A nail projects 25.0 mm horizontally outward from a wall.A 400 N picture is hung from the end of the nail and the nail deflects downward by 2.00 $\times$ 10^-5 m.If the shear modulus is 3.40 $\times$ 10¹⁰ N/m²,then what is the diameter of the nail? A) 1.60 mm B) 1.86 mm C) 2.16 mm D) 2.44 mm E) 2.65 mm

Question

Quizplus · Accepted Answer

The formula for deflection of a cantilever beam is given by:
δ = FL³ / 3EI
where δ is the deflection, F is the applied load, L is the length of the beam, E is the Young's modulus of the material, and I is the moment of inertia of the cross-sectional area.
In this case, since the beam is a circular cross-section, the moment of inertia I is given by:
I = πd⁴ / 64
where d is the diameter of the nail.
Plugging in the given values, we get:
2.00 x 10⁻⁵ m = (400 N) x (0.025 m)³ / (3 x (3.40 x 10¹⁰ N/m²) x (π/64) x d⁴)
Solving for d, we get:
d = 2.16 mm (approximately)

A Nail Projects 25 ×\times× 10-5 M ×\times× 1010 N/m2,then What Is the Diameter of the Nail? A)

A Nail Projects 25 $\times$ 10^-5 M $\times$ 10¹⁰ N/m²,then What Is the Diameter of the Nail?
A)