# Stupid Little Physics Question

This might be trivial, but where do apples get the momentum to fall off trees? Yes, they have potential energy, but who ever talks about “potential momentum”?

One one hand, one might think an impulse (Fdt) is always required, such as from a breeze. But, couldn’t one argue an apple falls when it grows to a sufficient weight? Or, would an apple never fall without a nudge from a breeze, or a bird, man, etc., etc., etc. (Note: Not picking on apples, here!)

What is this “etc.”? - “The King & I”

An outside force can certainly help, but even with none I think it will eventually fall. If I remember my high school biology, after it is fully ripe the stem seals off and separates, like dead leaves do. So it’s physics and biology: the tree lets go and it falls, or it can fall before the tree fully lets go if an outside force helps.
Of course, there was this cute girl sitting in front of me during that class…

Well as the apple grows bigger it gains mass. As it does the downward force (from gravity) increases. Eventually the downward force overcomes the tensile strength of the apple stem and it breaks loose from the branch. At this point gravity takes over and it falls to the ground.

I’m not sure what you mean by asking where the momentum comes from. Momentum is defined as mass times velocity. Before the apple starts falling it has no velocity an so no momentum. As it falls momentum increases as it gains speed, then drops to zero again when it hits the ground.

Momentum is only conserved in the absence of any outside force. In the case of the apple there is an outside force; gravity.

“Drink your coffee! Remember, there are people sleeping in China.”

Dennis Matheson — dennis@mountaindiver.com
Hike, Dive, Ski, Climb — www.mountaindiver.com

Isn’t the sealed off layer called the abscission layer?

I’ve never heard of that. The outside force (F) times the fraction of time the force is acting (dt) is known as impulse. (Best example is a bat striking a ball.) The momentum must come from somewhere. I guess this kind of question can go on ad infinitum on the microscopic scale.

Yeah, woodja, you’re correct on the Biology front…even if that girl might have scrambled your brains!

tanstaafl

Well as the apple grows bigger it gains mass. As it does the downward force (from gravity) increases. Eventually the downward force overcomes the tensile strength of the apple stem and it breaks loose from the branch.

This is true to a point, but I don’t think it’s the whole story. I think the stem is naturally sealed off and separated, so it could hang around a while after it has reached it’s maximum size and before it is dropped.

I’ve pulled on green (unripe) apples and they’re stuck on there quite well, like they’d have to weigh 4 or 5 lb. before they broke the stem. Later in the season when they’re ripe a gentle tug will pull them off. Give them more time, the stem separates altogether and just the weight of the apple is enough.

This true of all fruits afaik.
Lewinsky and Clinton have shown
What Kaczynski must surely have known
That an intern is better
Than a bomb in a letter
Given the choice of how to be blown.

[/quote]

Originally posted by tanstaafl: Momentum is only conserved in the absence of any outside force. In the case of the apple there is an outside force; gravity.

I’ve never heard of that. The outside force (F) times the fraction of time the force is acting (dt) is known as impulse. (Best example is a bat striking a ball.) The momentum must come from somewhere. I guess this kind of question can go on ad infinitum on the microscopic scale.
[/quote]

Hmm… I’m willing to accept I may be wrong there. (I’m trying to remember back to my college physics here.)

In the case of the apple, momentum is conserved because as the apple falls towards the Earth, the Earth is also falling towards the apple (mutual gravitational attraction). Since the velocity vectors are in opposite directions the total momentum of the system is zero.

## Well, as the stem seals off it weakens to the point where the weight of the apple is enough to break it, but the sealing off isn’t neccessary to break something off. Think of ice building up on a limb or snow piling up on a roof. (Those of us on the east coast have seen plenty of these lately.) If the weight of the ice or snow exceed the strength of the limb or roof they will break or collapse.

“Drink your coffee! Remember, there are people sleeping in China.”

Dennis Matheson — dennis@mountaindiver.com
Hike, Dive, Ski, Climb — www.mountaindiver.com

—Well, as the stem seals off it weakens to the point where the weight of the apple is enough to break it, but the sealing off isn’t necessary to break something off. Think of ice building up on a limb or snow piling up on a roof. (Those of us on the east coast have seen plenty of these lately.) If the weight of the ice or snow exceed strength of the limb or roof they will break or collapse.—

Never said it (sealing off of stem) was necessary to break the stem, in fact I specifically said it wasn’t, i.e. picking green apples. I just said that :

–Well as the apple grows bigger it gains mass. As it does the downward force (from gravity) increases.
Eventually the downward force overcomes the tensile strength of the apple stem and it breaks loose from the branch.–

was an incomplete answer. And it is. The sealing off most definitely is necessary for the weight of the apple to be sufficient to break the stem. Before the stem seals off and separates, it can hold several pounds before breaking, a great deal more than even the biggest ripe apple (or it could on the apple tree in my back yard when I was growing up. Maybe they don’t make 'em like they used to).

I think that logic dictates that when the apple becomes sufficiently massive to overcome the strength of the stem, irrespective of the reason for the breaking of the stem, the apple will fall. I’d really like to see proof that no apple has ever grown sufficiently large to break it’s stem before the tree’s desired time.

Another part of the equation is the momentum and potential energy of the branch holding the apple immediately prior to separation. At that moment, the weight of the apple is pulling the branch down, and the branch is storing potential energy as a “spring” kept in tension.

Once the apple releases (by whatever triggering event), the end of the branch will also shoot up until it releases the additional “spring” potential energy caused by the weight of the apple and returns to its “natural” position under its own weight (most likely oscilating for a bit).

You made me go pull out my dynamics book for this one.

Jinx, your understanding of the terms is incorrect. Conservation of momentum applies to a closed system, i.e. no external forces (as stated). When the apple is on the tree, it is at rest, and momentum is conserved. That is because there is a force down (gravity) and an equal force up (the tree). When the apple falls (whatever reason), there is no more upward force to counteract the downward force. Thus the momentum is imparted by the external force on the apple. Or as stated, take the apple and Earth as a system, and momentum is conserved.

I’ll use my text book statement of Newton’s second law.

“[T]he resultant of the forces acting on the particle is equal to the rate of change of the linear momentum of the particle.”

Linear momentum is just mass times velocity.

“Thus, if the resultant force acting on a particle is zero, the linear momentum of the particle remains constant, both in magnitude and direction. This is the principle of conservation of linear momentum…”

As for the impulse, it does not refer to a gust of wind or a bird or whatever. Impulse is defined as the linear momentum through the time it acts, i.e. force through time. So the impulse is the force of gravity pulling the apple times the time of the fall.

The reason no one talks about potential momentum is because it is a null concept. Potential energy has a value. Potential momentum is zero - the object is at rest. The concept of stored momentum is called mass, i.e. mass at rest (zero velocity).

android209:

Yes, when the apple is massive enough to overcome the strength of the stem, it will fall. This happens usually when the stem closes off and becomes weak. The stregth of the stem declines until it is low enough for the apples weight to break it. (It can also be picked or knocked off by an animal, or a gust of wind can aid the process before the stem is completely weakened.)

I’m not sure what you’re saying on the last sentence. Are you saying that there may be some apple somewhere in the course of time that grew large enough to fall off before it was ripe? Maybe, but not typically. That’s what the process of ripeness is about. That’s why the stem strength is so much stronger before it closes off - to ensure the unripe apple can withstand it’s own weight, a stiff breeze, etc.

After having this issue kick around in my brain for a while as well as having some long dormant physics come back to me, I think I have realized the core of the OP’s question (no pun intended). I think the OP’s concern is conservation of momentum.

Under Newton’s laws, bodies at rest stay at rest and bodies in motion stay in motion (i.e. bodies conserve momentum), unless there is an unbalanced force acting on them. In the apple tree example, we have an apple sitting there perfectly quietly at rest (at least relative to its surroundings), and then – BAM – all of a sudden it’s plummeting downward to hit the good Dr. Newton on the head. Where’s the conservation of momentum in that?

One of the ways that momentum can be changed, as the OP points out, is by an impulse – when when object with momentum strikes another object, transferring some momentum between them. When a baseball bat redirects the pitched ball toward the outfield, you can analyze the interaction through conservation of momentum, with the total net momentum of the system being equal before and after the interaction of bat and ball (ignoring practical problems like the friction losses in the short time they are interacting and the energy that is being transmitted into the system throught the period of interaction by the batter’s wrists, etc.).

But a near-instaneous impulse is not the only way that objects can gain or lose momentum (otherwise we’d be bouncing off the walls, quite literally). We can apply an unbalanced force to an object, and it will change its momentum.

So we have our apple sitting up in the tree seeming to us to be quietly at rest. But actually it has strong forces seething up and down through it. First there is the force of gravity, drawing it inexorably toward the center of the earth. Second there is the lifting force transmitted through the stem, drawing it upwards toward the heavens. The remarkable thing is these forces are perfectly balanced, one exactly countering the other.

Until, one day the stem, growing weary of this ceaseless battle between heaven and earth decides to part. Then, from the perspective of the apple, there is an unbalanced force, with no stemwise lift to counter gravity’s pull. Then slowly but surely the apple begins to pick up velocity, gaining momentum as the force of gravity works on it, exchanging its gravitational potential energy for kinetic energy, until that moment when it makes its impact on Doc Newton’s cranium. This sudden imbalance in force is what makes the apple appear to fall without anything “giving” it momentum.

(The coefficient of elasticity of Dr. Newton’s wig and how high the apple will bounce are left as an exercise for the reader.)

Well, sometimes the apple stays there. . .and the tree falls. You have to sit around much longer than Newton did, though, to record such an event. But be careful where you sit.

Ray (Or was that just a Cheshire smile? )

____/^^^^
,----.vvvv/

Momentum is conserved when an apple falls. To see it correctly, you have to identify the system correctly. The system is the Earth and the apple.

As the Earth pulls on the apple, the apple pulls on the Earth. When the stem breaks, the apple falls toward the Earth and the Earth falls toward the apple. The momentum of the apple and the momentum of the Earth (due to this particular interaction) are always exactly equal and of opposite sign. The total momentum at all times is zero.

## Re “conversion” of mass to energy: E=mc^2 is an identity. Energy is, as far as physics is concerned, indistinguishable from mass. There is no conversion. The world appears otherwise to us, but that’s an artifact of our inadequate senses.

jrf

The potential kinetic energy of the apple is the sum of all the matter that was gathered to make it. Energy was expended to move the water and soil nutrients up from the roots, out the branches, to the ovary (fruit) being grown.

When the stem breaks for whatever reason, the apple falls.

Judges 14:9 - So [Samson] scraped the honey into his hands and went on, eating as he went. When he came to his father and mother, he gave some to them and they ate it; but he did not tell them that he had scraped the honey out of the body of the lion.