Final answer:
The magnitude of free fall acceleration (g) can be found using an Atwood machine by equating the unbalanced force due to gravity to the total force causing the acceleration of the two masses. The formula derived from Newton's second law is g = a(m1 + m2) / (m2 - m1), where a is the measured acceleration of the masses.
Step-by-step explanation:
To find the magnitude of the free fall acceleration (g) using an Atwood machine with masses m1 and m2 where m1 > m2, we can use a derivation from Newton's second law. The unbalanced force acting on the system is (m2-m1)g, and this causes the acceleration of the two masses. The total force on the system then is F = (m1+m2)a, where a is the acceleration of the system.
Using these two relationships, we can equate the unbalanced force to the total force to get (m2 - m1)g = (m1 + m2)a. Solving for a, we get a = (m2 - m1)g / (m1 + m2). Now, if we wish to find the actual acceleration due to gravity, we can analyze a situation where the acceleration (a) of the objects is known, for example by measuring it. Since we know a and the masses m1 and m2, we can rearrange the equation to solve for g, which gives us g = a(m1 + m2) / (m2 - m1).