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I think I explained that a bit vaguely at first.
Let's start it again from the beginning. First, two things hold true at any moment:
1. F_c = F + F_g
2. F_g always acts downward
Now, since we know that a force has directions, that may affect its sign (positive / negative), let's suppose that, on the vertical axis, upward is positive, downward is negative.
F_g always acts downward, so we can say that F_g = - 3.0 N.
I know the question says that the stone's gravity is 3.0 N, without the negative sign. It actually means that the gravity has a magnitude of 3.0 N.
Here, the magnitude of something means the modulus, or absolute value, or that thing. For gravity, its magnitude means | F_g |.
We can also say that the magnitude of a force does not consider the force's direction, so it doesn't have a +/- discretion.
But once we start to consider directions, we need to use +/- signs to designate them. And surely you can designate downward as positive - either way is okay. But let's take upward as "+" for this time.
We know that F_c always acts towards the centre. And let's suppose that F_c has a magnitude of 10 N.
Then, when the stone is at the top, F_c is acting downward (centre is below the stone). At this moment, F_c = -10 N.
Based on F_c = F + F_g, we can get: -10 = F + (-3) --> F = -7 N then F has a magnitude of 7 N.
When the stone is at the bottom, F_c is acting upward (centre is above the stone). Then F_c = +10 N.
Again, using F_c = F + F_g, --> +10 = F + (-3) --> F = +13 N --> magnitude of F is 13 N.
You can see, at the top and the bottom, the gravity has opposite effects on the required magnitude of F.
This is why we need to take into account the stone's gravity.
P.S. We can also discuss on the moments when the stone is horizontally level with the centre (centripetal force acting horizontally), but that will involve the horizontal axis as well, and make things more complicated.
But if you are curious enough, we can discuss this in a separate chat.
Okay, I now did understand the significance of including the weight but the equation that you have given here F_c = F + F_g and the equation you used in the first reply where the tension is 18N, and is equal to the sum of the stone's gravity and the centripetal force. My confusion is that are these two the same?
From the question
Tension(F) = 18N
Centripetal force(net force)(F_c) = ??
Weight of the stone ( here it's F_g) = 3.0N
Net force = F - F_g = 18 - 3 = 15N
So is it "F_c = F - F_g" OR "F_c = F + F_g" ?
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