Page 153 - Fisika Terapan for Engineers and Scientists

11.4 Collisions in Two and Three Dimensions 353

The fraction of kinetic energy lost is the amount of kinetic energy lost divided by
the original kinetic energy:

2
2
2
1
1 m v a m v m v' b
1
1
K K ' 2 1 1 4 2 1 1 2 2 2
[fraction lost]
K 1 m v 2
2 1 1
2 2
1 m v' 2 3 32 (170 m s)
2
1
4 m 1 v 2 1 4 4.0 (1200 m s) 2
0.59
Thus, about 59% of the helium ion’s initial kinetic energy is lost to internal
motions of the oxygen molecule during the collision.

✔ Checkup 11.4

QUESTION 1: A car traveling south collides with and becomes entangled with a car
of the same mass and speed heading west. In what direction does the wreckage emerge
from the collision?
QUESTION 2: An object at rest explodes into three pieces; one travels due west and
another due north. In which quadrant of directions does the third piece travel?
(A) Northeast (B) Southeast (C) Southwest (D) Northwest

CONSERVATION OF ENERGY AND
PROBLEM-SOLVING TECHNIQUES
MOMENTUM IN COLLISIONS

For solving problems involving collisions, it is essential to know what conservation laws are applicable.The following table
summarizes the conservation laws applicable for different collisions:

TYPE OF CONSERVATION CONSERVATION
COLLISION OF KINETIC ENERGY OF MOMENTUM COMMENTS
Elastic Yes Yes For a one-dimensional collision, energy and momentum
conservation determine the final velocities in terms of the initial
velocities. For a 2- or 3-dimensional collision, there is not enough
information in the initial velocities alone to determine the final
velocities uniquely.
Totally No Yes The two colliding bodies stick together, and momentum conservation
inelastic determines the final velocities (in 1, 2, and 3 dimensions).
Inelastic No Yes If the collision is not totally inelastic, there is not enough
information in the initial velocities alone to determine the final
velocities. Some information about the energy loss and final
velocities must also be known.