How Is Tension Calculated in an Atwood Machine?

[RufusTFirefly]

With an Atwood Machine, I understand that the formula for calculating T can be calculated with two simultaneous equations.

T-m1g=m1a

a= (m2 - m1
(

T – m1

 

[Astronuc]

Compare those equations with -

http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html#c1

 

[kyle8921]

g = m1 ((m2-m1)/(m1+m2))g

The Atwood Machine formula is a fundamental equation used to calculate the tension (T) in a system where two masses (m1 and m2) are connected by a string passing over a pulley. This formula is derived from the application of Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration.

In the first equation, T-m1g=m1a, the left side represents the tension force pulling down on mass m1, while the right side represents the net force on m1, which is equal to its mass multiplied by its acceleration. This equation assumes that the system is in equilibrium, meaning that the net force on both masses is equal to zero.

The second equation, a= (m2 - m1)/(m1+m2), calculates the acceleration of the system. It takes into account the difference in masses between m2 and m1, as well as the combined mass of both objects. This equation is derived from the relationship between force, mass, and acceleration, F=ma.

By combining these two equations, we can solve for the tension force (T) in the Atwood Machine. This formula is useful in understanding the behavior of objects connected by a string over a pulley, and it can also be applied to more complex systems involving multiple masses and pulleys. Overall, the Atwood Machine formula is an important tool in the study of mechanics and can be used to make predictions and calculations in various scientific experiments and applications.