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Principle of conservation of linear momentum equation

  1. Jul 27, 2013 #1
    1. The problem statement, all variables and given/known data

    A massless spring attached to a wall lies on a frictionless table. It has a block of mass 2kg attached to one end, initially the block is at rest. Another block, also of mass 2kg is sliding on the table top with a speed 8m/s. At t = o the moving block collides with the block on the spring . The two stick together and oscillate back and forth. If the spring constant is 16 n/m, find an expression x(t) which describes the motion of the blocks that are stuck together.


    2. Relevant equations
    -Principle of conservation of linear momentum equation



    3. The attempt at a solution

    Step 1:
    I applied principle of conservation of linear momentum to the system to find the velocity after the collision.

    Step 2:
    I obtained the angular velocity with the data provided

    Step 3:
    I associated the harmonic motion of the system to that of a sin function - the rest/equilibrium postion equals zero

    Step 4: I don't know how to obtain the maximum positions for the oscillation -

    In my attempt the position at any time of the SHM is x(t) = 2 * sin2t

    Please correct me if i am wrong ...
     
  2. jcsd
  3. Jul 27, 2013 #2
    I don't remember the formulae, but use F=kx for the spring. Use F=ma (so basically kx=ma) Acceleration in SHM is opposite to the direction of travel Using that, you'll get an euqation for your SHM.

    The first 3 points are correct. The point of impact of the two blocks is the equilibrium position.
     
  4. Jul 27, 2013 #3

    ehild

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    Gold Member

    But you know the maximum speed...


    How did you get it? And how did you define x? In what direction is it positive? In what units is it written?
    (If you specify the direction and units, it is correct)

    ehild
     
  5. Jul 27, 2013 #4
    I obtained the maximum speed using the principle of conservation of linear momentum, i took the first derivative of the postion function with respect to time and equated the initial velocity at time zero - i then was able to determine the maximum displacement. Direction positive is along the positive x - axis(to the right).

    I just needed you to verify whether my approache is OK
     
    Last edited: Jul 27, 2013
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