Hi, I am having trouble with this problem. I'm thinking the solution is this but I'm not sure. Fnet=m1a+m2aFnet=m1a+m2a , m1a=kxm1a=kx, m2a=F−kxm2a=F−kx so x=m1ak=−(m2a−F)kx=m1ak=−(m2a−F)k
Actually, It is quite easy to do this if we assume the relation is equivalent (since symmetry means commutativity and proving associativeness follows very quickly) but under the definition of a group it doesn't have to be equivalent so I have to find another way to prove the associative property...
Well a group is defined as an ordered pair of a binary relation R and the set \mathbb{G} as (R, \mathbb{G} ) and the generalized associative law is that a_1 ~R~ a_2 ~R ~a_3~ R ...R~ a_n \in \mathbb{G} this is independent of how you place brackets around the elements.
If I can prove this for...
I'm new to proofs and I'm not sure from which assumptions one has to start with in a proof. I'm trying to prove the generalized associative law for groups and if I start with the axioms of a group as the assumptions then I already have the proof.
From what basic assumptions should one start...
Thanks for the advice. It's still months from now and I really can't bring myself to learn any more 'special cases' before learning about the big picture/architecture of something. I think the rigor will benefit me regardless :p
I just want to make sure my foundation is being built correctly. Will I learn abstract algebra at some later point in my physics/math education? I know they have very important applications in modern physics.
hi, I'm trying to learn linear algebra a bit before I take the course formally at my school. I picked up Axler's book "linear algebra done right" and have been formally introduced to vector spaces (although I have already studied them prior in physics). I learned that vector spaces are a...
Darn, the velocity equation I derived doesn't make sense. But, I multiplied acceleration by distance shouldn't I be able to get ##v^2## and consequently ##v## from that?
It's not a homework/coursework question but I did get the system from my textbook.
http://puu.sh/o03h7/32cdf7cffb.jpg
I solved the question by analyzing the system at different stages. Initially both objects are moving with a velocity and having some mass so their kinetic energies are the...
so it can be written as 2({m_1} + {m_2})X = ({m_1}{m_2})({v_1}^2 - {v_2}^2) and expressed such that ##X \ne 0## when (##{m_1} > 0## and ##{m_2} > 0##) and ##{v_2} \ne {v_1}##? is this correct or should I go further?
Yes I forgot a power of 2 2({m_1}+{m_2})X = {m_1}{m_2}{v_2}^2 + {m_1}{m_2}{v_1} - 2{m_1}{v_1}{m_2}{v_2} here
2({m_1}+{m_2})X = {m_1}{m_2}{v_2}^2 + {m_1}{m_2}{v_1}^2 - 2{m_1}{v_1}{m_2}{v_2}
and then 2({m_1} + {m_2})X = ({m_1}{m_2})({v_2}^2 + {v_1}^2 - 2{v_1}{v_2})
If this is correct, ##X \ne...
I don't really have the knowledge to be saying this since I haven't studied beyond classical mechanics. But, https://en.wikipedia.org/wiki/Kinetic_energy What I meant by kinetic energy was simply the energy due to motion of an object with 'mass' and I say it with '' because I have no idea how to...