Newton's Third Law & Impulse Formula
Newton's Third Law states that for every action, there is an equal but opposite reaction, impacting momentum and impulse. The change in momentum of one object is equal to the change in momentum of another. Impulse is calculated as the area under a force-time graph. Learn more about these fundamental concepts in physics.
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Presentation Transcript
Momentum (formula) And impulse
Newtons Third Law For every action there is an equal but opposite reaction! ?1= ?2 We know ? = ?? therefore ?1?1= ?2?2 But ? =? ? so substituting ? ?1 ?1 ?1 ?2 ?2 ?2 ?1 = ?2 Now the time of contact is the same so t cancels giving ?1(?1 ?1) = ?2(?2 ?2)
?1(?1 ?1) = ?2(?2 ?2) Expand the brackets ?1?1 ?1?1= ?2?2+ ?2?2 Rearrange ?1?1 ?1?1= ?2?2 ?2?2 Now lets look what this means and rearrange it
?1?1 ?1?1= ?2?2 ?2?2 ?1?1 ?1?1is the change in momentum of object 1 ?2?2 ?2?2is the change in momentum of object 2 So this says The change in momentum of object 1 is equal to the change in momentum of object 2. (notice that if object 1 gains momentum, object 2 loses momentum) Isn t this another way of saying In the absence of external forces momentum is conserved
?1?1 ?1?1= ?2?2 ?2?2 momentum or p is called IMPULSE ?1 ?1 ? ?2 ?2 ? ?1= ?1 Impulse must also equal ?1? = ?1(?1 ?1) so also has units Ns = ?2= ?2
Force time graphs F 12 Impulse or change in momentum must also be equal to the AREA under an F-t graph t 5 0
Force time graphs F For force-time graphs: area under graph = Ft = p (change in momentum) = impulse Impulse = area under the graph = x 12 x 5 = 30 N s. 12 t 5 0
Impulse = area under the graph 1 5 1 10 = = ( 43N s ) ( + ) ( + ) ( + ) ( + ) 1 15 1 10 1 3
Impulse area under the graph bh = = = = = F bh bh bh + + + 1 1 1 2 2 2 ( 19 area under the graph Ft ) ( + ) ( + ) ( + ) 1 3 N s 1 3 1 5 3 8 1 1 1 2 2 2 8 Impulse Ft Ft = = = + + 3 ) ( + ) ( 19 ) ( + 1 1 5 1 4 3 t 1 1 2 2 N s 0 5 1 2
