Atwood's machine is a device where two masses, M & m, with M > m, are connected by a massless string passing over a massless pulley. What is the acceleration of each mass?
Steps 14: See diagram and transparency.
Step 5: Apply Newton's 2nd law and constraints
Constraints: nonstretchy rope implies T_{1} = T_{2} = T and
a_{M}=a_{m}.
Newton's Second Law: ma_{m} = Tmg
and Ma_{M} = TMg
Step 6: Solve Newton's Second Law
+Ma_{M} = TMg
ma_{M} = Tmg
Subtracting the two equations gives: (M + m) a_{M} = (mM) g
a_{M}  = 

g 
Step 7: Check your answer! Look at simple limiting cases