Motion of Bodies Connected by a String Passing over a Frictionless Pulley

Motion of Bodies Connected by a String Passing over a Frictionless Pulley

Generally we come across two cases when we study the motion of bodies connected by a string passing over a pulley.

Case 1: When both the bodies move vertically

Consider two bodies A and B having unequal masses m1 and m2 connected by a string which passes over a frictionless pulley in such a way that the two bodies hang vertically.

Suppose m1 is greater than m2. Hence body A will move down with acceleration “a” while body B will move up with the same acceleration. Let T be the tension in the string.

To calculate the acceleration of the bodies and tension in the string, let us consider the motion of body A.

Two forces are acting on the body A.

(i) Weight of the body acting vertically downwards W1 = m1g

(ii) The tension in the string acting vertically upwards = T