Question

two particles a and b of masses 10kg and 12kg respectively, are connected by a light inextensible string which passes over a light smooth pulley P. Particle a rests on a smooth horizontal surface and b rests on a smooth plane inclined at 45 degrees to the horizontal with the string taut and perpendicular to the line of intersection of the table and the plane. The system is released from rest. what is the magnitude of the acceleration of the particles?

Answer 1

Draw a scheme

Newton's law

$$T=m_1a$$ $$-T+m_2gsin(\alpha)=m_2a$$

then, solving it system of equation

$$m_1a+m_2a=m_2gsin(\alpha)$$

$$a=\frac{m_2gsin(\alpha)}{m_1+m_2}$$

$$a=\frac{10\cdot 10 \cdot sin(45)}{12+10}=3.214 (m/c^2)$$