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Newtonian Mechanics: simultaneous equations

  1. Jun 19, 2016 #1
    1. The problem statement, all variables and given/known data
    Figure 5-12 shows a block S (the sliding block) with mass
    M 3.3 kg. The block is free to move along a horizontal
    frictionless surface and connected, by a cord that wraps over
    a frictionless pulley, to a second block H (the hanging
    block), with mass m 2.1 kg. The cord and pulley have neg-
    ligible masses compared to the blocks (they are “massless”).
    The hanging block H falls as the sliding block S accelerates
    to the right. Find (a) the acceleration of block S, (b) the ac-
    celeration of block H, and (c) the tension in the cord.

    2. Relevant equations
    Block S:
    Tx=ma (on the X axis)

    Block H:

    T-mg=-ma (y axis)

    3. The attempt at a solution
    I understand the theory and question, my problem lies with my math skills. Because of the two unknown variables you can solve them simultaneously, however the sample problem assumes I remember how to do it!

    I want to understand how you can mathematically go from the two equations on top to a=(m/M+m)g on the y axis.
    Thank you for the help!
  2. jcsd
  3. Jun 19, 2016 #2


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    Science Advisor

    To avoid confusion you need to use M and m in your relevant equations.
    Also note that what you've called Tx is equal to what you've called T (and of course a is the same also) so you can plug one equation into the other and solve for a.
  4. Jun 19, 2016 #3
    After playing around with the equations I got it. Thanks for the help! I should pay more attention to the variables. :D

    I ended up going like:
    T-mg=-ma -----> T=-ma+mg
    T=Ma -----> (plug in eqquation number 1) -ma+mg=Ma ----->Ma+ma=mg------->a(M+m)=mg----->a=mg/M+m

    Would this set up be okay?
  5. Jun 19, 2016 #4


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    Science Advisor

    That looks right. Good work.
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