Answer to Question #103987 in Mechanics | Relativity for Akinlua Richard

Question

Particles of mass m1 and m2 (m2>m1) are connected by a large inextensible string passing over a smooth fixed pulley. Initially both masses hang vertically with mass m2 at a height X above the floor. If the system is released from rest, what speed will mass m2 hit the floor and the mass m1 will rise a further distance (m2-m1)x/m1+m2 after this occurs

Answer 1

Let's use the law of conservation of energy.

$m_2gh=\frac{m_2 v^2}{2}$

$h=\frac{m_2-m_1}{m_2+m_1}x$

$m_2g\frac{m_2-m_1}{m_2+m_1}x=\frac{m_2 v^2}{2}\to v=\sqrt{2g\frac{m_2-m_1}{m_2+m_1}x}$ Answer.