A particle travels from a position r ₁ = (2 m ) i + (3 m ) j to a new position r ₂ = (3 m ) i + (2 m ) j while experiencing a force F = (5 N ) i + (5 N ) j . Determine the work done by this force on the particle over the displacement.

Step-by-step solution

The displacement vector of the particle is given by: r = r ₂ - r ₁ r = (3 i + 2 j ) - (2 i + 3 j ) r = i - j m The work done by the constant force is the dot product of the force and the displacement: W = F r W = (5 i + 5 j ) ( i - j ) W = (5)(1) + (5)(-1) W = 5 - 5 = 0 J