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Tension, mass, and velocity

  1. Aug 20, 2008 #1
    1. The problem statement, all variables and given/known data

    I have a 12kg block that is raised by a rope. If the velocity of the mass is decreasing at a rate of 5 m/s^2, what is tension in the rope?

    2. Relevant equations


    3. The attempt at a solution

    My solution: T = mg+ ma = 180N

    Book solution: T+ma = mg => 60N

    I am confused as why you are subtracting here. I see that acceleration is in the downward direction (as stated by the question stem), but the object is still been raised. So shouldn't it be T = mg+ ma? Because to me, T+ma =mg looks like that acceleration of the mass is the upward direction (if that were the case the object would be increasing it speed not decreasing),
  2. jcsd
  3. Aug 20, 2008 #2


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    Homework Helper

    Hi Gear2d,

    This equation is not true.

    I think you might need to be a bit more careful with this equation. This equation should be either:

    \sum \vec F = m \vec a \mbox{ or } \vec F_{\rm net} = m\vec a

    and when you actually use it here, for example in the [itex]y[/itex] direction, you get:

    \sum F_y = m a_y\nonumber\\
    F_{1y}+F_{2y} = m a_y\nonumber

    since there are two forces. So what are the [itex]y[/itex]-components, including sign, of the tension and weight forces? And what is the [itex]y[/itex]-component of the acceleration? Those, with the correct sign, are what go into the force equation.

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