Answer to Question #288793 in Electricity and Magnetism for jajang

Question

A ball of mass m1=4kg and a block of mass m2=10kg

are attached by a lightweight cord that passes

over a frictionless pulley of negligible mass, as in figure below. The block lies on a frictionless incline of

angle θ=48 degrees. Find the magnitude of the acceleration of the two objects and the tension in the cord.

Answer 1

By equilibrium of forces, for the block and ball, assuming that upward (for the ball) and up the incline (for the block) is the positive direction :

$$-m_1a=-m_1g+T,\\ m_2a=-m_2g\sin\theta+T.\\\space\\ a=-2.4\text{ m/s}^2,\\ T=48.8\text{ N}.$$