1. Conservation of Momentum

2. Review p: momentum m: mass v: velocity p = m v
Yeah!
I already know this.
p: momentum
m: mass
v: velocity
p = m v
ptot = pA0 + pB0 = pA1 + pB1
ptot = mtotv2  only if A & B stick together

3. Example

4. Steps to Solve a Problem
Draw a BEFORE (State 0) picture
Draw an AFTER (State 1) picture
Label everything
Find missing pieces
Find the total momentum
Solve for what you don’t know

5. Before (0) + -
Make sure you include:
Before (0)
Arrows
+ & -

6. After (1) + -
Make sure you include:
After (1)
Arrows
+ & -

7. Label Everything
Before (0)
After (1) - +

8. Label Everything - + Label each object A or B
Before (0)
After (1) A B A B - +
Label each object A or B
For every object include: m, v, p
Use subscripts to label m, v, and p with A or B
Use subscripts to label v, and p with 1 or 2

9. Label Everything - + Label each object A or B
Before (0)
After (1) A B A B - +
m =
v =
p =
m =
v =
p =
m =
v =
p =
m =
v =
p =
Label each object A or B
For every object include: m, v, p
Use subscripts to label m, v, and p with A or B
Use subscripts to label v, and p with 1 or 2

10. Label Everything - + Label each object A or B
Before (0)
After (1) A B A B - +
mA =
vA =
pA =
mB =
vB =
pB =
mA =
vA =
pA =
mB =
vB =
pB =
Label each object A or B
For every object include: m, v, p
Use subscripts to label m, v, and p with A or B
Use subscripts to label v, and p with 0 or 1

11. Label Everything - + Label each object A or B
Before (0)
After (1) A B A B - +
mA =
vA0 =
pA0 =
mB =
vB0 =
pB0 =
mA =
vA1 =
pA1 =
mB =
vB1 =
pB1 =
Label each object A or B
For every object include: m, v, p
Use subscripts to label m, v, and p with A or B
Use subscripts to label v, and p with 0 or 1

12. Label Everything - + Fill in all the numbers from the problem: mA =
Before (0)
After (1) A B A B - +
mA =
vA0 =
pA0 =
mB =
vB0 =
pB0 =
mA =
vA1 =
pA1 =
mB =
vB1 =
pB1 =
Fill in all the numbers from the problem:

13. Label Everything - + Fill in all the numbers from the problem:
Before (0)
After (1) A B A B - +
mA =
vA0 =
pA0 =
mB =
vB0 =
pB0 =
mA =
vA1 =
pA1 =
mB =
vB1 =
pB1 =
Fill in all the numbers from the problem:
A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

14. Label Everything - + Fill in all the numbers from the problem:
Before (0)
After (1) A B A B - +
mA =
vA0 =
pA0 =
mB =
vB0 =
pB0 =
mA =
vA1 =
pA1 =
mB =
vB1 =
pB1 =
Fill in all the numbers from the problem:
A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

15. Label Everything
Before (0)
After (1) A B A B - +
mA =
vA0 =
pA0 =
mB =
vB0 =
pB0 =
mA =
vA1 =
pA1 =
mB =
vB1 =
pB1 =
Use units to help you figure it out (kg = m, m/s = v, kgm/s = p):
A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

16. Label Everything
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 =
pB1 =
Use units to help you figure it out (kg = m, m/s = v, kgm/s = p):
A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

17. Label Everything - + Fill in what you don’t know with question marks:
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 = ?
mB = 8300 kg
vB0 = -34 m/s
pB0 = ?
mA = 3100 kg
vA1 = -45 m/s
pA1 = ?
mB = 8300 kg
vB1 = ?
pB1 = ?
Fill in what you don’t know with question marks:
A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

18. Find Missing Pieces
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 = ?
mB = 8300 kg
vB0 = -34 m/s
pB0 = ?
mA = 3100 kg
vA1 = -45 m/s
pA1 = ?
mB = 8300 kg
vB1 = ?
pB1 = ?
If you know 2 out of 3 (m, v, p) you can find what’s missing.

19. Find Missing Pieces
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 = ?
mB = 8300 kg
vB0 = -34 m/s
pB0 = ?
mA = 3100 kg
vA1 = -45 m/s
pA2 = ?
mB = 8300 kg
vB1 = ?
pB1 = ?
If you know 2 out of 3 (m, v, p) you can find what’s missing.

20. Find Missing Pieces
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
If you know 2 out of 3 (m, v, p) you can find what’s missing.
Use: p = mv

21. ptot = pA0 + pB0 & ptot = pA1 + pB1
Find Total Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
ptot = pA0 + pB & ptot = pA1 + pB1

22. ptot = pA0 + pB0 & ptot = pA1 + pB1
Find Total Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
ptot = pA0 + pB & ptot = pA1 + pB1
Use what you know:
ptot = =

23. Find the Missing Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
Use what you know and a little algebra:
ptot = pA0 + pB & ptot = pA1 + pB1
ptot =

24. Find the Missing Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
Use what you know and a little algebra:
ptot = pA1 + pB1

25. Find the Missing Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
Use what you know and a little algebra:
ptot = pA1 + pB1
-pA1 -pA1

26. Find the Missing Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
Use what you know and a little algebra:
ptot = pA1 + pB1
-pA1 -pA1
pB1 = ptot – pA1

27. Find the Missing Momentum
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = ?
Use what you know and a little algebra:
pB1 = ptot – pA1 = ( ) = 18500

28. Solve for What You Don’t Know
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = 18500
Use p = mv and a little algebra:

29. Solve for What You Don’t Know
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = 18500
Use p = mv and a little algebra:
pB1 = mBvB1

30. Solve for What You Don’t Know
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = 18500
Use p = mv and a little algebra:
pB1 = mBvB1
mB mB .

31. Solve for What You Don’t Know
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = 18500
pB1 = mBvB1
mB mB .
vB1 = pB1 mB

32. Solve for What You Don’t Know
Before (0)
After (1) A B A B - +
mA = 3100 kg
vA0 = 52 m/s
pA0 =
mB = 8300 kg
vB0 = -34 m/s
pB0 =
mA = 3100 kg
vA1 = -45 m/s
pA1 =
mB = 8300 kg
vB1 = ?
pB1 = 18500
vB1 = pB1 = 18500
mB kg
vB1 = 2.2 m/s

33. Celebrate! You Did It!
J. Gabrielse

34. Classwork
p. 210: 11 & 12