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Projecting a block up to compress a spring!

  1. Dec 7, 2012 #1
    1. The problem statement, all variables and given/known data

    A spring( k=200 n/m) is fixed at the top of a frictionless plane inclined at angle θ=40 degrees . A 1.0 kg block is projected up the plane from an initial position that is distance d=0.60m from the end of the relaxed spring with an initial kinetic energy of 16J.

    a) what is the kinetic energy of the block at the instant it has compressed the spring 0.20m?

    2. Relevant equations

    3. The attempt at a solution

    My Answer:

    Et1 = Et2

    Ek1 = Et1 = 16J

    Et2 = Ek2 +Eg2 + Es2
    16J = Ek2 + (1)(9.8)(0.6 +0.2)(sin40°) + (1/2)(0.2)(0.2)2
    16J = Ek2 + 5.04J + 4J
    Ek2 = 6.96J

    My question is: do we have to account for the increase in gravitational potential when the block compresses the spring? cuz the block moves up higher when it compresses the spring. Thanks

    Professor's Answer:

    Ug = mgh
    = 1(9.8)0.6 sin 40
    = 3.80 J
    Us = ½ k Δx2
    = ½ 200 (0.2)2
    = 4 J
    And we have
    Total Energy before = Total Energy after
    K0 + Ug0 + Us0 = K + Ug + Us
    16 + 0 + 0 = K + 3.8 + 4
    K = 8.2 J
     
  2. jcsd
  3. Dec 7, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Of course you do. Looks like your professor made an error.
     
  4. Dec 7, 2012 #3
    thanks a lot.
     
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