Editing Atwood machine (section)

== Equation for constant acceleration ==
[[Image:Atwood.svg|right|thumb|220px|The [[free body diagram]]s of the two hanging masses of the Atwood machine. Our [[sign convention]], depicted by the [[acceleration]] [[Euclidean vectors|vectors]] is that {{math|''m''<sub>1</sub>}} accelerates downward and that {{math|''m''<sub>2</sub>}} accelerates upward, as would be the case if {{math|''m''<sub>1</sub> > ''m''<sub>2</sub>}}]]

An equation for the acceleration can be derived by analyzing forces.
Assuming a massless, inextensible string and an ideal massless pulley, the only forces to consider are: tension force ({{mvar|T}}), and the weight of the two masses ({{math|''W''<sub>1</sub>}} and {{math|''W''<sub>2</sub>}}). To find an acceleration, consider the forces affecting each individual mass. 
Using [[Newton's second law]] (with a [[sign convention]] of {{nowrap|<math>m_1 > m_2</math>)}} derive a [[Simultaneous equations|system of equations]] for the acceleration ({{mvar|a}}).

As a sign convention, assume that ''a'' is positive when downward for <math>m_1</math> and upward for <math>m_2</math>. Weight of <math>m_1</math> and <math>m_2</math> is simply <math>W_1 = m_1 g</math> and <math>W_2 = m_2 g</math> respectively.

Forces affecting m<sub>1</sub>: <math display="block"> m_1 g - T = m_1 a</math>
Forces affecting m<sub>2</sub>: <math display="block"> T - m_2 g = m_2 a</math>
and adding the two previous equations yields <math display="block"> m_1 g - m_2 g = m_1 a + m_2 a,</math>
and the concluding formula for acceleration <math display="block">a = g \frac{m_1 - m_2}{m_1 + m_2}</math>

The Atwood machine is sometimes used to illustrate the [[Lagrangian mechanics|Lagrangian method]] of deriving equations of motion.<ref><!-- Again a cite to the most recent edition would be preferable -->{{cite book |last=Goldstein |first=Herbert |authorlink=Herbert Goldstein |year=1980 |title=Classical Mechanics |edition=2nd |publisher=Addison-Wesley/Narosa Indian Student Edition |location=New Delhi |isbn=81-85015-53-8 |pages=26–27}} Section 1-6, example 2</ref>