CK-12-Physics - Intermediate

7.3. Conservation of Momentum and Center of Mass http://www.ck12.org

Answer: If we redo the problem, we find thatvf is half of the initial speed of the car that caused the accident,
13. 4
2 =^6.^7

m

s.

2. If the accident had been between two identical trucks having masses of 8500-kg each, where one truck, moving
   with a speed of 13.4 m/s, collided with the other at rest, what would be their common speed after the collision?

Answer:The result is the same as in number 1, namely,^132.^4 = 6. 7 ms.

As long as two objects have the same mass, they will move off together with half the incoming speed after the
collision, as shown below.

pi= (mvi)+(m)( 0 ) =mvi

pf=mvf+mvf= 2 mvf

pi=pf→mvi= 2 mvf→vf=

vi

2

Illustrative Example 7.3.3

Consider the case of two objects,m 1 moving with initial velocityv 1 iandm 2 having an initial velocityv 2 i=0,
colliding head-on and moving together after the collision. Find their final common speed.

pi=m 1 v 1 i+m 2 ( 0 )and pf= (m 1 +m 2 )vf

pi=pf→m 1 v 1 i= (m 1 +m 2 )vf→vf=

m 1

m 1 +m 2

v 1 i

Note that form 1 =m 2 →vf=v 21 i

http://demonstrations.wolfram.com/InelasticCollisionsOfTwoSpheres/

Illustrative Example 7.3.4

InFigure7.12, a girl of mass 30-kg stands motionless upon a frictionless horizontal surface with a bag of ten
baseballs. The baseballs have a mass of 0.145 kg each and the total mass of the balls and bag is 1.70-kg. The girl
takes one baseball out of the bag and throws it with a velocity of 7.00 m/s due west relative to the ground. What is
the velocity of the girl after she throws the baseball?

Answer:

We assume that momentum conservation holds and therefore determine the initial and final momenta of the system.

The initial momentum of the system, (girl + bag + baseballs) is zero since the girl, baseballs and bag are at rest;
pi= 0

The final momentum of the system is composed of two motions, the baseball’s momentum and the momentum of
the girl, remaining baseballs, and bag. We find the final momentum of the baseball first:

pb f= ( 0. 145 kg)

(

7. 00 ms

)

The final momentum of the rest of the system belongs to the girl, baseballs, and bag. But we must remember that the
bag contains one fewer baseball. Thus, the mass of the remaining baseballs + mass of the bag is 1. 70 kg− 0. 145 kg=

1. 555 kg. The mass of the girl is 30-kg and therefore the total mass is 31.1555-kg. The final momentum of this part
   of the system is:

pg f= ( 31. 555 kg)vg f