Answer to Question #267690 in Classical Mechanics for zaw myo

Question

For the system of two blocks on a frictionless double incline where the blocks are linked by an inextensible massless string over a frictionless pulley (see figure),

(a). Draw the free body diagram for m₁ and m₂.

(b). Express the equations of motion of the two blocks using Newton's Laws

(c). Prove that for the system to be in equilibrium

Answer 1

$m_1\vec a=m_1\vec g+\vec N_1+\vec T,$

$m_2\vec a=m_2\vec g+\vec N_2+\vec T,$

$m_1a=T-m_1g\sin\alpha,$

$m_2a=-T+m_2g\sin \beta,$

$a=g\frac{m_2\sin\beta-m_1\sin\alpha}{m_1+m_2}.$