Answer to Question #262747 in Physics for jena

Question

A 15.0-kg load of bricks hangs from one end of an inextensible rope that passes

over a small, frictionless pulley. A 28.0-kg counterweight is suspended from the

other end of the rope. The system is released from rest. What is the magnitude of

the acceleration of the system? What is the tension acting on the rope?

Answer 1

Write the forces acting on both objects (bricks and counterweight). The y-axis bor both bodies points upward.

$$\text{Bricks:}-mg+T=ma,\\ \text{CW:}-Mg+T=-Ma.\\\space\\ a=g(M-m)/(M+m)=2.96\text{ m/s}^2,\\\space\\ T=m(a+g)=191.4\text{ N}.$$