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

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

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

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

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

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