

E = (0.5) x (25 x 10^10) x (2 x 10^-5) / Y

E = 2.5 x 10^(-5) Joules.

Answer 2

8.57 × 10^-6 j is the correct answer