Atwood Machine


If two masses are connected by a string and hang on the two sides of a pulley and let-go, if we want to find the masses' acceleration, we can do it by
mg-T=ma &
and solve for 'a'

But what are the assumptions taken in the calculation and why are they assumed?

Thanks again for your precious answers!


Your equations need to reflect that there are two different masses involved here, like this:
T-m1g=m1a and T-m2g=-m2a
where T is the tension in the string connecting the weights and the minus sign on -m2a reflects the fact that the weights move in opposite directions. Then we can solve these two equations giving:

In order for the equations to be correct we must assume that the pulley has no friction and negligible mass, and that the string has negligible mass. Otherwise additional inertial and gravitational forces would have to be considered. Also the string must not stretch. Otherwise the weights might have different accelerations at any instant.