Answer to Question #315577 in Mechanics | Relativity for Aune

Question

Suppose we experiment with an Atwood Machine consisting of two masses m

and 2m connected by an inextensible non-slip string running over a pulley of

radius a and mass 4m, as shown below.

(a) Determine the total kinetic energy of the system. (6)

(b) Find the gravitational potential energy of the system.

Answer 1

$a=g\frac{m_2-m_1}{m_2+m_1}=3.27~\frac m{s^2},$

$I=2mr^2,$

$\omega=\frac ar,$

$E=\frac{I\omega^2}2=10.7mr^2~J.$