Students will learn how to solve problems involving both energy and momentum conservation and where one is allowed to use either momentum conservation or energy conservation or both.
Key Equations
; The total energy does not change in closed systems
; The total momentum does not change in closed systems
Example 1
Watch this Explanation
Time for Practice
 You throw a lump of clay with a speed of at a bowling ball hanging from a vertical rope. The bowling ball swings up to a height of compared to its initial height. Was this an elastic collision? Justify your answer.

The
bullet shown above is traveling to the right with a speed of
. A
block is hanging from the ceiling from a rope
in length.
 What is the maximum height that the bulletblock system will reach, if the bullet embeds itself in the block?
 What is the maximum angle the rope makes with the vertical after the collision?

A new fun foam target on wheels for archery students has been invented. The arrow of mass,
, and speed,
, goes through the target and emerges at the other end with reduced speed,
. The mass of the target is
. Ignore friction and air resistance.
 What is the final speed of the target?
 What is the kinetic energy of the arrow after it leaves the target?
 What is the final kinetic energy of the target?
 What percent of the initial energy of the arrow was lost in the shooting?
Answers to Selected Problems
 .
 a. b. 5.
 a. b. c. d. %