( Now ( we ( ( will ( ( employ ( ( Figure 4 ) ( the ( well-known ( dynamic theorem ) ) ) ) ) ( by ( which ( ( if ( ( two ( identical particles ) ) ( ( undergo ( an ( elastic collision ) ) ) then ) ) ) ( they ( will ( ( exchange ( their velocities ) ) ( after colliding ) ) ) ) ) ) ) ) ) . ) ) )
(ROOT (S (ADVP (RB Now)) (NP (PRP we)) (VP (MD will) (VP (VB employ) (NP (QP (CD Figure) (CD 4)) (DT the) (ADJP (JJ well-known)) (JJ dynamic) (NN theorem)) (PP (IN by) (SBAR (WHNP (WDT which)) (S (SBAR (IN if) (S (NP (CD two) (JJ identical) (NNS particles)) (VP (VBP undergo) (NP (DT an) (JJ elastic) (NN collision)) (ADVP (RB then))))) (NP (PRP they)) (VP (MD will) (VP (VB exchange) (NP (PRP$ their) (NNS velocities)) (PP (IN after) (S (VP (VBG colliding))))))))))) (. .)))
Now we will employ Figure 4 the well-known dynamic theorem by which if two identical particles undergo an elastic collision then they will exchange their velocities after colliding.
(ROOT (S (SBAR (WHADVP (WRB When)) (S (NP (NN gas) (NNS particles)) (VP (VBP collide)))) (, ,) (NP (DT these) (NNS collisions)) (VP (VBP are) (VP (VBN considered) (S (ADJP (JJ elastic))))) (. .)))