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

Momentum

Momentum

• The “Quantity of Motion”

• p = momentum• m = mass• v = velocity

• Unit:

• Vector• Direction of momentum is determined by the

direction of the velocity

smkg sN or

Momentum

amFNET

t

vvm if

t

p

t

vmvm if

t

pFNET

Newton’s 2nd Law of Motion in terms of momentum

Net External Force = time rate of change of momentum

External to the system

Momentum

t

pF

ptF

Impulse

• I = Impulse

• F= force

• ∆t = change in time

ptFavg

I

p mv f m

v i

Force vs Time Graphs

F

t

Area = Impulse = Δp

Impulse

F

t

Area =

Actual force experienced during a collision

Favg

Impulse - Problems

F (N)

t (s)

Force on a 1 kg object

10

2 4

If v = 0 at t = 0, find vf at t = 4 s

Impulse - Problems

• Find the change in momentum

2 kg

2 kg

5 m/s

3 m/s

+-

If ∆t = 0.020 s, find the average force the wall exerts on the ball

Impulse - Problems

If mass = 2 kg and v = 0 at t = 0, find vf at t = 12 s

F (N)

t (s)

20

4 8 12

Momentum

40°

10 m/s

10 m/s

Find ΔP

m = 2 kg

Momentum

30°

15 m/s

15 m/s

Find ΔP

m = 3 kg

Momentum Example 2 cont’d

pFind

m = 2 kg

10 m/s

6 m/s

m = 2 kg

60°40°

Conservation of Momentum

• If no external unbalanced forces, NETF

• so

if ppp 0

if pp Conservation of momentum for a system

w/ no external imbalance in forces Total initial momentum of a system =

Total final momentum of a system

0

t

pFNET

0

1-D Explosion

5 kg 10 kg

0ivBefore

5 kg 10 kg

?fv After

smv 3

2-D Explosions

6 kg 3 kg

4 kg

6 kg

3 kg

4 kg

?afv

θ=?

30 m/s

50 m/s

Before

2 kg3 kg

10 m/s0biv

After

2 m/s

?afv

3 kg

2 kg

40◦

θ=?

Collisions and Explosions

Examples

3 kg 7 kg

0iv

Before

sm2

3 kg 7 kg?fv

After

sm8.0

Examples

5 kg 7 kg?fv

After

5 kg 7 kg

0iv

Before

3ms

Explosions and Collisions

ma= 950 kg

mb= 1300 kg

vai= 16 m/s

vbi= 21 m/s

= ?vf = ?

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”