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Kinematic question

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data
    A rectangular block of length L is travelling on a smooth surface at velocity u. When it encounters rough ground with coefficient of friction mu, it decelerates to a stop. What is the time taken for the rectangular block to stop?


    2. Relevant equations
    F= (mu)mg


    3. The attempt at a solution
    Deceleration of the block is given by a = (mu)gx/L if only part of the block is on the rough ground. If the entire block is on the rough ground, the maximum deceleration is given by a = (mu)g. This means i have to split the question into two cases.
    1. time taken when x is less than or equal to L
    2. time taken when x is greater than L

    But I am stuck here. I don't know how to relate x to t and u.
     
  2. jcsd
  3. Sep 6, 2010 #2
    Friction force is independent of area of contact. So I think there is no need for taking a part of the block.

    deceleration of the block is (mu)g
    apply kinematics equation
    v^2 - u^2 =2as
    v=0 s=L
    find a relation between u and s from here
    use another equation - s=ut +0.5at^2
    find out time from this equation. ( here discriminant will become 0 from previous equation.)
     
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