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28 July, 04:38

You slide a chair across a rough, horizontal surface. The chair's mass is 18.8 kg. The force you exert on the chair is 156 N directed 26 degrees below the horizontal. While you slide the chair a distance of 5.00 m, the chair's speed changes from 1.30 m/s to 3.10 m/s. Find the work done by friction on the chair.

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  1. 28 July, 05:46
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    626.612 J

    Explanation:

    Work done by friction on the chair is given as

    W-ΔEk = W' ... Equation 1

    Where W' = Work done by friction on the chair, W = Work done on the chair by me, Ek = change in Kinetic energy of the chair as a result of the slide.

    From the question,

    W = FdcosФ ... Equation 2

    ΔEk = 1/2m (v²-u²) ... Equation 3

    Where F = Force applied on the chair, d = distance of slide, Ф = angle between the force and the horizontal, m = mass of the chair, v = final velocity of the chair, u = initial velocity of the chair

    Substitute equation 2 and equation 3 into equation 1

    W' = FdcosФ-1/2m (v²-u²) ... Equation 4

    Given: F = 156, d = 5 m, Ф = 26°, m = 18.8 kg, v = 3.1 m/s, u = 1.3 m/s

    Substitute into equation 4

    W' = 156*5*cos26°-1/2*18 (3.1²-1.3²)

    W' = 701.06-74.448

    W' = 626.612 J.

    Hence the work done by friction = 626.612 J
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