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Homework Help: Finding Tension and Acceleration on Frictionless Surfaces

  1. Nov 8, 2008 #1
    1. The problem statement, all variables and given/known data
    For the following system 1) Find the tension in the string
    2) find the acceleration of each of the masses

    The diagram of the system looks like this

    __|__.................__|__ ( . ) are placeholders to make the diagram look accurate

    Basically a mass of 200g on a frictionless surface attached to 2 other masses (100g and 200g) hanging over the edge of the surface with a string on frictionless pulleys. String has no mass and can not expand. Gravity is 9.8 m/s^2.

    The attempt at a solution
    First off I converted all my masses to Kg
    I have numbered each mass from left to right from 1-3 and have drawn free body diagrams for them. These are the equations I got for each

    Fnet = ma
    Fnet = T-Fg
    Fg= mg
    ma = T-Fg
    (0.1)a = T-0.98
    So: T = 0.1a + 0.98
    a = (T- 0.98) / 0.1

    Fnet = ma
    Fnet = T1 - T2 (T1 and T2 are the tensions to the 1st and 3rd masses, respectively)
    T1 - T2 = ma
    T1 - T2 = 0.2a

    Fnet = ma
    Fnet = T-Fg
    Fg = mg
    ma= T-Fg
    0.2a = T-1.96
    So: T = 0.2a + 1.96
    a = (T-1.96) / 0.2

    I am stuck at whether the mass that is on the surface will even matter to the acceleration and tension of the system because the surface is frictionless so would that mean I could solve as if there is no mass there? Or would I have to isolate the system into 2 systems, 1,2 and 2,3, then solve for each tension and acceleration and go from there?
  2. jcsd
  3. Nov 8, 2008 #2


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    Science Advisor
    Homework Helper
    Gold Member

    You're doing OK except for a couple of things. You should first note that tensions in ideal strings wrapped around ideal pulleys are the same on both sides of the pulley. So what you call T in your FBD of mass 1, you should call T1; and what you call T in your FBD of mass 3 you should call T2. Secondly, be consistent with your plus and minus signs; since you have assumed that the lighter hanging mass is moving upward, then mass 3 must be moving downward, and mass 2 must be moving to the right. Then just solve the 3 equations for the 3 unknowns T1, T2, and a.
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