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19 January, 20:23

A basket has a mass of 5.5 kg. Find the magnitude of the normal force if the basket is at rest on a ramp inclined above the horizontal at:

a) 0 degrees (horizontal surface)

b) 12 degrees

c) 25 degrees

d) 45 degrees

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Answers (1)
  1. 19 January, 20:39
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    The free body diagram consists of:

    1) Weight force, which is a vertical arrow downward

    2) A Normal force that is perpendicular to the ramp.

    The Normal force can be decomposed in a vertical component and an horizontal component.

    The vertical component, Ny, must equal the weight force, due to equilibrium (rest) condiition = >

    Ny = weight = m*g = 5.5kg*9.8m/s^2 = 53.9 N

    By geometry the vertical component of the Normal force, Ny is such that

    cos (angle) = N / Ny = > N = Ny * cos (angle)

    => N = 53.9N * cos (angle)

    Now use that equation for each option:

    a) 0 ° = > N = 53.9N * cos (0) = 53.9N

    b) 12° = > N = 53.9 * cos (12) = 52.7N

    c) 25° = > N = 53.9 * cos (25) = 48.9N

    d) 45° = > N = 53.9 * cos (45) = 38.1N
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