1. Conservation of Momentum in 2-d (two dimensions)

2. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

3. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Strategy: Since this collision involves the negligible friction of ice, there is no external net force acting on the “system” of the two pucks. We have an “isolated system”.
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

4. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Strategy: Since this collision involves the negligible friction of ice, there is no external net force acting on the “system” of the two pucks. We have an “isolated system”
10.0 m/s
[E36.9°N]
During the collision, each puck exerts a force on each other. But remember, according to Newton's third law, these forces are equal and opposite, so when we consider the “system”, these internal forces cancel out.
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

5. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Strategy: Since this collision involves the negligible friction of ice, there is no external net force acting on the “system” of the two pucks. We have an “isolated system”
10.0 m/s
[E36.9°N]
During the collision, each puck exerts a force on each other. But remember, according to Newton's third law, these forces are equal and opposite, so when we consider the “system”, these internal forces cancel out.
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg
If Fnet system = 0, then what can we use here?

6. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Strategy: Since this collision involves the negligible friction of ice, there is no external net force acting on the “system” of the two pucks. We have an “isolated system”
10.0 m/s
[E36.9°N]
During the collision, each puck exerts a force on each other. But remember, according to Newton's third law, these forces are equal and opposite, so when we consider the “system”, these internal forces cancel out.
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
If Fnet system = 0, then
psystem stays constant before, during and after the collision.
3.00 kg

7. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
If psys (before) = psys (after) then...
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

8. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
If psys (before) = psys (after) then...
psys x (before) = psys x (after)
psys y (before) = psys y (after)
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

9. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step one: Draw a momentum component diagram of any “oblique” vectors.
10.0 m/s
[E36.9°N]
P'2 kg= mv = 2 X 10 = 20
2.00 kg
36.9°
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

10. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step one: Draw a momentum component diagram of any “oblique” vectors.
10.0 m/s
[E36.9°N]
p'2 kg= mv = 2 X 10 = 20
2.00 kg
P'2 kg y= ?
36.9°
36.9°
12.0 m/s [E]
P'2 kg x= ?
v and p = ?
3.00 kg

11. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step one: Draw a momentum component diagram of any “oblique” vectors.
10.0 m/s
[E36.9°N]
p'2 kg= mv = 2 X 10 = 20
2.00 kg
P'2 kg y= ?
36.9°
36.9°
12.0 m/s [E]
P'2 kg x= 20cos36.9°
+16.0 kgm/s
v and p = ?
3.00 kg

12. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step one: Draw a momentum component diagram of any “oblique” vectors.
10.0 m/s
[E36.9°N]
p'2 kg= mv = 2 X 10 = 20
P'2 kg y= 20sin36.9°
= kgm/s
2.00 kg
36.9°
36.9°
12.0 m/s [E]
P'2 kg x= 20cos36.9°
+16.0 kgm/s
v and p = ?
3.00 kg

13. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

14. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
v and p = ?
3 kg puck
3.00 kg
Total

15. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck ?
v and p = ?
3 kg puck
3.00 kg
Total

16. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
v and p = ?
3 kg puck
3.00 kg ?
Total

17. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
v and p = ?
3 kg puck
3.00 kg
Total

18. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
v and p = ?
3 kg puck
3.00 kg
Total ?

19. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
v and p = ?
3 kg puck
3.00 kg
Total
+24

20. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
v and p = ?
3 kg puck
3.00 kg
Total
+24 ?

21. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
v and p = ?
3 kg puck
3.00 kg
Total
+24
+ 24

22. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24 ?
v and p = ?
3 kg puck
3.00 kg
Total
+24
+ 24

23. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
Total
+24
+ 24

24. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

25. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16 ?
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

26. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

27. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x ?
Total
+24
+ 24

28. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

29. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24 ?

30. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

31. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24 ?

32. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

33. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16 ?
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

34. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
+12
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
Total
+24
+ 24

35. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step two: Set up a “MO” component chart:
P'2 kg y= kgm/s
P'2 kg x= kgm/s
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
+12
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
P'3 kg y
Total
+24
+ 24

36. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
X equation ?
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
+12
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
P'3 kg y
Total
+24
+ 24

37. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
+16 + P' 3 kg x = +24
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
+12
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
P'3 kg y
Total
+24
+ 24

38. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
+16 + P' 3 kg x = +24
Y equation ?
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
+12
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
P'3 kg y
Total
+24
+ 24

39. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
Object px p'x py p'y
2.00 kg
36.9°
12.0 m/s [E]
2 kg puck
2 X 12
= +24
+16
+12
v and p = ?
3 kg puck
3.00 kg
P' 3 kg x
P'3 kg y
Total
+24
+ 24

40. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

41. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

42. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
+16 + P' 3 kg x = +24
12.0 m/s [E]
v and p = ?
3.00 kg

43. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
+16 + P' 3 kg x = +24
P' 3 kg x =
12.0 m/s [E]
v and p = ?
3.00 kg

44. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
+16 + P' 3 kg x = +24
P' 3 kg x =
P' 3 kg x = 8.0 kgm/s [E]
12.0 m/s [E]
v and p = ?
3.00 kg

45. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
+16 + P' 3 kg x = +24
P' 3 kg x =
P' 3 kg x = 8.0 kgm/s [E]
12.0 m/s [E]
v and p = ?
3.00 kg
+12 + P'3 kg y = 0

46. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
+16 + P' 3 kg x = +24
P' 3 kg x =
P' 3 kg x = 8.0 kgm/s [E]
12.0 m/s [E]
v and p = ?
3.00 kg
+12 + P'3 kg y = 0
P'3 kg y = -12

47. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step three: Set up x and y equations:
Step four: Solve equations
+16 + P' 3 kg x = +24
+12 + P'3 kg y = 0
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
+16 + P' 3 kg x = +24
P' 3 kg x =
P' 3 kg x = 8.0 kgm/s [E]
12.0 m/s [E]
v and p = ?
3.00 kg
+12 + P'3 kg y = 0
P'3 kg y = -12
P'3 kg y = 12.0 kgm/s [S]

48. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
2.00 kg
36.9°
12.0 m/s [E]
v and p = ?
3.00 kg

49. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
36.9°
12.0 m/s [E]
12.0 kgm/s
v and p = ?
3.00 kg

50. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
36.9°
12.0 m/s [E]
12.0 kgm/s
P'3 kg = ?
v and p = ?
3.00 kg

51. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
36.9°
12.0 m/s [E]
12.0 kgm/s
P'3 kg = ?
v and p = ?
3.00 kg
| P'3 kg | = ?

52. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
36.9°
12.0 m/s [E]
12.0 kgm/s
P'3 kg = ?
v and p = ?
3.00 kg
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

53. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
P'3 kg = ?
v and p = ?
3.00 kg
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

54. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
P'3 kg = ?
v and p = ? Θ
= Tan-1(12/8)
= ?
3.00 kg
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

55. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
P'3 kg = ?
v and p = ? Θ
= Tan-1(12/8)
= 56.3°
3.00 kg
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

56. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
3.00 kg
P'3 kg = ? Θ
= Tan-1(12/8)
= 56.3°
v and p = ?
| P'3 kg |
= ( )1/2
= 14.4 kgm/s
Therefore p'3 kg= ?

57. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
3.00 kg
P'3 kg = ? Θ
= Tan-1(12/8)
= 56.3°
v and p = ?
| P'3 kg |
= ( )1/2
= 14.4 kgm/s
Therefore p'3 kg= 14.4 kgm/s [E56.3°S]

58. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
3.00 kg
P'3 kg = ? Θ
= Tan-1(12/8)
= 56.3°
v and p = ?
Therefore p'3 kg= 14.4 kgm/s [E56.3°S]
v'3 kg = ?
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

59. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
3.00 kg
P'3 kg = ? Θ
= Tan-1(12/8)
= 56.3°
v and p = ?
Therefore p'3 kg= 14.4 kgm/s [E56.3°S]
v'3 kg = p/m = ?
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

60. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
3.00 kg
P'3 kg = ? Θ
= Tan-1(12/8)
= 56.3°
v and p = ?
Therefore p'3 kg= 14.4 kgm/s [E56.3°S]
v'3 kg= p/m=14.4 kgm/s [E56.3°S] / 3 kg
| P'3 kg |
= ( )1/2
= 14.4 kgm/s

61. Conservation of Momentum in 2-d Example: A 2
Conservation of Momentum in 2-d Example: A 2.00 kg hockey puck moving at 12.0 m/s [E] makes a glancing collision with a stationary 3.00 kg hockey puck, After the collision, the 2.00 kg puck glances off at 10.0 m/s [E36.9°N]. What is the momentum and velocity of the 3.00 kg puck after the collision?
Step five: Draw a tip-to-tail diagram
P' 3 kg x = 8.0 kgm/s [E]
P'3 kg y = 12.0 kgm/s [S]
10.0 m/s
[E36.9°N]
8.0 kgm/s
2.00 kg
Θ =?
36.9°
12.0 m/s [E]
12.0 kgm/s
3.00 kg
P'3 kg = ? Θ
= Tan-1(12/8)
= 56.3°
v and p = ?
Therefore p'3 kg= 14.4 kgm/s [E56.3°S]
v'3 kg= p/m=14.4 kgm/s [E56.3°S] / 3 kg
= m/s [E56.3°S]
| P'3 kg |
= ( )1/2
= 14.4 kgm/s