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
Dv
F  ma  m
Dt
b)
F Dt  mDv
Impulse = force on an object times the time the force acts = FDt
i.
Impulse  FDt
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.
p  mv
ii. Vector quantity in same direction as velocity
iii. Momentum is directly proportional to velocity and mass
Dp  mDv
iv. Change in momentum
C)
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. F Dt  mDv
Applying the Impulse/Momentum Theorem
1) Bouncing Ball
a) What is Dp when the ball hits the floor?
b) v changes direction (p also must change direction)
c)
Add vectors: pi + Dp = pf
d)
v2 = -v1
i. Stop the ball (v = 0) Dp = -mDv1
ii. Accelerate up (v = -v1) Dp = -mDv1
e)
DpT = Dp + Dp = -mv1 + -mv1 = -2mv1
Change in
direction
2)
Magnitude of
Total mometum change
Hitting a Golf Ball
a) F = 500 N, m = 0.1 kg, Dt = 0.01 s
b)
Impulse?
c)
Dv?
3)
II.
Catching a ball
a) Pull your hand back as the ball hits it
b) Dt gets longer, so Force is less on your hand: Impulse = FDt
c) Less force means ball doesn’t bounce off or hurt your hand
d) Car airbag does the same thing
Conservation of Momentum
A) Collision of 2 football players: Fullback = Player 1, D-Back = Player 2
After
Before
1)
2)
Newton’s 3rd Law: equal and opposite forces at impact
Dt is same for both, Impulse must also be the same magnitude
[Dp1 = Impulse1 = F1Dt] = [-F2Dt = -Impulse2 = -Dp2]
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) Dp1 = -Dp2
or
Dp1 + Dp2 = 0
2)
Objects in the same system can exchange momentum, but the total
momentum of the system remains the same. Sum of Dp = 0.
3)
If external forces act on the system, then total p changes.
4)
Use Dp = 0 to solve the football tackle problem:
m1 = 100 kg m2 = 75 kg
v1 = +5 m/s v2 = -4 m/s
a)
b)
c)
d)
p1 = m1v1 = (100kg)(5m/s) = 500 kgm/s
p2 = m2v2 = (75kg)(-4m/s) = -300 kgm/s
pT = p1 + p2 = +200 kgm/s
vT = ?
pT = mTvT
vT 
pT 200kgm / s

 1.14m / s
mT
175kg