/sci/ - Science & Math

>>7971565
in SR, write the product of m times v

then write v = v(t) since v depends on time t, then differentiate with respect to time t

usual the chain rule

then render manifest some acceleration a, which is defined as whatever makes you get the final result on your sheet

>>7971586
>then write v = v(t) since v depends on time t, then differentiate with respect to time t
What I posted is the entire text of the problem. There's no v or m given elsewhere to differentiate, or any other functions for that matter.

>>7971593
you are wrong

you know that F = d/dt (mv) which is true in SR

but in SR the mass m= m(v) is what is given, with v depending on time t, so you must be careful when you differentiate wrt the time t

in newton, mass is cst wrt the time t and the velocity v.

your whole problem is a chain rule.


guys am I the one with a fucked white css for 4cha now which happened 1 minute ago?

okay so it is gook who want to turn it into plebbit

>>7971604
It's an April fools "joke" you illiterate autist.

>>7971605
and it is shit

>>7971600
This is out of my calculus 1 book. I don't have the slightest idea how Special Relativity works or what it entails.

I'm supposed to somehow show that I can arrive at F = $STUFF from F = (d/dt)(mv) using derivatives or something. I don't even know anymore.

>>7971600
I have it too, probably a new design

>>7971565
F= ma is incorrect. The modern formulation of Newton's 2nd law is F = d(p)/dt; p = momentum = mv. If mass is constant this reduces to F= ma.

Two significant examples why this definition of force is important:

- Special relativity. Mass increases as velocity approaches c.
- Rocket science. Shedding tons of fuel at a burn rate needs to be accounted for.

Relativistic momentum [math]p[/math] is defined as

[math]p=\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}[/math]

From Newton's second law, we know that [math]F=\frac{dp}{dt}[/math].

It follows that [math]F=\frac{d}{dt}(\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}})=m_0(\frac{\sqrt{1-\frac{v^2}{c^2}}-v\frac{d}{dv}(\sqrt{1-\frac{v^2}{c^2}})}{{1-\frac{v^2}{c^2}}})\frac{dv}{dt}[/math], where [math]\frac{dv}{dt}[/math] is just [math]a[/math].

[math]F=m_0(\frac{\sqrt{1-\frac{v^2}{c^2}}-v\frac{1}{2}(1-\frac{v^2}{c^2})^{-\frac{1}{2}}(-\frac{2v}{c^2})}{{1-\frac{v^2}{c^2}}})a=m_0(\frac{1-\frac{v^2}{c^2}+\frac{v^2}{c^2}}{{(1-\frac{v^2}{c^2}})^\frac{3}{2}})a=m_0γ^{-\frac{3}{2}}a[/math], for [math]γ=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/math]

Why would you even want to solve this problem when you've never taken physics?

>>7971955
[math]m_0γ^{3}a[/math]*

If you move too fast do you become a black hole?

The misleading concept of 'relativistic mass' has been abandoned in the middle of the last century. It was invented by his epigones as a paedagogic shortcut, but Einstein himself never used it and always advised against it in favor of energy and momentum.

>>7971955
This is just a retard level calculus problem to get kids to learn the chain rule and really the "physics" is just a cute motivation.

>>7971610
>calculus 1 book

Kill the author.

>>7972188
Everything is explained in the problem introduction. It's just application of the chain rule. While it's not trivial to a student in their first calculus class, it's certainly doable and can also expose them to relativity.

The real crime is the relativistic mass formulation.

>>7972205
>The real crime is the relativistic mass formulation.
This.

>>7972205
>It's just application of the chain rule
But the author takes it so far out of the context of the book (teach basic calculus) that it's just unhelpful and distracting. If he wanted to show that the chain rule is useful in other fields, he should've picked literally anything else besides special relativity.

>>7972188
>My fucking sides

>>7971565
>the mass of a particle can vary
your professor's a fucking fag

>>7972508
Relativistic mass is useless, but mass can still be a function of time. See: rockets using fuel.
N2L is really F=dp/dt=m*dv/dt + v*dm/dt