Particles connected by pulleys

The string will always be inextensible and light and the pulley (or peg) will always be smooth

or light.

1) As the string is inextensible the accelerations of the two particles at its ends will have the

same magnitude.

2) As the string is light, the tension in the string will be constant along its length.

3) As the pulley (or peg) is smooth or light, the tensions in the string on either side of the

pulley (or peg) will be equal.

Example: Particles of mass 3 kg and 5 kg are attached to the ends of a light inextensible

string which passes over a fixed smooth pulley. The 5 kg particle is initially 2 m above the

floor.

The system is released from rest; find the greatest height of the lighter mass above its initial

position in the subsequent motion. Assume that the lighter mass does not reach the pulley.

Solution:

The two particles will move together until the heavier one hits

the floor. Then the string will become slack, and the lighter

particle will move freely under gravity.

Thus, our problem has two distinct parts.

1) What happens before the heavy particle hits the floor?

2) What happens after the heavy particle hits the floor?

Since the string is inextensible the accelerations of both

particles will be equal in magnitude.

Since the string is light and the pulley is smooth the tensions on both sides will be equal in

magnitude.