Calculate the net work done by the force F whose variation w... | Physics - Work done by variable forces | SolveeIt | Solveeit

Today, August 19

Question

Calculate the net work done by the force F whose variation with position has been shown as above.

Visual representation for Physics

A

$\frac{\pi}{4}F_0X_0$

B

$\frac{\pi}{2}F_0^2$

C

$\frac{\pi}{8}X_0^2$

D

All of the above

Answer

All of the above

Explanation

Solution

The semicircular force–displacement graph represents a semicircle with diameter on the x‐axis if the string is taken to be “just touching” F₀. Then
F₀ = (X₀/2) ⇒ Area = (½)π(F₀)² = (πX₀²)/8 = (π/4)F₀X₀ = (π/2)F₀².
All three forms are equivalent.