Why Does Physics Use Positive g Value and What Does -kx Represent?

[nomorenomore]

http://physics.ucsd.edu/students/courses/summer2009/session1/managed/session1/physics1a/documents/Ch5_solutions.pdf

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!

 

[DrewD]

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.

 

[jtbell]

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.

 

[bigfooted]

... 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.

http://en.wikipedia.org/wiki/Free_body_diagram