Can I slice them as turtles?
If you really like soup…
De Chelonian Mobile
While the apple is settling into the cushion, it is in motion. Therefore, the forces are not balanced. Gravity is stronger than the compression of the foam. As the foam compresses (much like a spring) the force becomes greater, until they equal out. At that point (minus some harmonic bouncing until the system settles) the forces are balanced.
while the apple is in motion, the equal and opposite force is the force of gravity. Gravity pulls the apple and the earth together - F=Ma The problem is that the massive (sorry) disparity in the earth vs. apple is such that we don’t see the earth’s equal and opposite reaction, being pulled to the apple.
This is the key to gravity and “equal and opposite”. Things are not “pulled to the earth” - gravity pulls two objects together with the same force. The difference is in the mas of those two objects. We don’t notice when the earth moves - at least in this context.
Maybe it can be considered that gravity is imparting a downward force to both the the glass and the table top. The table top achieves equilibrium. Then when the glass is added on top of it. The table bows ever so slightly more under the weight of the glass, imparted by gravity as well. Then the table top glass combination once again achieves equilibrium. The table top by bowing slightly absorbs the added energy of the weight of the glass. Which it will release when the glass is removed at some point. Energy will be expended by an outside force to lift the glass. The table will rebound in equal amount. While the glass is on the table, there is equilibrium. But whatever energy is required to lift the glass, was always pressing on the table, as well as the table resisting it.
A more long winded explanation of what others have already said. But maybe a better way to state it? When imagining a table and glass instead of the spring example directly.
I just thought of maybe an easier visualization.
A weight hanging on a string. Gravity pulls the weight down. All the individual atoms and molecules in the string have attractive forces to each other. So they hold the weight. So those forces are resisting the weight. Pulling up against it as well in all other directions. Too much weight and it overcomes those forces.
If you remove the table, the glass will fall. The glass is prevented from falling by the force from the table.
If you try lifting the table, the table with the glass will require more force than the table without the glass, the additional force comes from the glass pressing down on the table.
(Or, you know, the spring thing.)
You’re on the right path, but don’t conflate static analysis with Newton’s Third Law.
Statics: the weight is not accelerating, so the net force must be zero (Newton’s First Law). There are two forces on the weight: gravity pulling down and the tension in the string pulling up. The magnitudes must be the same for the sum to be zero.
Third Law: gravity pulls down on the weight. The weight pulls up on the Earth. Those forces are equal and opposite, to conserve momentum. Also, the tension of the string pulls up on the weight, while the weight pulls down on the string.
A good rule of thumb: if you’re looking at the forces on one object, you’re using the First Law. If you’re looking at forces on different objects, you’re using the Third Law.
I think that one of the reasons that it’s hard to see this intuitively is because if we hold something, then that requires effort.
Even if no work is being done on the object being held steady, lots of work is being done within your muscles to do so. This requires a precise amount of effort to keep it from raising or falling, we need to know how much force to apply to overcome gravity.
When we look at a table holding an object, we intuit that it is doing the same thing, that it is exerting an effort to hold that object. But a table is a solid and static object, it does not have various physiological costs involved.
A better demonstration would be to put your open hand on a table, then put an object on it. You are no longer exerting any effort to keep it up (assuming it’s not so heavy that it’s crushing your hand).
Here’s something else I don’t understand. If an apple is falling from a tree, it has an acceleration (a) of around 9.8 m·s⁻², and the downward force on the apple is f = ma. O.K., I get that. And then the apple comes to a rest on the ground. After it has come to a rest, we’re told it still has a downward force on it, and we are further told this force is f = ma. The apple is not accelerating anymore, but for some reason we still use 9.8 m·s⁻² to compute the force on it. I don’t understand why 9.8 m·s⁻² should still come in to play when it’s obviously not accelerating; after it comes to rest on the ground, a = 0 m·s⁻², not 9.8 m·s⁻².
I can “shut up and do the math.” But this has always bothered me.
An apple at rest on the ground still experiences the force of gravity; if it were eg a really really big boulder instead of an apple you could tell as you would be crushed beneath it. It does not have to move to experience this force.
It’s the same force, but now it’s not the only force. The sum of the forces is zero. It’s still 9.8 m·s⁻² because that is the a you will get if you instantly dig a hole under it.
Gravity doesn’t turn off; it’s always there. If an object isn’t accelerating, it’s because the net force on it is zero. You’ll need to look at all the forces on it.
For your apple examples, you’re getting different points of the process confused.
First example: apple in free fall. The forces on the apple are 1) the force of gravity. The force of gravity, in a convenient approximation is W = m g (“W” for “weight”), where m is the mass of the object and g is the local gravity constant (see Newtonian gravitation as evaluated at the surface of the Earth). Newton’s Second Law of Motion, m a = \Sigma F. We know the sum of the forces, so m a = m g, and thus the acceleration is a = g.
Second example: apple resting on the ground. The forces on the apple are 1) the force of gravity W = m g, and 2) the force of the ground on apple N (“N” for “normal”). We don’t know the normal force, but we do know the acceleration is zero, m a = \Sigma F = 0. That gives us 0 = W - N, and N = mg.
It still seems weird: when the apple is falling, it has a downward force on it because it has a non-zero mass and because it has a non-zero acceleration. After it comes to rest on the ground, it still has a downward force on it, even though the the acceleration is now zero.
And yea, I understand the two forces cancel. But it just seems weird that the acceleration component for each force is still a non-zero number, even though the two forces cancel.
ETA: I posted this before reading the above post by @Pleonast. Will read it now.
Relativity says that the apple laying on the ground is accelerating, the apple falling from the tree is not.
As an example, you, sitting in your chair right now, feel as though you are accelerating upward at ~9.8 m/s/s. If you were to jump out of a plane, then, until air friction becomes a factor, you are not feeling an acceleration.
So, if you think about the surface of the Earth accelerating at 9.8 m/s/s, then it makes more sense that that is the same rate at which the apple on the ground is accelerating, and why, when it fell from the tree, it stopped accelerating for a bit, until the Earth caught up.
If you want to lift the apple, you have to overcome the acceleration that it is already undergoing, and add to that.
No. The apple resting on the ground and that still falling from the tree are both under acceleration from the external observer’s frame of reference, and both have a reactive force opposing them (on the ground it is the impressed force of the reaction to the ground, and in mid-fall the ‘virtual force’ of inertia from D’Alembert’s principle). If you are in the apple’s frame of reference (an inertial frame of reference with no impressed forces) then it does not appear to be accelerating but rather the entire universe around it is accelerating.
Stranger
Right, if I am in a specific frame of reference, namely an accelerating or non-inertial one by standing on Earth’s surface, then I measure that the apple accelerates towards the ground. But that is only in that one frame of reference, a fairly arbitrary one, only given any weight as it’s the one that we all experience most of our lives, and so it is “intuitive”.
Yes, and the inertial frame of reference gives a better understanding of what is actually going on, once we can get over our intuitions formed by living our lives in an non-inertial reference frame.
It’s not arbitrary; it is literally any frame of reference other than the one attached to the motion of the apple. In any other frame of reference, either ‘inertial’ or under differential acceleration, the apple itself is seen as accelerating.
Stranger
Doesn’t this sentence use two different senses/meanings of the word “work”?
Right, but the frame attached to the apple is the one that gives the best explanation for what is actually happening, and why an apple on the ground feels weight, while one that is falling does not. The falling apple itself feels no acceleration (neglecting air resistance). A worm in that apple will have no weight.
There are two useful reference frames for this thought experiment. One is the non-inertial one standing next to the tree, watching the apple fall and then picking it up. The other is that of the apple itself, as it spends its life being accelerated, overcoming this acceleration with its stem, until one day, for a brief time, it is no longer accelerating, and the ground beneath the tree catches up accelerating it once more, then is accelerated even more as it is lifted in your hand.
Anyway, the point being is that @Crafter_Man asked why we measure weight in terms of acceleration, and explaining the difference between the two reference frames seems the most sensible answer. That there are an infinite number of other reference frames doesn’t really contribute to that understanding.