Problem 1

An ideal Atwood machine has masses

2m

and

m

hanging on opposite sides of a light inextensible string over a frictionless, massless pulley; take

g

as the gravitational acceleration and assume the system is released from rest. The heavier mass moves downward, with both masses having the same acceleration magnitude because the string length is fixed. (a) Find the acceleration. (b) Find the string tension. (c) Find the speed after the heavier mass has descended a distance

h

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{a=g/3,\quad T=4mg/3,\quad v=\sqrt{2gh/3}}

problems.proof.analysis

Collect the results for all parts in one place. This makes clear that they use the same data and a consistent sign convention.