A uniform elastic plank moves due to a constant force F0 distributed uniformly over the end face whose area is S. The Young’s modulus of the plank is Y. The strain produced in the direction of force is

Engineering

Physics

Newtons Second Law of Motion

Forces and Types of Forces

Stress Strain and Hookes Law New

Question

A uniform elastic plank moves due to a constant force F₀ distributed uniformly over the end face whose area is S. The Young’s modulus of the plank is Y. The strain produced in the direction of force is

$\frac{2 F_{0}}{SY}$

$\frac{F_{0}}{2 SY}$

$\frac{F_{0}}{SY}$

$\frac{\sqrt{2} F_{0}}{SY}$

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Young's modulus Y relates stress (σ) and strain (ε) in elastic materials: $Y = \frac{σ}{ε}$ . Therefore, strain is $ε = \frac{σ}{Y}$ .

Stress is force per unit area. The constant force F₀ is distributed uniformly over the end face of area S, so the stress is $σ = \frac{F_{0}}{S}$ .

Substituting this into the strain equation gives the final result: $ε = \frac{F_{0}}{S Y}$ .

Final Answer: $\frac{F_{0}}{S Y}$