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Energy and springs

  1. Sep 26, 2007 #1
    1. The problem statement, all variables and given/known data
    A 2.0 kg package is released on a 53.1◦
    incline, 4.0 m from a long spring with force
    constant 120 N/m that is attached at the
    bottom of the incline. The coefficient of
    friction between the package and the incline
    are µs=0.40 and µk=0.20. The mass of the
    spring is negligible.
    a. Show that the maximum
    compression of the spring is 1.06m.
    b. The package rebounds back up the
    incline. Show that the package
    comes to rest at a distance 1.32 m
    below its initial position.

    3. The attempt at a solution

    I want to use that K_1 + U_1 + W_other = K_2 + U_2

    W_other in this case is the work of friction and the work of the spring?
  2. jcsd
  3. Sep 26, 2007 #2
    - which are both negative, because they work opposite of the direction of motin?
  4. Sep 26, 2007 #3


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    Staff: Mentor

    Sliding down the incline, before the spring contact, the gravitational potential energy transform into kinetic energy as the mass accelerations and frictional energy which is dissipated (lost). Then the spring is being compressed, the mass is doing work on the spring (compressing it) and the spring is storing the energy (which is equal to the KE - energy lost to friction). Then the spring stops at some deflection and recoils the mass.

    Without friction, the springs stored energy would become the KE of the mass. But with friction some energy is lost.
  5. Sep 26, 2007 #4
    So at the point where the spring and block hit eachother (I know the velocity at this point), I can use:

    K_1 - W_fric - W_spring = U_2

    to find the distance the spring is compressed?
  6. Sep 26, 2007 #5
    I mean

    K_1 + W_fric + W_spring = U_2

    but W_fric and W_spring are negative.
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