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Trains
Momentum
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Which hurts more if it hits you?
Why?
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Left one has more mass
Left one has more velocity
Left one has more momentum!
Momentum
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What does the word momentum mean to you?
Newton referred to what modern physicists term linear
momentum as “the quantity of motion…arising from velocity
and the quantity of matter conjointly.”
In other words, the momentum of the body is
proportional to both its mass and its velocity. By
definition,
p = mv
It is a vector quantity that has units of a kg•m/s.
(There’s no short version, like with Force and Energy)
Newton’s Second Law
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If an object has a change in velocity, a net force must be acting
on it.
Similarly, since momentum is directly related to velocity (as well
as mass), a change in momentum also requires a net force.
In fact, Newton originally expressed his second law of motion in
terms of momentum rather than acceleration.
m(v  vo ) mv  mvo p  po p
Fnet  ma 



t
t
t
t
Change in Momentum
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Newton’s second law
states that the net external
force acting on an object is
equal to the time rate of
change of the object’s
momentum.
p
Fnet 
t
Hammering a Nail…
Impulse
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When two objects—such as a hammer and a nail, a golf club and
a golf ball, or even two cars—collide, they can exert large forces
on one another for a short period of time.
The force is not constant in this case. However, Newton’s
second law in momentum form is still useful for analyzing such
situations by using average values.
Written in this form, the law states that the net average force is
equal to the time rate of change of momentum: F = Δp/Δt.
Rewriting the equation to express the change in momentum, we
have
FΔt = Δp = p - po
Impulse
The term FΔt is known as the impulse of the force:
Impulse = FΔt = Δp = mv – mvo
The SI unit of impulse is a N•s.
Thus, the impulse exerted on a body is equal to the change in the body’s
momentum.
Why are you always instructed to “follow through” in sports?
Baseball
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Who exerts the greater
impulse on a
baseball…the pitcher or
the catcher?
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Who exerts the greater
force on a baseball…the
pitcher or the catcher?
Pitchers and Catchers
Pitcher:
Low force,
long time
Catcher:
High force, short time
Ergo: Big mitt.
Air Bags
Air Bags
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In an accident, the magnitude
of the acceleration is about
32 g’s. Such an acceleration
means a net force about 32
times the weight of the
dummy, clearly enough to
cause serious injuries.
What does an air bag do?
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Increases the stopping distance
(increase stopping time).
Allows the force to be
distributed over a much larger
area (more on this later).
Air Bags can be dangerous too!
Problem #1
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A woman, driving a golf ball off a tee, gives the
ball a velocity of 28 m/s. The mass of the ball
is 0.045 kg, and the duration of the impact with
the golf club is 6 ms. (a) What is the change in
momentum of the ball? (b) Determine the
average force applied to the ball by the club?
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Answer:
1.3 kg•m/s
 220 N
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Problem #2
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A baseball (m=0.14 kg) has an initial velocity of
vo = 38 m/s as it approaches the bat. The
applies a force that is much larger than the
weight of the ball, and the ball departs from the
bat with a final velocity of vf = 58 m/s. The
contact time between the bat and ball is Δt = 4.0
x 10-3 s. Find the average force exerted on the
ball by the bat.
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Answer:
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3400 N