Answer to Question #214474 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

$$(m+M)a=(m-M\sin{30})g\\(3+4)a=(3-4\sin{30})9.8\\a=1.4\frac{m}{s^2}$$

Direction: vertically downwards.

$$T=3(9.8-1.4)=25\ N$$