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

 

[PJC01]

The use of g=9.8ms^2 in the solution is based on the convention that downward direction is considered positive. This convention is used in many physics problems and does not change the overall result of the solution. It is important to note that the value of g may vary depending on the location and altitude, but for simplicity, a standard value of 9.8ms^2 is often used.

As for -kx in the solution, it represents the force exerted by a spring with spring constant k at a displacement of x. This value is derived from the formula for the potential energy of a spring, which is given by -1/2kx^2. Therefore, -kx is used to calculate the potential energy of the spring in the given problem. I hope this helps clarify your understanding.