# How do I find the speed of a block at the bottom in a half circle cavity?

#### Chemist116

You are right, we need the mass of the (blue) block.

@Chemist116: I just have to ask.. Where are you getting these problems from?
In response to your curiosity the original source doesn't really say where did it got it from (as it comes from a collection of problems) but apparently (after looking into that) it seems to come from a rare soviet era textbook from the 70s or mid 80s.

I did a search on bookfinder and I got this

@skeeter was particularly interested in finding the original source of this problems. I cannot guarantee that problems from my class and homework are in those books but judging that there is one which matched those there could be a big chance that it will also be more.

This almost begs for a simple Lagrangian methods problem. It is not obvious about how to do it otherwise.
When you mentioned a Lagrangian methods, did you mean this?

Why is it so?.

${\color{red}mgR} = \dfrac{1}{2}[mv^2 + MV^2]$
also, $\vec{p_0} = \vec{p_f} = 0$