Answer to Question #214181 in Physics for ...

Question

A string attached to a body of mass 4 kg which rests on a frictionless plane that is 

inclined 30o with the horizontal. The string passes over a pulley at the upper end of the 

plane and another body of mass 3 kg is attached to the other end of the string, this 

body hanging vertically. (a) Find the direction and magnitude of the acceleration of 

the two bodies and (b) the tension in the string

Answer 1

(a) $T-m_1g\sin30°=m_1a\to T=m_1a+m_1g\sin30°$

$m_2g-T=m_2a\to m_2g-m_1a-m_1g\sin30°=m_2a$ . So, we have

$a=\frac{m_2g-m_1g\sin30°}{m_1+m_2}=\frac{3\cdot9.81-4\cdot9.81\cdot \sin30°}{4+3}=1.4\ (m/s^2)$ .

The body moves upwards on an inclined plane

(b) $T=m_1a+m_1g\sin30°=4\cdot1.4+4\cdot9.81\cdot\sin30°=25.22\ (N)$