(b) Find the distance traveled on the horizontal, rough surface.
Apply the work-energy theorem as the skier movers from (B) to (C).
Wnet = -fkd = ΔKE = 1/2mvc^2 - 1/2mvB^2
Substitute vC = 0 and fk = xμkn = xμkmg.
- xμkmgd = - 1/2mvB^2
Solve for d.
d = vB^2 / (2μkg) = (19.8 m/s)^2 / (2(0.192)(9.80 m/s^2))
d = 104.18 m
Remarks Substituting the symbolic expression vB = √(2gh) into the equation for the distance d shows that d is linearly proportional to h: Doubling the height doubles the distance traveled.
Exercise 5.8
Find the horizontal distance the skier travels before coming to rest if the incline also has a coefficient of kinetic friction equal to 0.192.
Compute the distance traveled when there is no friction on the incline. When there is friction on the incline, do you expect the distance traveled to be larger or smaller than this?