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Energy and Block on Incline

  1. Feb 27, 2008 #1
    1. The problem statement, all variables and given/known data
    A block with a mass of 8.7kg slides down a hill with an angle of 27.4 degrees at an initial velocity of 1.66m/s. The friction uk between the block and hill is 0.62. What is the distance the block slides down the hill?

    I solved the equation using components and kinetics, but I'm not quite sure how to solve it using energy conservation.

    2. Relevant equations
    For energy:
    I know
    initial energy=final energy
    KE+PE= ? +ukNx ?????

    3. The attempt at a solution

    Here is my work solving it with components
    N(0,1)+mg(sin27.4, -cos27.4)+ukN (-1,0)=ma (1,0)



    hopefully doing it this way is also right. Thank you for any help!
  2. jcsd
  3. Mar 1, 2008 #2

    Shooting Star

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    > a=gsin27.4-ukmgcos27.4

    m shouldn't be there.
  4. Mar 1, 2008 #3
    Oops, looks like i made a typo. but regardless of that the acceleration is still -0.89m/s^2

    however, i'm still pondering on how to do this que with energy conservation.

  5. Mar 1, 2008 #4

    Shooting Star

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    Initial KE + difference of PE_grav between initial and final positions = work done against friction = frictional force*distance.
  6. Mar 1, 2008 #5
    KE_f - KE_i = Work by gravity + Work by friction
    0 - KE_i = Work by gravity + Work by friction
    - 0.5 m * (1.66)^2 = (m * 9.81 * sin 27.4 - m * 9.81 * 0.62 * cos 27.4)*ans
    ans = 1.56 m

    Sorry, I wouldn't be able to explain any concepts behind what I did: use geometry and FBDs.
    But, this is the way you should be doing this; if you keep doing these questions
    your way, you will be in a big mess one day (maybe on your exam day)
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