When Should 'g' Be Negative in Physics Equations?

[jteh]

Hi PF, just a quick question that always seems to confuse me.. when should 'g' be negative in equations? Intuitively, I tend to always substitute -9.81 m/s into equations but it seems that this can be incorrect in special cases.

Are there certain situations where 'g' should be or shouldn't be negative??

Thank you!
Jess.

 

[ideasrule]

For kinematics equations, when you're using g as the acceleration, define a coordinate system first. That is, define an axis and choose a direction to be positive. If the acceleration due to gravity is in that direction, you use positive g. If the acceleration is in the opposite direction, you use negative g.

For equations like F=mg, you never want to use -g in place of g. This is because you want F to be positive, since positive forces are easier to think about.

 

[jteh]

Thank you so much! Great explanation.

 

[Redbelly98]

Just adding to ideasrule's excellent explanation...

I've noticed that textbooks tend to use upward as the positive direction (a=-9.81 m/s²) when the motion is upward, or at least is upward at the beginning of a projectile's trajectory. Downward might be taken as positive (a=+9.81 m/s²), but only when the motion is always downward, i.e. the object is initially falling or it is dropped from rest.

If you're ever in doubt in a kinematics problem, just take upward as positive and use -9.81 m/s².

p.s. Welcome to Physics Forums, jteh.

 

[rwisz]

Hello Jess,

That is a great question! The value of 'g' in equations depends on the direction of the acceleration due to gravity. In most cases, we assume that the acceleration due to gravity is acting downwards, towards the center of the Earth, which is why we use a negative value for 'g' (-9.81 m/s^2).

However, there are some situations where the acceleration due to gravity may act in the opposite direction, for example, if you are considering an object in freefall near the surface of a planet with a very low mass. In such cases, the value of 'g' would be positive.

It is important to carefully consider the direction of acceleration in each specific case and use the appropriate sign for 'g' in the equation. Using a negative value of 'g' when it should be positive, or vice versa, can lead to incorrect results.

I hope this helps clarify any confusion about the use of 'g' in equations. Keep up the great questioning!

Best,