1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    [/tex]

    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}
    [/tex]

    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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Blocks and Strings, Force Analysis
  1. Force on blocks (Replies: 1)

  2. Force on a block (Replies: 7)

  3. Force on block A (Replies: 9)

Loading...