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30 December, 18:43

A skier with a 65kg mass skies down a 30 degree incline hill. The coefficient of friction is 0.1.

a. Draw a free body diagram.

b. Determine the normal force.

c. Determine the acceleration of the skier down the hill.

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Answers (1)
  1. 30 December, 20:31
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    Part a.

    Refer to the diagram shown below.

    m = 65 kg, the mass of the skier

    θ = 30°, the angle of the incline

    μ = 0.1, the coefficient of friction

    W = mg, the weight of the skier

    N = mg cosθ, the normal reaction

    F = mg sinθ, the component of the weight acting down the hill

    R = μN, the frictional force resisting motion down the plane

    a = the acceleration down the plane.

    The weight is

    W = mg = (65 kg) * (9.8 m/s) = 637 N

    Part b.

    The normal force is

    N = (637 N) * cos (30) = 551.658 N

    The frictional force is

    R = 0.1 (551.658 N) = 55.1658 N

    Part c.

    Calculate the component of the weight acting down the hill.

    F = mg sin (30) = (637 N) * sin (30) = 318.5 N

    The equation of motion is

    ma = F - R

    (65 kg) * (a m/s²) = 318.5 - 55.1658 N

    a = 263.3342/65 = 4.05 m/s²

    Answers:

    N = 551.7 N

    a = 4.05 m/s²
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