Answer to Question #276918 in Classical Mechanics for Alex

Question

A particle A of mass m moves on a smooth horizontal table and is connected by a light

inextensible string passing through a smooth hole O in the table to a particle B of the

same mas; m, which moves along the vertical through O. Initially B is at rest and a is the

distance from A to O, moving with velocity $sqrt{ga/3}$ perpendicular to O A.

What is the kinetic energy of the system?

Answer 1

$E=\frac{E_1+E_2}2,$

$E_1=mga,$

$E_2=\frac{mv^2}2,$

$E=\frac{mga}2+m\sqrt{\frac{ga}{12}}.$