Answer:
There's a decrease in width of 2.18 × 10^(-6) m
Explanation:
We are given;
Shear Modulus;E = 207 GPa = 207 × 10^(9) N/m²
Force;F = 60000 N.
Poisson’s ratio; υ =0.30
We are told width is 20 mm and thickness 40 mm.
Thus;
Area = 20 × 10^(-3) × 40 × 10^(-3)
Area = 8 × 10^(-4) m²
Now formula for shear modulus is;
E = σ/ε_z
Where σ is stress given by the formula Force(F)/Area(A)
While ε_z is longitudinal strain.
Thus;
E = (F/A)/ε_z
ε_z = (F/A)/E
ε_z = (60,000/(8 × 10^(-4)))/(207 × 10^(9))
ε_z = 3.62 × 10^(-4)
Now, formula for lateral strain is;
ε_x = - υ × ε_z
ε_x = -0.3 × 3.62 × 10^(-4)
ε_x = -1.09 × 10^(-4)
Now, change in width is given by;
Δw = w_o × ε_x
Where w_o is initial width = 20 × 10^(-3) m
So; Δw = 20 × 10^(-3) × -1.09 × 10^(-4)
Δw = -2.18 × 10^(-6) m
Negative means the width decreased.
So there's a decrease in width of 2.18 × 10^(-6) m
