Chapter 7 Momentum and Impulse

I. What are Momentum and Impulse?A. Motion of a Bouncing Ball

1) First part of motion is like falling object: g, v, d

2) Impact, then changes direction quickly

3) Requires strong force for such large acceleration: Floor

provides the force

4) At impact the ball’s shape is distorted: spring

a) Compresses then expands

b) Need strong force to activate a spring

5) Impact is very short time: a = large, F = large

B. Analyzing Bouncing Ball

1) Newton’s Laws

a) Force is large and always changing

b) Time is very short

c) Hard to get accurate description using F = ma

2) Total Change in Motion

a) Examine velocity by rewriting Newton’s 2nd Law

b) Impulse = force on an object times the time the force acts = Ft

i.

ii. Often, force is continually changing; use average F

iii. Impulse is a vector quantity with same direction as F

iv. Impulse directly proportional to F

c) Momentum = p = mass of an object times its velocity = mv

i.

ii. Vector quantity in same direction as velocity

iii. Momentum is directly proportional to velocity and mass

iv. Change in momentum

t

vmamF

vmtF

tFImpulse

vmp

vmp

d) Example: m1 = 7 kg, m2 = 0.07 kg, v1 = 2 m/s, v2 = 200 m/s

e) Impulse/Momentum Theorem

i. An impulse acting on an object produces an equivalent change in the objects momentum

ii. Impulse = Change in Momentum

iii.

C) Applying the Impulse/Momentum Theorem

1) Bouncing Ball

a) What is p when the ball hits the floor?

b) v changes direction (p also must change direction)

vmtF

c) Add vectors: pi + p = pf

d) v2 = -v1

i. Stop the ball (v = 0) p = -mv1

ii. Accelerate up (v = -v1) p = -mv1

e) pT = p + p = -mv1 + -mv1 = -2mv1

2) Hitting a Golf Ball

a) F = 500 N, m = 0.1 kg, t = 0.01 s

b) Impulse?

c) v?

Change in direction

Magnitude ofTotal mometum change

3) Catching a ball

a) Pull your hand back as the ball hits it

b) t gets longer, so Force is less on your hand: Impulse = Ft

c) Less force means ball doesn’t bounce off or hurt your hand

d) Car airbag does the same thing

II. Conservation of MomentumA) Collision of 2 football players: Fullback = Player 1, D-Back = Player 2

1) Newton’s 3rd Law: equal and opposite forces at impact

2) t is same for both, Impulse must also be the same magnitude

[p1 = Impulse1 = F1t] = [-F2t = -Impulse2 = -p2]

BeforeAfter

Player 1 Player 2

B) Conservation of Momentum: Total change in momentum of a

closed system = 0. F1 and F2 are forces internal to this system.

1) p1 = -p2 or p1 + p2 = 0

2) Objects in the same system can exchange momentum, but the total momentum of the system remains the same. Sum of p = 0.

3) If external forces act on the system, then total p changes.

4) Use p = 0 to solve the football tackle problem:

m1 = 100 kg m2 = 75 kg v1 = +5 m/s v2 = -4 m/s

a) p1 = m1v1 = (100kg)(5m/s) = 500 kgm/s

b) p2 = m2v2 = (75kg)(-4m/s) = -300 kgm/s

c) pT = p1 + p2 = +200 kgm/s

d) vT = ? pT = mTvT

smkg

skgm

m

pv

T

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