CK-12-Physics - Intermediate

7.4. Collisions and Conservation Principles http://www.ck12.org

1b. Verify that both momentum and energy are conserved in Example 7.4.1.

Answers:You should be able to show thatpi=pf= 70 kgs∗mandKEi=KEf= 245 J

2a. If both masses in Example 7.4.1 are identical, does the equation forvc fyield a reasonable result?

Answer:Yes. If the masses are identical, thenvc fmust be zero as the equation shows. The result of the collision is
that all the momentum ofmcis transferred tomb.

2b. Ifmcandmbof Example 7.4.1 can be altered as we wish, is possible for the final velocity ofmbto be three times
the initial velocity ofmc?

Answer:No. The limiting value ofvb fis 2vci. In principle, it can take on values in the range( 0 , 2 vci).

(Hint: Consider what happens asmcgrows infinitely large andmbremains constant in the equation forvb f.)

http://demonstrations.wolfram.com/ElasticCollisionOfTwoSpheres/

Inelastic Collisions

If the collision is elastic, then the sum of the kinetic energies of the objects after the collision must be equal to the
kinetic energy of the moving object before the collision.

Illustrative Example 7.4.2

InFigure7.15 blockBis initially at rest and blockAis moving with a velocity of 10.00 m/s. Both blocks have
masses of 3.00-kg and move together after the blocks collide. Determine if the kinetic energy of the system is
conserved, and if not, determine the amount of heat generated in the collision.

FIGURE 7.15

Answer:

The initial kinetic energy of BlockAis

KEi=

1

2

mvAi^2 =

1

2

( 3. 00 kg)

(

10. 0

m

s

) 2

= 150 J

The final kinetic energy of the system is

KEf=

1

2

(mA+mB)

(v

Ai

2

) 2

=

1

2

( 6. 00 kg)( 5. 00 )^2 = 75. 0 J

Clearly, the kinetic energy is not conserved and, therefore, the collision is not elastic. In fact, 50% of the kinetic
energy is lost in the collision and 75.0 J of kinetic energy is transformed into heat. Do you think it is possible to lose
more than 50% of the energy is an inelastic collision?