1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Free Response: Skier moving down a slope

  1. Jan 22, 2004 #1
    19) An Olympic skier moving at 20m/s down a 30degree slope encounters a region of wet snow, of coefficient of friction, .74

    a. How far down the slope does he go before stopping?

    I know the answer is 144m, but how do I get there?


    b. How much mechanical energy is lost in this process?
    1/2(3.06)(20)^2 + (3.06)(9.8)(72)
    612+ 2159.136 = 2771.136J lost
     
  2. jcsd
  3. Jan 23, 2004 #2

    HallsofIvy

    User Avatar
    Science Advisor

    There are three forces acting on the skier- the force of gravity downward which breaks into components -mg sin(30) down the slope and
    -gm cos(30) perpendicular to the slope- the push of the slope upward which opposes the force perpendicular to the slope- and the friction force which opposes the down slope force and 0.74 mg cos(30). The net force, down the slope is -mg sin(30)+ 0.74 mg cos(30)= mg(.74 cos(30)-sin(30))= 0.14mg= 1.38m.
    The acceleration due to that is F/m= 1.38 m/s2.
    Since the acceleration is a constant and the initial speed was 20 m/s down the slope, the speed at time t is 1.38t- 20 m/s. The distance down the slope at time t is 0.69t2- 20t.
    The skier stops when her speed is 0: 1.38t- 20= 0 or t= 20/1.38= 14.5 seconds. In that time she has gone (0.69)(14.52- 20(14.5)= -145 m (negative because it is down the slope).

    "b. How much mechanical energy is lost in this process?
    1/2(3.06)(20)^2 + (3.06)(9.8)(72)
    612+ 2159.136 = 2771.136J lost"

    Where did the "3.06" come from? You didn't tell us the mass of the skier!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook