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.

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.