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Work & Energy Problem

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    A block of mass 5.00 kg is given an initial velocity of 8.0 m/s. It travels 5.0 m over a rough surface with μ[itex]_{k}[/itex] = 0.250. It then slides up a ramp that rises at a 30° angle above the horizontal. How high does it go before coming to rest


    2. Relevant equations

    W = FΔs
    F[itex]_{k}[/itex] = μ[itex]_{k}[/itex] N
    Δk = 1/2 m v[itex]_{f}[/itex][itex]^{2}[/itex] - 1/2 m v[itex]_{i}[/itex][itex]^{2}[/itex]
    v = √2gh

    3. The attempt at a solution

    W = μ[itex]_{k}[/itex] Δs = (0.25)(5)(9.8)(5) = 61.25 J

    -61.25 = Δk
    -61.25 = 1/2 m v[itex]_{f}[/itex][itex]^{2}[/itex] - 1/2 m v[itex]_{i}[/itex][itex]^{2}[/itex]
    -61.25 = 2.5 v[itex]_{f}[/itex][itex]^{2}[/itex] - (0.5)(5)(8[itex]^{2}[/itex]
    v[itex]_{f}[/itex] = √((-61.25+160)/2.5)

    v = √2gh
    h = v[itex]^{2}[/itex]/2gh
    h = 6.28[itex]^{2}[/itex]/(2)(9.8)
    h = 2.01m


    Is this the right way to answer this question?
     
  2. jcsd
  3. Oct 23, 2012 #2
    is the ramp frictionless or is it also a rough surface? It looks like you assumed that it is frictionless, but I guess it makes sense to do that since it doesn't specify that in the problem.

    But yes, assuming the ramp is frictionless, it looks like you did it right.
     
  4. Oct 23, 2012 #3
    I believe the ramp is frictionless but the one thing that bothers me about my solution is the lack of the 30° angle in my calculations.
     
  5. Oct 24, 2012 #4
    yeah that would be a piece of extraneous information for this problem

    since you are using conservation of energy, the path that the object takes doesn't matter, only the initial and final states
     
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