Sign of acceleration due to gravity doubt

[MarcoAurelio]

I have a question, according to rules for the sign of x and y-acceleration; when I should use the negative sign for gravity (g) in a problem, because it's confusing since I've seen that according to my textbook when an object is free falling g is negative (therefore acceleration is -9.8 ms^-2) but also my teacher said that when we throw an object upwards g is also negative. I'm confused, since I don't know when I should use a negative sign and when a positive sign for acceleration due to gravity.

 

[Dale]

Hi MarcoAurelio, welcome to PF!

The acceleration of gravity is down. So you use a negative sign whenever your coordinates are set up so that up is positive. It has nothing to do with the direction of the velocity of some object.

 

[Astrum]

The sign of any vector is determined by your coordinate system. As long as you stay consistent with your choices, the physics is the same.

When working with gravity in classical mechanics, it's standard to call it a force in the negative direction.

 

[MarcoAurelio]

Yeah, but I'm still confused, I reviewed rules for sign of acceleration, so if velocity is increasing in the negative y direction, shouldn't acceleration be positive since velocity is increasing?

 

[Dale]

The sign of the acceleration has nothing to do with the sign of the velocity. They are completely independent.

If your coordinates label up as the positive direction then the acceleration due to gravity will be negative, regardless of velocity. If you throw a ball up its velocity will initially be positive and acceleration will be negative. After it reaches the peak it will start traveling downward. Its velocity will then be negative and acceleration will remain negative as always.

 

[MarcoAurelio]

So acceleration of gravity is negative regardless the velocity of the object?

 

[Ethan0718]

So acceleration of gravity is negative regardless the velocity of the object?

Suppose that the positive y-axis is upward.

so, if the velocity is increasing in negative y direction.

For example:

$V_{iy}=-5\:m/s,\:V_{fy}=-10\:m/s,\:Δt=0.5\:s$

Then

$a_{avg,y}=\frac{V_{fy}-V_{iy}}{Δt}$

$a_{avg,y}=\frac{(-10)-(-5)}{0.5}=\frac{-5}{0.5}=-10\:m/s^{2}$

So, even if the velocity is increasing in negative y direction, the average acceleration is still positive so long as we choose the positive direction of y-axis is upward.

 

[MarcoAurelio]

Ah, so when the object goes down it's velocity is increasing negatively and therefore acceleration is negative?

 

[MarcoAurelio]

And when the object is thrown upwards the positive velocity is decreasing and therefore acceleration is still negative?

 

[Ethan0718]

Ah, so when the object goes down it's velocity is increasing negatively and therefore acceleration is negative?

And when the object is thrown upwards the positive velocity is decreasing and therefore acceleration is still negative?

1. Position, velocity and acceleration has two properties: magnitude and direction.

2. The above three quantities manifests their direction with positive or negative sign.

3. The sign of acceleration can be shown by its definition, the time rate of change of instantaneous velocity. Just like what I did.

4.The sign of acceleration can be judged by its direction. You can know its direction without calculating its value by definition because, according to Newton's Second Law, the direction of acceleration and net force are same. As long as you know (intuitively) the direction of net force (in your case, only gravity which is downward), you could know the direction of acceleration.

Here is the deduction:

$∵F_{net,y}\:=\:ma_{y}$

$∵Universal\;gravitational\;law$

$∴the\;gravity\;is\;downward.$

Let the positive y-axis direction be upward

$∴(-mg)\:=\:ma_{y}$

$∴-g=a_{y}$

In the fifth line, you should not rewrite (-mg) in this different form, m(-g), because the implication of latter is not force.

Anyway, the only way to determine the value of any physics quantity is calculating them by definition or by physics law.

 

[Mark44]

Ah, so when the object goes down it's velocity is increasing negatively and therefore acceleration is negative?

Yes, assuming that downward is the negative direction.

We usually don't say that the velocity is "increasing negatively." If the velocity is getting more negative, it is actually decreasing. On the other hand, if the velocity is negative (object is moving downward), but becoming less negative (such as, say, due to the deployment of a parachute), the velocity is increasing.

 

[MarcoAurelio]

Found this video



LOOK, I FOUND THIS VIDEO, THE INSTRUCTOR SAYS HE USES g as POSITIVE since he is considering the vectors to be referenced to such motion, what I'm saying comes from this comment the instructor made: "You can pick any direction you want to be positive, up or down. In that problem, we chose down as positive, so all other vectors are referenced to it. You could also have solved it by choosing up as positive. In that case, the acceleration due to gravity would be negative, and the velocities and displacements would be negative". IS THAT WHAT YOU WANTED TO SAY?

 

[Ethan0718]

Yes! The direction of positive y-axis is arbitrary but you should be careful if you're not always set positive y-axis direction upward. Sometime you would forget your positive direction.

 

[MarcoAurelio]

That's what I wanted to hear! Thanks Ethan0718, seriously my Teacher didn't explain this topic with enough seriousness, since was extremely confusing the sign.

 

[Dale]

Ah, so when the object goes down it's velocity is increasing negatively and therefore acceleration is negative?

Yes. If your velocity is initially -5 m/s and you accelerate at a rate of -1 m/s² for 2 s then your final velocity is -5 m/s + (-1 m/s² * 2 s) = -7 m/s.

And when the object is thrown upwards the positive velocity is decreasing and therefore acceleration is still negative?

Yes. If your velocity is initially 5 m/s and you accelerate at a rate of -1 m/s² for 2 s then your final velocity is 5 m/s + (-1 m/s² * 2 s) = 3 m/s.

 

[MarcoAurelio]

Thanks, also one more question, so according to this, when I'm calculating weight (which is the product of mass and gravitational acceleration), should I consider acceleration as negative since it's pointing down, or shouldn't I?

 

[Office_Shredder]

It doesn't matter whether acceleration is positive or negative as weight will be reported as a positive number regardless.

 

[MarcoAurelio]

Thanks people this really helped a lot.