Find the work done by the force on the particle. Answer in units of J.

Question

A force F~ = Fx ˆı + Fy ˆ acts on a particle that undergoes a displacement of ~s = sx ˆı + sy ˆ where Fx = 1 N, Fy = −2 N, sx = 5 m, and sy = 3 m. Find the work done by the force on the particle. Answer in units of J.

Answer 1

Work (in J) is the vector dot product of Force (1 N, –2 N) and displacement (5 m, 3 m):

Another common formula for work is W = F×d cos(θ), where

F is the magnitude or the force vector, here F = √(1² + (–2)²) = √(5) ≈ 2.24 N

s is the magnitude or the displacement vector, here s = √(5² + 3²) = √(34) ≈ 5.83 m

θ is the angle between the vectors, here tan⁻¹(3/5) – tan⁻¹(–2/1) ≈ 31.0° – (–63.4°) = 94.4°

So W = (2.24 N)(5.83 m)cos(94.4°) = –1.00 J

Answer

Work = 1 J