When two masses suspended by a string over a pulley seem to be unequal, acceleration would result as the larger mass falls down and also the smaller mass is pulled up. So this acceleration will be constant for both masses, according to Newton’s second law of motion. Using the standard sign convention, the summing up equation for forces on each mass can be written with the upward force as positive and the downward force as negative.
On solving (1) and (2), we get
Where, T= Tension in the string
a= acceleration of 2 masses
There are 3 distinct cases that really can help one in understanding how an Atwood machine works, and they are as follows:
No Acceleration and Equal Mass:
No Acceleration and Equal Mass" width="215" height="332" />
The diagram depicts an equilibrium situation. Since the two masses (M) are equal, the gravitational force on each is equal. Because it opposes gravity in the string, an upwards force will be referred to as tension (T).
As a result, for such a system to remain in equilibrium, T must equal Fg. The net force is written as \(\mathrm = 0\), indicating the absence of acceleration.
The tension inside the string is 2T or 2Fg. Since the string supports both masses, the tension could be expected to represent the sum of the two downward forces.
Constant Velocity and Equal Mass:
Because constant velocity implies no acceleration, the force applied in the system would be zero. As a result, this situation differs from a static situation. There isn’t net velocity in just this case because velocity in the upward and downward directions are of the same value or magnitude but also in opposite directions. This causes no kind of acceleration to occur.
The above type of situation is all too common in our daily lives: For example, if a sliding object is subjected to an equal and opposite constant force of friction, the object would then move at constant velocity to zero acceleration.
After all course, the acceleration would then exist if the system’s velocity changes.
Acceleration with Unequal Mass:
Things get interesting whenever the masses are unequal. If we let the system run, we will still get acceleration in the direction of the heavier mass.
The gravitational forces on each mass are now unequal, as well as the vector of the two gravitational forces seems to be the net force inside the direction of the heavier mass. That is, the net acceleration vector appears to exist in the direction of M2, as shown in the figure.
The overall acceleration of the system is the same for both masses; the rate of acceleration of M1 upward is the same as the rate of acceleration of M2 downward because they are linked together.
The entire system cannot be considered a single mass, M = M1 + M2
