|Class 11 Physics Mechanical Properties of Solids||Longitudinal stress|
Types of Stress: Longitudinal stress
Problem:- A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path.
Answer:- Mass, m = 14.5 kg
Length of the steel wire, l = 1.0 m
Angular velocity, ω = 2 rev/s
Cross-sectional area of the wire, a = 0.065 cm2
Let Δl be the elongation of the wire when the mass is at the lowest point of its path.
When the mass is placed at the position of the vertical circle, the total force on the mass is:
F = mg + mlω2
= 14.5 × 9.8 + 14.5 × 1 × (2)2 = 200.1 N
Young’s modulus =Stress/Strain
Y = (F/A)/ Δl/l
= (F l)/A Δl
Therefore Δl = F l/A Y
Young’s modulus for steel = 2 × 1011 Pa
Therefore Δl = 200.1/0.065x10-4x2x1011 = 1539.23x107
Hence, the elongation of the wire is 1.539 × 10–4 m.
Types of Longitudinal Stress:-
Force is applied on both the sides as a result length of cylinder increases
Compressing the cylinder