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6 February, 01:52

Susan's 10 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30° above the floor. The tension is a constant 30 N and the coefficient of friction is 0.20. Use work and energy to find Paul's speed after being pulled 3.0 m.

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  1. 6 February, 02:11
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    2.37 m/s

    Explanation:

    From the question

    W = W'-Wf ... Equation 1

    Where W = net work done by Susan, W' = Work done by Susan, Wf = Work done against friction

    W = FdcosФ-[d (mgμ-FsinФ) ] ... Equation 2

    Where F = the force applied by Susan, d = distance, Φ = angle of the force to the horizontal, m = mass, μ = coefficient of friction, g = acceleration due to gravity.

    Given: F = 30 N, d = 3 m, m = 10 kg, μ = 0.2, g = 9.8 m/s², Ф = 30°

    Substitute into equation 2

    W = 30 (3) (cos30°) - 0.6[ (9.8) (10) - 30sin30°]

    W = 77.94-49.8

    W = 28.14 J.

    But,

    W = 1/2mv² ... Equation 3

    Where v = Paul's speed

    make v the subject of the equation

    v = √ (2W/m) ... Equation 3

    Given: W = 28.14 J, m = 10 kg.

    Substitute into equation 3

    v = √ (2*28.14/10)

    v = √ (56.28/10)

    v = √5.628

    v = 2.37 m/s
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