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So let's say I'm sitting in a chair. Say I have very strong arms for my weight class. I pull up on my chair with all my might -- why can't I pull myself up off the ground?

I imagine the answer is "Newton's third law" but then how come in practice I actually can pull myself up off the ground in the chair if I sort of "jump it" first? Stand on the chair, squat down, spring up and grab the chair and it sort of comes up with you off the ground. Hard to describe but it's sort of like "jumping up off the chair and taking the chair with you."

Why is the first situation impossible but not the second?

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When you try and lift the chair up, you're really doing something else.

You're just clamping your butt down firmly on the seat. The force you apply upwards on the chair is causing a reaction in your arms, which actually pushes your body downwards. If you remain still, the system is in static equilibrium; and the centre of mass remains the same.

In your situation where you "jump off the chair, but take the chair with you"; the main point is that you jump off the chair to raise your centre of mass (since we have internal energy in our bodies we can produce the energy for that, and in fact, it raises the centre of mass of the man-chair system). You then apply a force from your hands upwards. The reaction force still pulls you downwards. The difference is, since you are no longer firmly planted on the chair; this downwards motion isn't resisted by the chair (and thus required from your hands, leading to infinite force required). Instead, the force you apply moves your mass down, and the chairs mass up (keeping the centre of mass the same, until you begin to fall due to gravity; turn the potential energy to kinetic energy, and dissipate that on the ground).

You don't need to even "jump" on your chair to test this. Just crouch low in the chair and then bring your upper body up quickly while trying to pull the chair up. The chair will actually be able to make a (small) jump.

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Accelerating an object by pulling on it works because you apply a force to it, then push against a different (more massive) object; the force the third object applies back to you allows the system of you and the object you are pulling to move. If you pull up on the chair with your arms, you are simultaneously pushing down on it with your body. You and the chair are a closed system. Whenever you pull on something, you must resist its paired force on you against some other object (e.g., pulling a wagon with your arm while pushing against the ground with your legs allows you and the wagon to accelerate, whereas pulling on the wagon and pushing on it with your legs just results in a greater force on the wagon, and thus a greater pull on you equal to the pull on the wagon).

If you propel yourself up from the chair, once your body is in the air you already have upward momentum, which you can "share" (for lack of a better term) with the chair by holding onto it.

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The key difference is that if you attempt to pull yourself up slowly, you're basically not accelerating. For all intents and purposes, your acceleration is 0. This means the forces on you must be balanced so that the sum to 0. The act of pulling up on the chair means the chair must pull down on your hands (equal and opposite reactions). This downward pull on your hands is exactly countered by an upward push from the seat of the chair through the seat of your pants. The harder you pull with your hands, the more force you will observe through the seat.

If you squat, "jump," and then pull up, the story is a bit different. During the brief momentary period where you are "jumping," you leave the seat a bit and have a velocity upwards. Now there is no force pushing up through the seat of your pants at all. If you pull up on the chair, no force counteracts it.

How does that work with Newton's laws? As you pull up on the chair, the chair pulls down on your (equal and opposite reactions). This gives you a net non-zero force on your body and you are accelerated downwards by that force. This acceleration eventually pulls you back down to the chair, at which point no more pulling with your hands is going to make the chair go any higher!

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protected by Qmechanic May 19 '17 at 15:39

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