A 12 N force with a fixed orientation does work on a particle as the particle moves through displacement . What is the angle between the force and the displacement if the change in the particle's kinetic energy is (a) +8.49 J and (b) -8.49 J?

Check Explanation

Explanation:

According to the work-energy theorem,

workdone between two points = Change in kinetic energy between the two points

And workdone is given mathematically as the dot product of the force and the displacement the force moves through.

W = F.d = /F/ × /d/ cos θ

where /F/ = magnitude of the force

/d/ = magnitude of the displacement

θ = angle between the line of action of the force and the displacement it moves through

a) W = ΔK.E

/F/ × /d/ cos θ = 8.49 J

/F/ = 12 N

/d/ = √[(1²) + (-1)² + (1²)] = √3

12 × √3 × cos θ = 8.49

θ = cos⁻¹ (0.4085)

θ = 65.9°

b) W = ΔK.E

/F/ × /d/ cos θ = -8.49 J

/F/ = 12 N

/d/ = √[(1²) + (-1)² + (1²)] = √3

12 × √3 × cos θ = - 8.49

θ = cos⁻¹ (- 0.4085)

θ = 114.1°

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