1. Momentum

2. Momentum The “Quantity of Motion” Unit: Vector p = momentum m = mass
v = velocity
Unit:
Vector
Direction of momentum is determined by the direction of the velocity

3. Momentum Newton’s 2nd Law of Motion in terms of momentum
Net External Force = time rate of change of momentum
External to the system

4. Momentum

5. Impulse
I = Impulse
F= force
∆t = change in time

6. Force vs Time Graphs F t
Area = Impulse = Δp

7. Impulse
Actual force experienced during a collision F t
Area =
Favg

8. Impulse - Problems Force on a 1 kg object F (N)
If v = 0 at t = 0, find vf at t = 4 s 10 2 4
t (s)

9. Impulse - Problems Find the change in momentum
2 kg
3 m/s
2 kg - +
If ∆t = s, find the average force the wall exerts on the ball

10. Impulse - Problems
If mass = 2 kg and v = 0 at t = 0, find vf at t = 12 s
F (N) 20
t (s) 4 8 12

11. Momentum
Find ΔP
10 m/s
40°
10 m/s
m = 2 kg

12. Momentum
Find ΔP
15 m/s
30°
15 m/s
m = 3 kg 12

13. Momentum Example 2 cont’d
m = 2 kg
10 m/s
6 m/s
60°
40° 13

14. Conservation of Momentum
If no external unbalanced forces, so
Conservation of momentum for a system w/ no external imbalance in forces
Total initial momentum of a system =
Total final momentum of a system

15. 1-D Explosion
Before
5 kg
10 kg
After
10 kg
5 kg

16. 2-D Explosions
6 kg
3 kg
θ=?
6 kg
50 m/s
4 kg
3 kg
4 kg
30 m/s

17. Collisions and Explosions
Before
10 m/s
2 kg
3 kg
After
θ=?
2 kg
3 kg
40◦
2 m/s

18. Examples
3 kg
7 kg
Before
3 kg
7 kg
After 18

19. Examples
5 kg
7 kg
Before
5 kg
7 kg
After 19

20. Explosions and Collisions
vf = ?
 = ?
ma= 950 kg
vai= 16 m/s
vbi= 21 m/s
mb= 1300 kg

21. Types of Collisions Elastic Collisions – Kinetic energy is conserved
KEi = KEf
Inelastic collision – Some kinetic energy is lost
Typically lost to friction, sound, deformation, etc.
Most collisions in “real life” 21