In an Atwood's machine, two masses are connected by a string passing over a pulley. The system is designed such that the masses move vertically and are subject to the force of gravity.
If we assume that the pulley and the string are massless and there is no friction, the tension in the string will be the same on both sides of the pulley. Let's denote the masses as follows:
m1: Mass of the first object m2: Mass of the second object
To achieve a constant velocity, the net force on the system must be zero. The forces acting on the system are the tension in the string and the weight of the masses. The weight of an object is given by:
Weight = mass × gravitational acceleration
Since the masses are connected, the magnitudes of their weights will be different:
Weight of m1 = m1 × g Weight of m2 = m2 × g
To maintain a constant velocity, the net force must be zero. The net force is given by:
Net Force = Tension - Weight
Since the tension is the same on both sides of the pulley, we can write the net force equation for the two masses:
m2 × g - m1 × g = 0
Simplifying the equation, we find:
m2 = m1
Therefore, for the two masses to have a constant velocity, the mass of m2 should be equal to the mass of m1, i.e., m2 = m1.