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23 February, 13:31

A 45-kg box containing a new bicycle has just arrived in the front porch and two brothers are fighting over it. The first brother pulls with a five of 52 N, while the second brother pulls on the opposite direction with a force of 125 N. What is the minimum coefficient of static friction that will prevent the box from moving?

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  1. 23 February, 15:04
    0
    0.17

    Explanation:

    Draw a free body diagram. There are five forces on the box:

    Weight force mg pulling down

    Normal force Fn pushing up

    Applied force 52 N pulling to the left

    Applied force 125 N pulling to the right

    Friction force Fnμ pulling to the left

    Sum of the forces in the y direction:

    ∑F = ma

    Fn - mg = 0

    Fn = mg

    Fn = (45) (9.8)

    Fn = 441

    Sum of the forces in the x direction:

    ∑F = ma

    125 - 52 - Fnμ = 0

    Fnμ = 73

    μ = 73 / Fn

    μ = 73 / 441

    μ = 0.17
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