Atwood Machine

## Question:

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 &

T-mg=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!

## Answer:

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:

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

T=((2m1m2)/(m1+m2))g
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.