A 100 N picture hangs from a nail in the wall.The diameter of the nail is 3.00 mm.The shear stress on the nail is A) 1.98 $\times$ 10⁷ N/m². B) 1.86 $\times$ 10⁷ N/m². C) 1.62 $\times$ 10⁷ N/m². D) 1.41 $\times$ 10⁷ N/m². E) 1.34 $\times$ 10⁷ N/m².

Question

Quizplus · Accepted Answer

The equation for shear stress is:

τ = F/A

Where F is the force (in N) and A is the cross-sectional area (in m^2).

To find the cross-sectional area of the nail, we need to know its radius. The diameter of the nail is 3.00 mm, so its radius is 1.50 mm (or 0.00150 m). The cross-sectional area is then:

A = πr^2
A = π(0.00150)^2
A = 7.07 x 10^-6 m^2

Now we can calculate the shear stress:

τ = F/A
τ = 100 N / 7.07 x 10^-6 m^2
τ ≈ 1.41 x 10^7 N/m^2
τ ≈ 1.41 MPa

We can also convert this to units of N/mm^2, which gives us:

τ = 1.41 x 10^7 N/m^2
τ = 1.41 x 10^-3 N/mm^2
τ ≈ 1.41 MPa

Therefore, the shear stress on the nail is 1.41 MPa, which corresponds to choice D.

A 100 N Picture Hangs from a Nail in the Wall.The