1. 1D Collisions
Unit A Momentum

2. Objectives
You will be able to state and apply the Law of Conservation of Momentum to linear collisions.
You will be able to define isolated system, and be able to determine if a system is or is not isolated.

3. Collisions and systems
A collision is an interaction between two objects where a force acts on each object for a period of time.
A group of two or more objects that interact is known as a system.
A system where the system’s mass is constant, and no external net force acts on the system is an isolated system.

4. Momentum of a system…
… is defined as the sum of the momenta of all objects in the system.

5. The belief in the fact that momentum is conserved in all collisions has led to the
Law of Conservation of Momentum. 1)
Use when objects do not stick together. 2)
Use when objects stick together. 3)
Use for explosions (momentum total is zero before).
Note: These formulas are not on your formula sheets and you can use the first formula exclusively if you like. *

6. Example:
Fred sits in a stationary, frictionless wheelchair and throws a 3.0 kg ball outward at 8.0 m/s. If the mass of Fred and his chair is 75 kg, what will be the velocity of Fred and the chair immediately after the ball is thrown?

7. Solution
Before:
After
Because both velocities are zero.

8. Solution

9. Example
A 50 g bullet is fired into a 650 g block of wood, which sits on a frictionless surface. After impact the bullet and block move right at 30 m/s. Find the bullet’s velocity just before impact.

10. Solution
Before:
After

11. Solution

12. Using “Conservation of Momentum”
Colliding Objects Stick Together
Example : A 1.50 g pellet is fired into a 12.3 g wood block. The block and imbedded pellet fly off at 2.78 m/s E. What was the pellet’s velocity before impact?
Answer is
“+” *

13. Example 2: A 980 kg Toyota going at 52
Example 2: A 980 kg Toyota going at 52.8 km/h N collides with and becomes entangled with a 738 kg Honda going 79.3 km/h S. What is the velocity of the wreckage immediately after impact?
Note: It does not matter what units of mass or velocity are used - just be consistent!
Answer was “–” *

14. Examples of “Explosion” Conservation of Momentum Problems
Example : When a 960 g plate is dropped, the first 370 g piece flies off at 2.63 m/s  S. What is the velocity of the second piece?
Note: In order for the total final momentum to be “0”, if one piece flies north, the other must fly south. *

15. Example 2: What is the ratio of the velocities of the 3
Example 2: What is the ratio of the velocities of the 3.46 g piece of an exploded firecracker to the other 5.96 g piece?
Note: The smaller piece has a velocity 1.72 times the velocity of the larger piece! *