Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 8, Problem 91P
To determine

The total kinetic energy before collision in terms of m1 ,m2 and p1 , the total kinetic energy after collision in terms of m1 ,m2 and p1 and the situation for p1=+p1 .

Expert Solution & Answer
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Answer to Problem 91P

The total kinetic energy before collision in terms of m1 ,m2 and p1 is (K.E)I=p122(1m1+1m2) , The total kinetic energy after collision in terms of m1 ,m2 and p1 is (K.E)F=p122(1m1+1m2) . If p1=p1 , then particle collides with each other and rebounds back and have same speed. The situation p1=+p1 can only occur if particle does not collide, but they pass by each other.

Explanation of Solution

Given:

The mass of particle 1 is m1 .

The mass of particle 2 is m2 .

Formula Used:

The expression for conservation of momentum is given by,

  p1+p2=pcm

The expression for kinetic energy before collision is given by,

  

  (K.E)I=12m1v12+12m2v22

The expression for kinetic energy after collision is given by,

  

  (K.E)F=12m1v12+12m2v22

The expression for conservation of energy is,

  (K.E)I=(K.E)F

Calculation:

The expression for conservation of momentum is calculated as,

  p1+p2=pcmp1+p2=0p2=p1

The expression for kinetic energy before collision is calculated as,

  (K.E)I=12m1v12+12m2v22=12m1v12m1m1+12m2v22m2m2=m12v122m1+m12v222m2=p122m1+p222m2

Further simplify the above,

  (K.E)I=p122m1+ ( p 1 )22m2=p122m1+p122m2(K.E)I=p122(1 m 1 +1 m 2 )

The expression for kinetic energy after collision is calculated as,

  (K.E)F=12m1v12+12m2v22=12m1v12m1m1+12m2v22m2m2=m12 v 122m1+m12 v 222m2= p 122m1+ p 222m2

Further simplify the above,

  (K.E)F= p 122m1+ ( p 1 )22m2= p 122m1+ p 122m2(K.E)F= p 122(1 m 1 +1 m 2 )

The expression for conservation of energy is calculated as,

  (K.E)F=(K.E)I p 122(1 m 1 +1 m 2 )=p122(1 m 1 +1 m 2 )p12=p12p1=±p1

Conclusion:

Therefore, the total kinetic energy before collision in terms of m1 ,m2 and p1 is. (K.E)I=p122(1m1+1m2) , The total kinetic energy after collision in terms of m1 ,m2 and p1 is (K.E)F=p122(1m1+1m2) . If p1=p1 , then particle collides with each other and rebounds back and have same speed. The situation p1=+p1 can only occur if particle does not collide, but they pass by each other.

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Chapter 8 Solutions

Physics for Scientists and Engineers

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