Problem Solving Strategies

My father explained to me how rockets work, and he told me Newton's Third Law of motion worked here. I asked him why it works and he didn't answer. I have wasted over a week thinking about this problem, now I am giving up. Can anyone explain why Newton's Third Law works? For reference, Newton's ...

But, no source explains it clearly. So could you please tell why this law works sir?

Even the highly voted answer did not clarify this concept sir.

John Rennie

The third law is just a statement that momentum is conserved.

Intellex

@JohnRennie Then, why is momentum conserved sir? I understood the mathematical derivation of it.

John Rennie

Conservation of momentum is due to a fundamental symmetry of the universe called shift symmetry.

Basically this symmetry says the laws of physics are the same everywhere.

That symmetry implies that momentum is a conserved quantity. This is described by Noether's theorem, though the maths involved is a bit advanced for all but physics undergrads.

Intellex

@JohnRennie So, temporarily we must accept them and move on, as I am unaware of Noether's theorm? Further I am not an undergraduate student sir.

How did you understand this 3rd law when you were in school sir? I will do the same way.

John Rennie

You have to accept that momentum is conserved. If you accept that the third law follows automatically.

I can go through the derivation of the third law if you want, though it's very simple.

Intellex

8:58 AM

@JohnRennie Yes sir. Then I understood that. Thank you :)

@JohnRennie Using conservation of momentum right? If yes I am aware of it sir. Else please proceed.

John Rennie

Yes, using conservation of momentum.

Intellex

@JohnRennie Then fine sir. Thank you for your time :)

John Rennie

:-)

Intellex

Good bye sir.

2 hours later…

user8718165

11:16 AM

Hello sir @JohnRennie

John Rennie

@user8718165 hi :-)

user8718165

@JohnRennie sir can I ask you a question?

John Rennie

@user8718165 Yes ...

user8718165

@JohnRennie sir a metal ball is fixed to a fully compressed spring...when the spring is released...what will happen sir? this

John Rennie

That's a straightforward mechanics problem. Let's take the origin at the uncompressed length of the spring, so the initial position of the ball is at $x = -d$ where $d$ is the distance the spring has been compressed.

Then the force on the ball is $F = -kx$

user8718165

11:31 AM

@JohnRennie sure sir...

John Rennie

And that's the equation or simple harmonic motion.

So the motion of the ball up to the point where the spring reaches its equilibrium length is just SHM.

user8718165

@JohnRennie okay sir...got it...so the spring will just expand and contract...will the ball also perform SHM?

@JohnRennie or will the free end of the spring only move?

John Rennie

Is the ball fixed to the spring, or will the ball leave the spring and fly off to the left once the spring has reached its equilibrium length?

user8718165

@JohnRennie its fixed sir

@JohnRennie I think the ball will also oscillate

John Rennie

@user8718165 Yes, it's just a mass on a spring so it will just execute simple harmonic motion. The period will be $T = 2\pi\sqrt{k/m}$

user8718165

11:40 AM

@JohnRennie sir...the $KE_{\text{avg}}$ of the ball will be $0$...right sir?

John Rennie

No. The average velocity will be zero because the velocity swings negative and positive. But remember KE is always positive, so it won't average to zero.

user8718165

@JohnRennie sorry...got it sir :) Thank you very much

@JohnRennie well sir, did you see the vid ? :)

John Rennie

@user8718165 not yet ...

user8718165

@JohnRennie okay sir...just when you find time :) I hope you'll like it :)

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