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27 November, 10:50

A 61 kg skier on level snow coasts 184 m to a stop from a speed of 12 m/s. (a) Use the Work-Energy Theorem to find the coefficient of kinetic friction between the skis and snow. (b) Suppose a 75 kg skier with twice the starting speed coasted the same distance before stopping. Find the coefficient of kinetic friction between that skier's skis and the snow.

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  1. 27 November, 11:28
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    a) μ = 0.0398

    b) μ = 0.1595

    Explanation:

    a) d = 184 m

    Vi = 12 m/s

    vf = 0 m/s

    m = 61 Kg

    μ = ?

    We use the equation

    W = Kf - Ki (I)

    then we have

    W = F (friction) * d = - μ*N*d = - μ*m*g*d (II)

    Kf = m * (vf) ²/2 = m * (0) ²/2 = 0 J

    If (I) = (II)

    0 - m * (vi) ²/2 = - μ*m*g*d ⇒ μ = (vi) ² / (2*g*d)

    ⇒ μ = (12 m/s) ² / (2*9.81 m/s²*184 m) = 0.0398

    b) d = 184 m

    Vi = 24 m/s

    vf = 0 m/s

    m = 75 Kg

    μ = ?

    We use the equation

    W = Kf - Ki (I)

    then we have

    W = F (friction) * d = - μ*N*d = - μ*m*g*d (II)

    Kf = m * (vf) ²/2 = m * (0) ²/2 = 0 J

    If (I) = (II)

    0 - m * (vi) ²/2 = - μ*m*g*d ⇒ μ = (vi) ² / (2*g*d)

    ⇒ μ = (24 m/s) ² / (2*9.81 m/s²*184 m) = 0.1595

    The mass of the skier is not important in the analysis.
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