Recent content by Celso

With this information I concluded that the diagonal elements of ##\hat{A}## are equal to the eigenvalue ##a##, so ##\hat{A} = \begin{bmatrix} a & A_{12} & A_{13} \\ A_{21}& a & A_{23}\\A_{31} & A_{32} & a \end{bmatrix}## but I can't see how to go from this to the commuting relation, since I...

Each different boundary condition means a different charge configuration, how can this problem be solved using superposition?

Why is the gravitational potential energy of the chain's center of mass equal to the total kinetic energy of the disc after it was fully wrapped? My first thought was to write ##E_{0}=(M/2+M)g∗2πR=E_{f}= Ep## (from the chain) ##+Ec## (from the disc). Instead he wrote ## mg \frac{l}{2} ## = ##...

Honestly I don't know where to begin. I started differentiating alpha trying to show that its absolute value is constant, but the equation got complicated and didn't seem right.

What do you mean by soliving in the direction of m1?

How do I interpret geometrically the partial derivative in respect to a constant of a function such as ##\frac{ \partial}{\partial c} (acos(x) + be^x + c)^2##?

I'm doing some exercises about special relativity and one of them asks to find the speed in an arbitrary frame of reference (1) in such a way that it perceives two events at the same time that didn't happen simultaneously in other frame of reference(2). Is it correct to state that if the...

How do I start this? I plugged the differential equation at wolfram alpha and it semmed too complicated for such an exercise. I've also looked at a sample of an answer on cheeg where the initial approach is to rewrite the equation as ##\frac{d}{dt} (\frac{\dot\theta^2}{2}-cos(\theta)) = 0## How...

because if the problem is consistent (which I'm not sure), ##h_{2}## can be written as function of the other given variables

yes, it's in portuguese. I don't have the file now (it's on my PC), apart from what I've written in my previous answer, it only asks to find: •The velocity at B •The x and y components of the velocity at B •The height h2 knowing that the horizontal distance between B and C is 10m The first two...

That's all, as far as I know. This is actually an That's all, the problem's statement is simply "the following picture represents the configuration of a falling objetc". It's actually a problem I tried to solve for another person but I couldn't figure out after an hour

I first found ##v_{B}## by ##E_{p,A,B} = mgh_{1} = E_{c, B} = \frac{1}{2}mv_{B}^2 \therefore v_{B} = \sqrt{2gh_{1}} ## After this I made several failed attempts basically trying to find its final velocity so I could use conservation of energy. Spliting the velocity into its components never...

To write ##v## as a function of time, I wrote the equation ##m\frac{dv}{dt} = c_{2}v^2 + c_{1}v - mg \implies \frac{mdv}{c_{2}v^2 + c_{1}v - mg} = dt## To solve this, I thought about partial fractions, but several factors of ##-c_{1} \pm \sqrt {c_{1}^2 +4c_{2}*mg}## would appear and they don't...

ah that's my mistake, thank you guys

It has a root in ##x/A = 1##, but in that case the distance would be equal to the amplitude, not zero