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: Conceptual difficulty - Work

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data

    I am worried that I don't understand a basic part of figuring out the component forces in the following problem. I have a full worked example but there is a few steps which I don't understand why we use sin for the x component and not cos (understand why I am really worried as it appears to be basic trig :/)

    A 58-kg skier is coasting down a 25° slope, as Figure 6.7a shows. Near the top of the slope, her speed is 3.6 m/s. She accelerates down the slope because of the gravitational force, even though a kinetic frictional force of magnitude 71 N opposes her motion. Ignoring air resistance, determine the speed at a point that is displaced 57 m downhill.

    2. Relevant equations
    vf = √2(KEf) / m
    = √(2(1/2 mv02 + Sigma F cos theta s)/m
    = √(2(1/2 mv02 + mg sin 25 - fk s) /m
    = √(2(1/2 mv02 + 170N cos 0 x 57) / 58
    = 19m/s

    3. The attempt at a solution

    This was in my textbook:

    a free-body diagram for the skier and shows the three external forces acting on her: the gravitational force , the kinetic frictional force , and the normal force . The net external force along the y axis is zero, because there is no acceleration in that direction (the normal force balances the component mg cos 25° of the weight perpendicular to the slope). Using the data from the table of knowns and unknowns, we find that the net external force along the x axis is:

    SigmaF = mg sin 25 - fk
    = (58)(9.8)(sin 25)(71)
    = 170N

    I look at sin and think we are looking at y component. I can't see why we would used sin for x component - can someone explain?

    Many thanks


    ps. please forgive formating - each time I use latex it just puts large gaps in the place of symbols :)
  2. jcsd
  3. Sep 13, 2010 #2
    AH! My free body diagram was incorrect - all good don't need a reply. thanks anyway those who read through my problem. Sorry for inconvenience.
  4. Sep 13, 2010 #3
    Friction is a nonconservative force, so you can't use conservation of energy.

    Sin is used for the x component because you have to draw a similar triangle for the normal force of the skiier. The angle between the force opposite the normal force and gravity is theta. Then trig will tell you that the x component is mgsin(theta).
  5. Sep 14, 2010 #4
    Thank you very much! This really helped me consolidate my understanding :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook