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Acceleration of a Bucket and Tension Forces

  1. Feb 9, 2012 #1
    1. The problem statement, all variables and given/known data

    A 14.0 bucket is lowered vertically by a rope in which there is 169 of tension at a given instant.

    What is the acceleration of the bucket?

    Is it up or down?

    2. Relevant equations

    F = ma

    3. The attempt at a solution

    F / m = a

    (169 N) / (14 kg ) = 9.81 m/s^2 - x

    12.07 m / s ^2 - 9.81 m/s^2 = - x

    2.3 m/s^2 = - x
    -2.3 m/s^2 = x

    I initially thought the acceleration of the bucket was down because of what I got for "x" but that is incorrect. Is the acceleration of the bucket up because 9.81 - (-2.3 ) = +12.07 ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 9, 2012 #2

    PhanthomJay

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    Science Advisor
    Homework Helper
    Gold Member

    You are correct that the acceleration is up. But you shouldn't be solving the problem by your method. Instead, draw a free body diagram and use Newton's 2nd law, which states that [itex]F_{net} = ma [/itex], where [itex]F_{net} [/itex] is the sum of the tension force up and the weight force mg down. Since the Tension force is greater than the weight, the net force, and acceleration, must be up.
    a = __?___?
     
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