Why is Gravity Considered Positive in Applications of Newton's Laws?

[rambo5330]

Homework Statement

I was asked a very simple question today about finding the tension in a cable as a 1200kg elevator is accelerating downward at -1.05 m/s^2 . now I could answer the question easily
ma = T - mg
solve for T but what I couldn't answer was just the basic question when the peer asked mee why isn't gravity negative in this case. and that got me thinking why isn't gravity negative in the applications of Newtons laws?

If I have a 60 kg object sitting stationary on the ground it will have a normal force of N = mg obviously the object isn't accelerating in any direction but why are able to consider the acelleration of gravity as being positive in these scenarios? It's probably been explained several times on here but after searching I have found nothing that explains it in any detail.

Homework Equations

The Attempt at a Solution

 

[Matterwave]

the negative/positive g depends on your conventions.

If I say I accelerate at g downwards, then g is obviously "positive" in that scenario because I already indicated the direction as downwards.

In N=mg N is a force that points up, while mg is a force that points down. As long as we are aware of the scenario played out, and we get all the directions in check, we can just take g to be positive in that case.

The original equation was F=N-mg=0 which leads to N=mg. In that equation, because we put a minus sign in front of the mg, we are assuming g is positive. If we wanted a negative g, the equation should be F=N+mg=0 which leads to N=-mg.

This is the same with your original example. F=T-mg already takes care of the negative in that minus sign. We could also say F=T+mg=0 if we designate g as being negative.

 

[rambo5330]

thanks for the fast reply. That helps clear it up !