Question

The shear modulus of steel is 8.1 × 1010 N/m2. A steel nail of radius 7.5 × 10–4 m projects 0.040 m horizontally outward from a wall. A man hangs a wet raincoat of weight 28.5 N from the end of the nail. Assuming the wall holds its end of the nail, what is the vertical deflection of the other end of the nail?

Answer 1

Answer:

$\Delta\ y =7.96 \times 10^{-6}\ m$

Explanation:

given,

shear modulus of steel = 8.1 × 10¹⁰ N/m²

radius of steel nail =  7.5 × 10⁻⁴ m

Projection outward = 0.040 m

Weight of wet raincoat = 28.5 N

Vertical deflection of other end of the nail = ?

we know

$G = \dfrac{\dfrac{F}{A}}{\dfrac{\Delta y}{L}}$

$\Delta\ y = \dfrac{FL}{AG}$

A = π r²

A = π x (7.5 x 10⁻⁴)²

A = 1.767 x 10⁻⁶ m²

$\Delta\ y =\dfrac{28.5 \times 0.04}{1.767\times 10^{-6}\times 8.1\times 10^{10}}$

$\Delta\ y =7.96 \times 10^{-6}\ m$

Thus, the vertical deflection of the other end of the nail is$\Delta\ y =7.96 \times 10^{-6}\ m$