In free-fall acceleration, how do I figure when g is positive or negative?

In summary, the direction of g, or acceleration due to gravity, can be positive or negative depending on the chosen system of coordinates. It is important to be consistent with sign assignments when describing motion in a particular direction. In general, the acceleration is always downwards, but the sign of g can change depending on the chosen direction of the y-axis.
  • #1
Elis
2
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In free-fall acceleration, how do I figure when "g" is positive or negative?

Homework Statement


My textbook is confusing me a bit. In general, when would "g" be positive and when would be negative? I thought it was when the particle was falling downward, it was positive and when it's going upward it's negative, but I seem to have that incorrect.

Somebody also told me that if I have y-coordinate with the bottom portion as positive and the top portion as negative, g would then be positive. However, she said it would also be positive if the reverse occurred. I don't quite understand that.

Could someone please explain this?


Homework Equations


No, eq. General question.


The Attempt at a Solution

 
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  • #2


It depends on what system of coordinates you choose to adopt. If the positive direction of your y-axis is up, then g will be negative. If your y-axis is pointing down, then g is positive.

All you need to make sure is that your sign assignments are consistent, so if your y-axis is pointing up, then a throw up against gravity would be described by: [tex]y(t)=vt-\tfrac{1}{2}gt^2[/tex]

If, however, I were to choose a y-axis pointing down, then the motion of the thrown object would be described by:
[tex]y(t)=-vt+\tfrac{1}{2}gt^2[/tex]
 
Last edited:
  • #3


Elis said:

Homework Statement


My textbook is confusing me a bit. In general, when would "g" be positive and when would be negative? I thought it was when the particle was falling downward, it was positive and when it's going upward it's negative, but I seem to have that incorrect.

It is a matter of convention whether you defined up as positive, or negative.

The acceleration is always downwards.

When an object is thrown upwards, its velocity is continually changing. You can think of this as adding small increments of velocity. If something is moving up at 20 m/s, and one second later it is moving up at 10.2 m/s, what is the velocity that has been added? Have you added a velocity going up, or added a velocity going down?

Cheers -- sylas
 
  • #4


I understand that now; thank you very much for your help.
 

What is free-fall acceleration?

Free-fall acceleration is the acceleration that an object experiences when it is falling under the sole influence of gravity. This acceleration is always directed towards the center of the Earth and is constant at approximately 9.8 meters per second squared.

How do I determine if g is positive or negative?

The sign of g (positive or negative) depends on the direction of acceleration. If the object is moving towards the Earth, the acceleration is considered to be positive. If the object is moving away from the Earth, the acceleration is considered to be negative.

What factors affect the value of g?

The value of g is affected by two factors: the mass of the object and the distance from the center of the Earth. The greater the mass of the object, the greater the force of gravity and therefore the greater the value of g. The further an object is from the center of the Earth, the weaker the force of gravity and therefore the smaller the value of g.

How does air resistance affect free-fall acceleration?

Air resistance, also known as drag, can affect the value of g by slowing down the acceleration of an object. This is because air resistance creates an opposing force on the object, reducing its acceleration towards the Earth. However, for most objects in free-fall, air resistance is negligible and does not significantly impact the value of g.

Does the value of g change on different planets?

Yes, the value of g can vary on different planets due to differences in their mass and size. For example, on the Moon, where the mass and size are smaller than the Earth, the value of g is only 1.62 meters per second squared. On the other hand, on Jupiter, which is much larger and more massive than Earth, the value of g is 24.79 meters per second squared.

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