StudentAidUnit 17: Physics of Solids — Numericals
12th Class Physics · Unit 17: Physics of Solids
17.1.A steel wire 12 mm in diameter is fastened to a log and is then pulled by tractor. The length of steel wire between the log and the tractor is 11 m. A force of 10,000 N is required to pull the log. Calculate (a) the stress in the wire and (b) the strain in the wire. (c) How much does the wire stretch when the log is pulled? (E = 200 × 10^9 Nm^-2)
Given
Diameter
d = 12 mm = 12 × 10-3 m
Radius
r = d2 = 122 × 10-3 = 6 × 10-3 m
Length
l = 11 m
Force
F = 10,000 N
Modulus of elasticity
E = 200 × 109 Nm-2
Formula
Stress (part a)
sigma = FA = Fpi r2
Working
Substituting values
sigma = 10,0003.14 × (6 × 10-3)2
sigma = frac{10,000}{3.14 × 36 × 10-6
sigma = 88.46 × 106 Nm-2
Result
Stress
sigma = 88.46 MPa
Formula
Young's modulus relation
E = frac{Stress{Strain
Strain (part b)
Strain = frac{Stress{E}
Working
Substituting values
Strain = frac{88.46 × 106{200 × 109
Strain = 44.23 × 10-5
Strain = 4.4 × 10-4
Result
Strain
Strain = 4.4 × 10-4
Formula
Change in length (part c)
Strain = Δll
Solving for Δl
Δl = Strain × l
Working
Substituting values
Δl = 4.4 × 10-4 × 11
Δl = 4.84 × 10-5 m
Δl = 4.84 × 10-3 m
Result
Change in length
Δl = 4.84 mm