Newton’s second law states that the force acting on an object is directly related to the acceleration. The law is formulated as F = m x a, where F = force, a = acceleration and m = mass of the object in motion. In terms of Atwood’s machine, a force equal to the difference in the suspended weights accelerates the total mass, m1+ m2.
For two masses hanging on an Atwood machine, acceleration is numerically the same, according to Georgia State University’s Hyperphysics. If one of the two masses, m2, is greater than the other, m1, the system accelerates in the direction dictated by m2. The net force is given by Fnet = m2 x gravity – m1 x gravity, which is the difference in the two weights. Acceleration is given by the net force divided by total mass (m1 + m2). Thus, a = ((m2-m1) x g) / (m1+m2). The system assumes negligible friction and pulley mass.
The law of motion means that increasing a force acting on a moving object increases the acceleration, provided the mass of the object remains constant. If the force remains constant, but the mass increases, the object decelerates. Thus, mass and acceleration are inversely related.