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Blocks and Strings, Force Analysis

  1. Mar 23, 2014 #1
    1. The problem statement, all variables and given/known data
    A block of mass M is connected with a particle of mass m by a light in-extensible string as shown in the figure. Assuming all the contacts as smooth, find the acceleration of the block after releasing the system. 2wmhw5u.png

    2. Relevant equations
    F = Mass * Acceleration
    Normal Constraint : The acceleration of two particles in contact is same along the line perpendicular to their line of contact.
    String Constraint : The length of the string is constant and could be used to find out the acceleration of the corresponding components using differentiation(using geometry).

    3. The attempt at a solution

    Using the FBD and Translational equations 501504.png

    The particle will have the acceleration both in x and y direction. The block will have the acceleration in x direction due to tension in the string and contact force .

    for block M
    [tex]\ T\ -\ N\ =\ Ma_x[/tex]

    The particle's acceleration in the x direction will be the same as that of the block in the x direction in accordance to the normal constraint.

    for particle m
    [tex]mg\ -\ T\ =\ ma_y\\
    \ N\ =\ ma_x\\
    \implies\ T\ =\ (m+M)a_x

    Using string constraint we get than the particle's acceleration in the y-direction would be 4times the acceleration of the particle in x-direction
    [tex]4a_x\ =\ a_y\\
    \implies\ mg\ -\ T\ =\ 4ma_x\\
    \implies\ mg\ -\ (m+M)a_x\ =\ 4ma_x\\
    \implies\ a_x\ =\ \frac{mg}{5m+M}

    But the answer I get is wrong and the correct answer is [itex]\frac{4mg}{17m+M}[/itex]

    Please help me out. :smile:
    Thanks for your time
  2. jcsd
  3. Mar 23, 2014 #2


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    Look at all those horizontal sections under tension. What are they pulling on?
  4. Mar 23, 2014 #3
    Right that won't be T but 4T.
    ie [tex]4T\ -\ N\ =\ Ma_x[/tex]
  5. Mar 23, 2014 #4
    Thanks for your input.
    I get the correct answer
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