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

`\Delta\ y =7.96 * 10^(-6)\ m`

Step-by-step 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 = ((F)/(A))/((\Delta y)/(L))`

`\Delta\ y = (FL)/(AG)`

A = π r²

A = π x (7.5 x 10⁻⁴)²

A = 1.767 x 10⁻⁶ m²

`\Delta\ y =(28.5 * 0.04)/(1.767* 10^(-6)* 8.1* 10^(10))`

`\Delta\ y =7.96 * 10^(-6)\ m`

Thus, the vertical deflection of the other end of the nail is
`\Delta\ y =7.96 * 10^(-6)\ m`