Elastic and Plastic Collisions Application physics momentum impulse mechanics

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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∗

†

•  

•  

•  

•  

•  

  v1    v2

∗  

†  

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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v1i =  v

v2i = −2v

v1f  = v1

v2f  = v2

m1v1i + m2v2

i =  m1v1

f  +  m2v2

f 

⇒ mv − 2mX 2v =  mv1 + 2mv2

⇒ v1 + 2v2  = −3v

v1i − v2i  =  v2f  − v1f 

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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⇒ v − (−2v) =  v2 − v1

⇒ v2 − v1  = 3v

⇒ 2v2 + v2  = 0

⇒ v2  = 0

⇒ v1 + 2v2  = −3v

⇒ v1 + 0 = −3v

⇒ v1  = −3v

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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t = 2πr

v

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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  P 1    P 2    θ

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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P 2 = P 21  + P 2

2  + 2P 1P 2cosθ

⇒ P 2 = m2v2 + m2v2 + 2mvmvcosθ

⇒ P 2

= 2m2

v2

+ 2m2

v2

cosθ

P 2 = {2mv

2

}2 = m2v2

⇒ m2v2 = 2m2v2 + 2m2v2cosθ

⇒ cosθ =

 −

1

2

 = cos1200

⇒ θ  = 1200

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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m1v1i + m2v2i  =  m1v1f  +  m2v2f 

⇒ mv − mX 0 =  mV   + mV 

⇒ V   = v

2

⇒ K i =  K  =  12mv2

⇒ Kc = 1

2X 2mXV  2 = mX 

v2

2

= mv2/4 = K 

2

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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 θ  

θ

 θ

  θ

θ  

θ

7/18/2019 Elastic and Plastic Collisions Application physics momentum impulse mechanics

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⇒ K i =  K f  = 1

2mv2 = 2

⇒  1

2X 1Xv2 = 2

⇒ v2 = 4

⇒ v  = 2   m/s

mv + mX 0 = 2mv

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v =  v

2

K f  =  12

2m(v)2 = 12

2mv2

2

⇒  v2

4  = 2

⇒ v  = 2√ 

2   m/s