Elastic collisions

In an elastic collision, kinetic energy is conserved as well as momentum. An example of a perfectly elastic collision occurs when an ideal (frictionless) rubber ball bounces off a floor and reaches the same height from which it was initially dropped. A nearly-elastic collision occurs in billiards when a fast-moving cue ball strikes another ball, causing the cue ball to stop in place and the target ball to move off in the same direction. Real collisions are rarely perfectly elastic however, the amount of kinetic energy lost may be so small that it is often a good approximation to assume perfect elasticity. Read the text aloud Show A puzzling device
(11.4) 1 2 m 1 v i1 2 + 1 2 m 2 v i2 2 = 1 2 m 1 v f1 2 + 1 2 m 2 v f2 2
Conservation of energy
for elastic collisions
Elastic collision problems typically involve two equations: conservation of momentum and conservation of kinetic energy. The momentum equation involves the masses and velocities before and after the collision. The energy equation involves the masses and the velocities squared before and after the collision. The squared velocities make the algebra of solving momentum problems a little more challenging. In problems involving two and three dimensions, momentum must be conserved separately in each direction. Kinetic energy is a scalar however, and there is typically only one kinetic energy equation. Read the text aloud Show Quadratic solution to elastic collision problems
Is this collision elastic?
A 0.16 kg cue ball traveling at 4 m/s strikes a stationary 0.16 kg eight ball. After the collision, the cue ball travels at 0.2 m/s while the eight ball travels at 3.8 m/s. Is this an elastic collision? Why or why not?
Asked: whether it is an elastic collision; i.e., is kinetic energy conserved?
Given: masses of the balls, m1 = m2 = 0.16 kg; initial speed vi1 = 4 m/s of the cue ball; initial speed vi2 = 0 m/s of the eight-ball; final speed vf1 = 0.2 m/s of the cue ball; final speed vf1 = 3.8 m/s of the eight ball
Relationships: conservation of energy for two objects in an elastic collision:
1 2 m 1 v i1 2 + 1 2 m 2 v i2 2 = 1 2 m 1 v f1 2 + 1 2 m 2 v f2 2
Solution: Compare the kinetic energies of the balls before and after the collision:
1 2 (0.16 kg) (4 m/s) 2 + 1 2 (0.16 kg) (0) 2 = ? 1 2 (0.16 kg) (0.2 m/s) 2 + 1 2 (0.16 kg) (3.8 m/s) 2 1.28 J+0 J 0.003 J+1.155 J
Answer: The collision is not elastic because some kinetic energy is lost. (Since only a small amount of the kinetic energy is lost, the collision is “nearly elastic.”)
Read the text aloud
In elastic collisions, which of the following quantities are conserved?
  1. velocity
  2. momentum
  3. kinetic energy
  1. I only
  2. I and III only
  3. II and III only
  4. I, II, and III
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