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Chapter 8 | Linear Momentum and Collisions 333
Figure 8.9 An elastic one-dimensional two-object collision. Momentum and internal kinetic energy are conserved.
Now, to solve problems involving one-dimensional elastic collisions between two objects we can use the equations for conservation of momentum and conservation of internal kinetic energy. First, the equation for conservation of momentum for two objects in a one-dimensional collision is
or
(8.43)
(8.44)
where the primes (') indicate values after the collision. By definition, an elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision. Thus,
(8.45) expresses the equation for conservation of internal kinetic energy in a one-dimensional collision.
Making Connections: Collisions
Suppose data are collected on a collision between two masses sliding across a frictionless surface. Mass A (1.0 kg) moves with a velocity of +12 m/s, and mass B (2.0 kg) moves with a velocity of −12 m/s. The two masses collide and stick together after the collision. The table below shows the measured velocities of each mass at times before and after the collision:
Table 8.1
The total mass of the system is 3.0 kg. The velocity of the center of mass of this system can be determined from the conservation of momentum. Consider the system before the collision:
(8.46)
(8.47) (8.48)
Time (s)
Velocity A (m/s) Velocity B (m/s)
0 +12 −12
1.0 s +12 −12
2.0 s −4.0 −4.0
3.0 s −4.0 −4.0
