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-g or g? and what's -kx?

  1. Mar 4, 2014 #1
    http://physics.ucsd.edu/students/courses/summer2009/session1/managed/session1/physics1a/documents/Ch5_solutions.pdf [Broken]

    Please go to the website and scroll down to question 75a,
    why is g=9.8ms^2 is used in the solution instead of g=-9.8ms^2?
    Isn't it defined by the question that downward is negative? ( x1=-0.100m )

    For part d,
    what is -kx in the solution?
    Isn't it -1/2kx^2?

    Thank you very much!!
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 4, 2014 #2
    g is usually defined as ##9.8\frac{m}{s^2}##. If you want the negative, then you write -g. In this problem, the positive value is used since it is used in an expression for potential energy. If I were writing the force of gravity on an object of mass ##m##, I would write ##F=-mg##.

    ##-kx## is a force ##\frac12kx^2## is an energy.

    Even though you aren't asking for help on your homework, this might be better posted in the homework section.
  4. Mar 5, 2014 #3


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    Staff: Mentor

    By convention, g is generally understood to be the magnitude of the acceleration due to gravity. The magnitude of a vector is always positive. When we use g in an equation, if we need a minus sign to indicate direction, we show it explicitly in the equation instead of "burying" it inside g.
  5. Mar 5, 2014 #4
    ... so the sign in your equation depends on what you define as 'up'. The basis of determining the sign in practice is by drawing a free body diagram, define the 'x' and 'y' direction, and write down the force-balance. This balance is of course independent on what you choose as up or down.

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