Recent content by Murilo T

OMG, it looks like I was blind before! Indeed, my conservation of energy: ##\frac {dmu^2} {2} + \frac {Mv^2} {2} = \frac {M(v + dv)^2} {2} + \frac {dmu^2} {2}## gives ## \frac {Mv^2} {2} = \frac {M(v + dv)^2} {2}##! The initial velocity of the ball and its final velocity are different...

Since in the first collision the car has zero speed, ##v = 0## and the expression becomes ##dmu = Mdv - dmu##. But the mass isn't really an infinitesimal mass and the velocity isn't really an infinitesimal velocity. So I think that it could be rewrited to: ##m_{i}u + Mv_{i-1} = Mv_{i} -...

Sorry! It should be ##dmu + Mv = M(v +dv) -dmu## I wrote the V instead of v

I aready got the solution for this exercise. However, the solution used the referance frame from the car: What I'm trying to understand is the line: Because before reading the solution, I was trying to solve it using the lab frame. So this is my work so far: Using conservation of momentum and...

Yep. I can integrate to get a equation with only φ' and φ. With the initial conditions I can solve it now :D

Yees, I realized when I substituted u and u', but it was missing a φ'! Thank you very very much again! Hahhaha

Is it safe to say that this equals u'φ' + uφ'' = -sin(φ) ?

I guess that what you are saying is to isolate u = cosϕ/ϕ', and then take the derivative of u with respect to ϕ, right?

I've began to learn how to solve differential equations to eliminate u in those two equations, but it seems that it is a nonlinear differential equation. I'm wondering if there is other way to eliminate u, or will I just have to learn how to solve nonlienar differential equations? The...

Aaaah, yeees. I see it now! Thank you very very much :)

The most inspiring video that touches my hearth every time that I see:

This question is from the David Morin ( Classical Mechanics ) - problem 3.7. I spent some time trying to figure it out the solution by myself, but since I couldn't, I looked into the solution in the book, but I got even more lost. So I searched for an online solution that could help me at least...