How to determine sign of $g$? It is said that we take it negative if any body is in upward motion. So why we don't take it positive when we observe downward motion.It is very confusing.
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$\begingroup$ You can use both, if you do it consequently, all the results will be the same. $\endgroup$– peterhCommented Jan 10, 2018 at 8:57
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2 Answers
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$g$ has no sign. That is just the size of the gravitational acceleration. In the same way that your pushing force on a table has no sign.
But when you decide on a coordinate system, then you might add negative signs to everything that points in the negative direction. You will add negative signs to accelerations and forces and so on. Not because they "are negative", but only because they happen to point opposite to whichever choice of axis we have made.
$g$ is just a number with no sign that says how much gravity affects you. It will never have a sign - but an acceleration might happen to be equal to $g$, and it might happen to point opposite to whichever axis we choose. And then you will see $-g$. But again, that is not due to $g$ being negative; it is only due to us choosing the coordinate system.
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$\begingroup$ Yes i asked this question with refering to coordinate systems. It is said that g will be negative for upward or downward motion if we take upward direction as increasing or positive direction. Moreover g will positive if take downward direction as increase or positive direction. These two points are making me confused. How to understand them? $\endgroup$– ADRCommented Jan 10, 2018 at 6:38
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$\begingroup$ @AmritDas Imagine a ball falling. Weight $w=mg$ pulls downwards. Air resistance $D$ pulls upwards. If we choose an axis pointing upwards, then we will write $$D-w=m(-a)\Leftrightarrow D-mg=m(-a)$$ The weight $w=mg$ is negative due to our choice of axis. Not $g$, but $w=mg$. If we choose an axis pointing downwards, then we will write $$-D+w=ma\Leftrightarrow -D+mg=ma$$ Here the weight $w=mg$ is positive due to our choice of axis. As you see, we are never dealing with a sign for $g$, only with a sign for the force. And signs only depend on choice of axis. $\endgroup$– SteevenCommented Jan 10, 2018 at 7:12
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$g$ refers to gravitational acceleration due to gravitational force. When an object moves upwards, it moves against gravity, so it decelerates at a rate of $9.81\;\mathrm{ms^{-2}}$, meaning it accelerates at a rate of $-9.81\;\mathrm{ms^{-2}}$. When moving downwards, it moves with gravity, so it accelerates at a rate of $9.81\;\mathrm{ms^{-2}}$.
answered Jan 10, 2018 at 5:43
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$\begingroup$ In most of the examples g has been taken negative no matters whether any body is in upward or downward motion. The idea behind this is stated as "It will be always negative if we take up as positive ". How ? $\endgroup$– ADRCommented Jan 10, 2018 at 6:00
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$\begingroup$ What do you mean? Where did you get such an idea? $\endgroup$ Commented Jan 10, 2018 at 6:02
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$\begingroup$ I am sorry I don’t understand what you mean $\endgroup$ Commented Jan 10, 2018 at 6:07