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 for

Question

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?

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Acacia 5 months 2021-08-31T06:42:59+00:00 1 Answers 0 views 0

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    2021-08-31T06:44:39+00:00

    Answer:

    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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