@Ray Vickson No, we are not required to do it the way the book does it, but there is a certain structure to the types of proofs in this section of the book and we are implicitly supposed to follow that structure because we are not experienced with proofs yet. That's an interesting approach, some...
@wabbit I agree, and feel the same way :D. I actually did prove the identity to myself, and it was very tedious... I just hope that proofs like these don't show up on a test, because I'm just going to skip it if it is not this exact same proof (because now I know the answer xD). There was...
Thanks for all the replies guys, I appreciate it! I am actually in a Foundations of Mathematics course (Intro to proofs) and preparing for Advanced Calculus that I'm taking next Fall, so most of the suggestions you guys have made are probably way above my level :D, but thanks anyway! Really...
Thanks for the reply! Yes, I will eventually be taking an advanced undergraduate EM course. I feel already like I've learned so much more from my current CM class that I have in any other physics course I've taken. That being said though, I've been struggling in the class lately because every...
My CM class is about to head into Lagrangian Mechanics so that's cool. But, yeah I totally understand how things can get overwhelming in school especially with any kind of job...
Thanks for the reply! Yeah that sounds about right. It definitely and suddenly changed from "here's a formula (never mind where it comes from) and here's where you use it, and I'll give you all the numbers" to "Here's a few general symbols (like m, l, x, v) and some constraints and now find a...
Hello PhysicsForums!
I am a Physics/Math double major undergraduate junior. I've always loved math, and to study the universe; so I decided to combine both and become a physicist! I did my Gen Phys 1-2 (with Calc) and most of my math at a state college and then I transferred to a university...
Well, I got overwhelmed with homework today and haven't had a chance to revisit this problem; and its due tomorrow. So, unless anyone knows how to finish this, I no longer have time to work on it.
@haruspex Thank you for helping me, even though I've run out of time! If you want to, you can...
Crap, didn't think about the gamma, and totally forgot to keep the square on that c; this is what happens when I've been up since 7:15 AM (1:33 AM now), went to university, and have been doing homework problems several at a time for the rest of the day, lol.
From the end, do you mean from the...
Ok, so here is how far I got using that info:
\vec a = \frac{\vec F}{\gamma m} - \frac{\vec F}{\gamma mc^2}(\vec F \cdot \vec v)
2\vec a \cdot \vec v = \frac{2\vec F \cdot \vec v}{\gamma m} - \frac{2\vec v \cdot \vec v}{\gamma mc^2}(\vec F \cdot \vec v)
\frac{d}{dt}[\vec v \cdot \vec v] =...
Then maybe I need to dot both sides of the equation with velocity and multiply both sides by 2?
Unless my logic is wrong, F, v, and a should all be in the same direction if it starts from rest.
The only thing that comes to my mind is solving \frac{d}{dt}[\vec v \cdot \vec v] = 2\vec a \cdot \vec v for \vec a and substituting it in the starting equation, but this involves "dividing" by a vector, which doesn't make sense. I am sorry that I can't figure this out very easily (I am easily...