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Kinematics - spring + friction

  1. Jan 10, 2010 #1
    1. The problem statement, all variables and given/known data
    http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam2/fa09/fig8.gif [Broken]
    A small block having a mass of 2 kg is in contact with an ideal spring of relaxed length 1 m and spring constant k = 100 N/m . The spring is compressed to a length of 0.5 m. The block is released from rest at x = 0.5 m. At x = 1 m the mass leaves the spring and comes to rest at x = 2 m. Throughout its entire motion the block slides on a rough surface with a coefficient of kinetic friction μk .

    Q1) The maximum acceleration of the block occurs the instant the block begins to move.

    Q2) What is the coefficient of kinetic friction of the surface?

    2. Relevant equations

    3. The attempt at a solution

    For the first question, i thought the acceleration is at maximum when the spring is about to move(at x=0.5m)... 'cause i thought the friction force will be exerted after this point reducing the acceleration...
    What's wrong in my thought?

    And, for the second question, i tried to get the velocity when x=1m using energy-conservation theorem, and i got m*v2 = k*x2 and hence v = 3.53

    Now i used the constant acceleration formula, the final velocity is zero, and initial v = 3.53,
    a= [tex]\mu[/tex]mg/2 and the displacement = 1.

    But then i got the answer as 0.62 which is wrong....

    What's wrong in here?

    Please help me out with those tiny little(?) two questions....
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 10, 2010 #2
    I think it`s related to hook`s law ( F =-kx )
    and newton`s second law
    hope somebody help us to solve this
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