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Mechanical Energy question (Skier going down a slope confusing )

  1. Jan 4, 2009 #1
    Mechanical Energy question (Skier going down a slope...confusing!!)

    First of all, I apologize ahead of time if my question seems to be really simple, but I have been working on it for at least two hours and still no progress (which is why this post made so late lol). My class has been working on standard/semi easy Mechanical energy questions and there was a day when we were tossed with this question that I feel was never covered. I've tried to solve this with several of my friends, but no luck.

    Here is the question:

    A skier takes off from the top of a slope 30.0m vertically above the bottom with an initial velocity of 1.90 m/s. The length of the slop along the surface to the bottom is 50.0m. During the ski run, the skis have an average frictional force exerted on them equal to one-third times the gravitational force. Calculate the velocity of the skier at the bottom of the hill.


    What I first noticed was that the Slope seemed to be in a 3:4:5 ratio. So the angles of the slope would be 90 degrees, 30 degrees, and 60 degrees.

    What I tried to do was...

    1.Take gravity and mutiply it by 1/3 resulting of a average frictional force of about 3.27
    2.Use the equation for WorkNet: WorkNet=∆KE
    =Final Kinetic Energy - Initial Kinetic Energy
    =(1/2 * mass * final velocity²) minus (1/2 * mass * inital velocity²)
    3.Find WorkNet:
    WNet= |Fa||d|cosѲ + |Ff||d|cosѲ
    *I ended up with a negative number but I pretended it was in absolute values*
    4.Changed "WorkNet=(1/2 * mass * final velocity²) minus (1/2 * mass * inital velocity²)" algebraicly so that Vf= √InitalVelocity + 2*WNet

    ...and from there I ended up with a final velocity of 16.7m/s


    Again I apologize if this question seems simple... it's just that I have no idea what to do. I hope the method I took was correct and ended up with the answer. If not, any advice would be greatly appreciated. I'd like to know the solution by a fellow member.



    Thanks in advance!!
     
  2. jcsd
  3. Jan 4, 2009 #2
    Re: Mechanical Energy question (Skier going down a slope...confusing!!)

    I dont know what youve done when you subtracted the kinetic energies, but that isnt how the energy equation would be set up. Net energy is conserved, so what energy the gravitational field loses is converted into kinetic energy of the skier plus the energy lost to friction.

    Here, the main part is finding the energy lost to friction. This problem was probably given to elucidate the working of the frictional force. You would tend to think that the net energy lost to friction would be frictional force * length of slope, but that is not so.

    Make a free body diagram of the skier going down the slope and start from there.
     
  4. Jan 4, 2009 #3
    Re: Mechanical Energy question (Skier going down a slope...confusing!!)

    Yeah I started off with the Free Body Diagram, but I realized that there was no mass on the skier. I did some researching around the net and read that mass would just be cancelled out instead, so im not sure what to do. What if I added the change in kinetic energy, would that work instead?

    Oh I thought the Kinetic Energy for the Frictional Force would be FrictionForce * Displacement * CosѲ.
     
    Last edited: Jan 4, 2009
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