Find Work Done in Moving Particle

Question

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When a particle is located a distance x meters from the origin, a force of cos⁡(pi(x/5)) newtons acts on it.

Find the work done in moving the particle from x=2 to x=2.5. ?

Find the work done in moving the particle from x=2.5 to x=3. ?

Find the work done in moving the particle from x=2 to x=3. ?

Answer 1

W = ∫₂^2.5cos(π(x/5))dx = 5/πsin(π(x/5))₂^2.5 = 5/π(sinπ/2 - sin2π/5) = 0.0779 J

W = ∫_2.5³cos(π(x/5))dx = 5/πsin(π(x/5))_2.5³ = 5/π(sin3π/5 - sinπ/2) = - 0.0779 J

W = ∫₂³cos(π(x/5))dx = 5/πsin(π(x/5))₂³ = 5/π(sin3π/5 - sin2π/5) = 0 J