Practice It Use the worked example above to help you solve this problem. A skier

Question

Practice It

Use the worked example above to help you solve this problem. A skier starts from rest at the top of a frictionless incline of height 20.0 m, as shown in the figure. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.186. Neglect air resistance.

(a) Find the skier's speed at the bottom.
  19.8m/s

(b) How far does the skier travel on the horizontal surface before coming to rest?
  108m

EXERCISE

Use the values from PRACTICE IT to help you work this exercise. Find the horizontal distance the skier travels before coming to rest if the incline also has a coefficient of kinetic friction equal to 0.186. Assume that = 20.0°.

Explanation / Answer

a)
use conservation of energy
potential energy at top = kinetic energy at bottom
m*g*h = 0.5*m*V^2
g*h = 0.5*V^2
9.8*20 = 0.5*V^2
V=19.8 m/s
Answer: 19.8 m/s

b)
Now friction will do some work and dissipate energy
frictional force = miu*m*g
magnitude of work done by friction = miu*m*g*d

use work energy theorem:
kinetic energy at bottom = work done by friction
0.5*m*v^2 = miu*m*g*d
0.5*v^2 = miu*g*d
0.5*(19.8)^2 = 0.186*9.8*d
d=108 m
Answer: 108 m

Exercise:
length of incline = h/sin 20=20/sin 20 = 58.5 m
frictional force on incline = miu*m*g*cos 20
Total work done = initial potential energy
miu*m*g*cos 20 * 58.5 + miu*m*g*d = m*g*h
miu*g*cos 20 * 58.5 + miu*g*d = g*h
0.186*9.8*cos 20 * 58.5 + 0.186*9.8*d = 9.8*20
100.2+ 0.186*9.8*d = 19.6
d=-44 m

Since d is negative So, it will be stuck on the incline itself
It will never come at the bottom

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