1. Conservation of Momentum
Unit 6:
Momentum, Impulse, and
Conservation of Momentum

2. I. Momentum “mass in motion”
Depends on mass and velocity of an object.
Equation (See Ref. Tables):
p = mv
Units: kg*m/s
Vector quantity: (same direction as object’s velocity)

3. I. Momentum
Example: What is the momentum of a 40,000 kg train going 2 m/s? What is the momentum of a 2,000 kg car going 40 m/s? How do they compare? 3

4. II. Impulse What causes a change in velocity (acceleration)? FORCES!!!
Definition: How long (time) a force acts on an object
Equation (see ref. tabs)
J = Fnet t = Δp
Units: N*s OR kg*m/s 4

5. III. Relating Impulse and Momentum
Example: A ball is stopped by a 100 N force over a time period of 2 s. Determine the impulse acting on the ball. 5

6. III. Relating Impulse and Momentum
Impulse-Momentum Theorem:
The impulse acting on an object is equal to the object’s change in momentum
Video (1 min)- Stopping an egg against a brick wall and stopping an egg against a bed sheet
Video (2 min)- Football helmets and pads decrease the force by extending the time of the impact 6

7. IV. Momentum and Impulse Egg Demo Questions
How does the impulse of an egg being thrown against a wall compare to the impulse of an egg being thrown against a bed sheet?
In terms of force and time, why does an egg thrown against a bed sheet not break, but thrown against a wall it does?
The same
The sheet spreads the force over a longer time, so the force is less since the impulse is the same 7

8. Science of Airbags – Video (3 min)
V. Application of Impulse-Momentum Theorem
An airbag spreads the force over a greater time, therefore decreasing the magnitude of the force acting on the person
Science of Airbags – Video (3 min) 8

9. VI. Momentum and Impulse Examples
A force of 20 N acts on a 3.5 kg mass for 10 s. What is the impulse of the object?
2. A 2,000 kg car traveling at 10 m/s accelerates to a speed of 25 m/s. What is the impulse of the car? 9

10. VI. Collisions and Conservation of Momentum
Review of Newton’s Third Law of Motion: “For every action…”
… there is an equal and opposite reaction.
F on bug = - F on bus

11. VI. Conservation of Momentum
The total momentum before the collision is equal to the total momentum after the collision.
Conservation of Momentum in Space video (2 min)
Equation: (see reference tables) 11

12. VII. Elastic Collision Elastic Collision:
Objects collide and move off with different momentums (momenta)
Equation:
mAvAi +mBvBi = mAvAf+ mBvBf 12

13. mAvAi +mBvBi = mAvAf+ mBvBf
VII. Elastic Collision
mAvAi +mBvBi = mAvAf+ mBvBf
Example: A 3000 kg truck traveling 10 m/s collides with a 1000 kg car at rest. After the collision, the car travels with a speed of 15 m/s.
A) What is the total momentum before the collision? 13

14. mAvAi +mBvBi = mAvAf+ mBvBf
VII. Elastic Collision
mAvAi +mBvBi = mAvAf+ mBvBf
Example: A 3000 kg truck traveling 10 m/s collides with a 1000 kg car at rest. After the collision, the car travels with a speed of 15 m/s.
B) What is the total momentum after the collision? 14

15. mAvAi +mBvBi = mAvAf+ mBvBf
VII. Elastic Collision
mAvAi +mBvBi = mAvAf+ mBvBf
Example: A 3000 kg truck traveling 10 m/s collides with a 1000 kg car at rest. After the collision, the car travels with a speed of 15 m/s.
C) What is speed of the truck after the collision? 15

16. VIII. Inelastic Collision
Objects collide and move off with the same velocity (“stick together”)
Equation:
mAvAi +mBvBi = (mA+ mB)vf 16

17. VIII. Inelastic Collision
mAvAi +mBvBi = (mA+ mB)vf
Example: An 80 kg grandma traveling 6 m/s on roller skates collides with her 40 kg grandchild initially at rest. After they collide, she picks him up and travel together.
A) What it the total momentum before the collision? 17

18. VIII. Inelastic Collision
mAvAi +mBvBi = (mA+ mB)vf
Example: An 80 kg grandma traveling 6 m/s on roller skates collides with her 40 kg grandchild initially at rest. After they collide, she picks him up and travel together.
B) What it the total momentum after the collision? 18

19. VIII. Inelastic Collision
mAvAi +mBvBi = (mA+ mB)vf
Example: An 80 kg grandma traveling 6 m/s on roller skates collides with her 40 kg grandchild initially at rest. After they collide, she picks him up and travel together.
C) What is the speed of the grandma and child after the collision? 19

20. IX. Explosions and Recoil
The total momentum before and after is equal to zero
Equation:
- mAvAf = mBvBf 20

21. IX. Explosions and Recoil
-mAvAf = mBvBf
Example: A kg tennis ball is placed in a 20 kg cannon. The tennis ball is launched out of the cannon with a speed of 100 m/s.
What is the total momentum before the explosion?
What is the total momentum after the explosion?
C) What is the recoil speed of the cannon? 21