Transcript Impulse and Momentum

Impulse & Momentum
Have you ever wondered…
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Why golfers and bowlers “follow through”?
Why skydivers bend their knees upon
impact?
Why falling on a wood floor (or into a
swimming pool) hurts less than falling on a
cement one?
Have you ever wondered…
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What’s the best strategy to win a “water
balloon toss” or an “egg toss”?
Why we make auto air bags and padded
dash boards?
How the police can figure out how fast you
were going BEFORE an accident by
measuring your skid marks?
Impulse and Momentum
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To answer all of these questions--you need
to understand: Impulse and Momentum
Recall, Newton’s first law…The Law of Inertia
The study of inertia for moving objects is the
study of “momentum”
Consider the following:
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When a baseball
bat hits a baseball,
a force is applied
OVER A SHORT
PERIOD OF TIME.
Impulse
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Defn: A force applied over a period of time is
called an IMPULSE.
I  F  t
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What are the SI units of Impulse?
Example - Impulse
A batter hits a 500g ball with a force of 200N. If
the time of contact was 0.205 seconds, find the
impulse of the ball.
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I  F  t
I  200N  0.205sec
I  41N  sec
Example #2
A batter hits a 500g ball with a force of 500N. If
the time of contact was 0.205 seconds, find the
impulse of the ball.
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a)
b)
c)
d)
e)
0 N·s
102.5 N·s
51250 N·s
250000 N·s
I have no clue…
I  F  t
Answer: (b)
A batter hits a 500g ball with a force of 500N. If
the time of contact was 0.205 seconds, find the
impulse of the ball.
I  F  t
 (500 N)  0.205 sec
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kg m
= 102.5 N sec = 102.5
s
Example #3
A batter hits a 500g ball with a force of 500N. If
the impulse is 75 N·s, then what is the contact
time between the ball & bat?
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a)
b)
c)
d)
e)
0 sec
0.150 sec
75 sec
37500 sec
I have no clue…
I  F  t
Answer: (b)
A batter hits a 500g ball with a
force of 500N. If the impulse
is 75 N·s, then what is the
contact time between the ball
& bat?
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I  F  t
I
t =
F
75 N sec
t =
500 N
t = 0.150 sec
Example #4
A batter hits a 500g ball and the impulse given to
the ball is 125 N·s. If the ball & bat are in contact
for 200 milli-seconds, then what is the force of the
bat?
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a)
b)
c)
d)
e)
0N
0.625 N
2.5 N
625 N
I have no clue…
I  F  t
Answer: (d)
A batter hits a 500g ball and
the impulse given to the ball
is 125 N·s. If the ball & bat
are in contact for 200 milliseconds, then what is the
force of the bat?
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I  F  t
I
F
t
125N sec
F
0.200 sec
F  625 N
Back to baseball...Which will have
the greater speed afterward?
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A large or a small ball?
A fast or a slow ball?
A large or a small bat?
A fast or a slow swing?
Momentum
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Defn: The MOMENTUM of a body is equal
to the product of its mass and its velocity.
p  mv
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Is momentum a vector or a scalar?
What are the SI units of momentum?
Determine the following
momentums…
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Ex #1 - A 1200lb car moving at 60mph
Ex #2 - A 5.0g bullet moving at 900m/s
Ex #3 - A 3 ton elephant sitting still
Ex #4 - A 150g hummingbird flying at 40mph
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ALL answers need to be in kg m/s
1 lb = 0.454 kg; 1 mph = 0.447 m/s
Determine the following
momentums…Solution
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Ex #1 - A 1200lb car moving at 60mph
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Ex #2 - A 5.0g bullet moving at 900m/s
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= 4.5 kg m/s
Ex #3 - A 3 ton elephant sitting still
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= 14599.7 kg m /s
= 0 kg m/s
Ex #4 - A 150g hummingbird flying at 40mph
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= 2.68 kg m/s
Determine the following
momentums…
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Can the hummingbird and the car ever have
the same momentum?
Explain…
Example #5
A boy standing at one end of a floating raft that
is stationary relative to the shore walks to the
opposite end of the raft, away from the shore.
As a consequence, the raft.
(a) remains stationary,
(b) moves away from the shore,
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(c) moves toward the shore
(d) Not enough information given
Answer: (c)
A boy standing at one end of a floating raft that
is stationary relative to the shore walks to the
opposite end of the raft, away from the shore.
As a consequence, the raft.
Answer: (c) moves toward the
shore - Newton’s 3 law
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Example #6
Which has a greater momentum, a heavy truck
at rest or a moving skateboard?
(a) Heavy truck,
(b) Skateboard,
(c) Neither (same momentum)
(d) Not enough information given
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Answer: (b)
Which has a greater momentum, a heavy truck
at rest or a moving skateboard?
Answer: (b) The truck at rest has no
speed, hence no momentum. So the
moving skateboard has greater
momentum.
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Making the Connection:
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Look at the units of Impulse and
Momentum…Do you notice
anything?
Recall, F = m·a…can you
rearrange the equation to say
something about Impulse or
Momentum?
The Impulse-Momentum Theorem
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When a net force acts upon a body for a
period of time, the Impulse applied by the
force is equal to the body’s change in
Momentum!
F  t  mv   m(v f  v0 )
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Impulse-Momentum Theorem #1:
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If your Force is limited, how can you
MAXIMIZE the impulse you apply?
By increasing the time of contact!
Golfing…Baseball…
Example – Impulse & Momentum
A batter hits a 500g ball with a force of 200N. If
the time of contact was 0.205 seconds, find the
speed of the baseball if:
(a) it is on a batting tee when hit
(b) it is moving toward homeplate with a
speed of 35 m/s
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Impulse & Momentum – Solution (a)
I  F  t  m  v  m  (vf  v 0 )
(200 N)  0.205sec  0.5 kg  v f
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(200 N)  0.205sec
 vf
0.5 kg
m
v f  82
s
Impulse & Momentum – Solution (b)
I  F  t  m  v  m  (vf  v 0 )
m
(200 N)  0.205sec  0.5 kg  (vf  -35 )
s
(200 N)  0.205sec
m
 (vf  -35 )
0.5 kg
s
m
m
(vf  -35 )  82
s
s
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m
m
(vf  35 )  82
s
s
m
m
m
m
(vf  35  35 )  82  35
s
s
s
s
m
v f  47
s
Impulse-Momentum Theorem #2
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If your change in momentum is constant,
how can you MINIMIZE the force applied to
you?
By increasing the time of contact!
Bending knees upon impact, rolling with the
punches, crumple zones, running shoes, air
bags…
Momentum Changes and Bouncing
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Is it more dangerous when a flower pot falls
on your head and breaks or stays in one
piece and bounces back up?
When an object bounces, what happens to
it’s velocity? How does that effect it’s change
of momentum?
Since ∆p is greater in bouncing situations, the
Impulse applied will be greater!
The Law of Conservation of Momentum
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Internal forces are forces that act within a
system, external forces are forces that act on
a system from outside…
If a system is not affected by any net external
force, it is said to be “ISOLATED”.
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an isolated system, the total
linear momentum is always
conserved!
Example - Recoil
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A hunter shoots a 0.22 rifle
and the 3.0 kg gun recoils
with a speed of 0.042 m/s.
If the bullet has a mass of
0.5 g, find the muzzle speed
of the gun.
Example - Recoil ~ Answer
(P) before  (P) after
P
rifle
 Pbulletbefore  Prifle  Pbulletafter
m V  m V   m V  m V 
3000g  0 m s  0.5g  0 m s  3000g  0.042m s  0.5g V m s 
rifle
0  126
g m
 0.5V
sec
g m
 0.5V
sec
m
V  252  564m ph
s
126
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bullet before
rifle
bullet after
Example #7
Jocko, who has a mass of
60kg and stands at rest on
ice, catches a 20kg ball
that is thrown to him at
10km/h. How fast do
Jocko and the ball move
across the ice?
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(a) 0 km/hr (b) 2.5 km/hr (c) 200 km/hr
(d) no way to determine
Answer: (b)
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(b): The momentum before the
catch is all in the ball, 20kg x
10km/h = 200kg·km/h. This is
also the momentum after the
catch, where the moving mass
is 80kg—60kg for Jocko and
20kg for the caught ball.
80kg x v = 200kg·km/h v =
200kg·km/h/80kg = 2.5km/h
Answer: (b)
(P) before  (P) after
Pball  PJockobefore  Pball  PJockoafter
m V
ball
 m VJocko
before
 m Vball  m VJocko
after
20kg 10 km hr 60kg 0 km hr 80kg  V km hr
kg km
 80kg  V km
hr
hr
 kg  km   1 
V  200
 


hr  80kg 
V  2.5 km hr
200
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Example #8
Which would be more
damaging:
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(a)Driving into a massive concrete wall
(b)Driving at the same speed into a head-on
collision with an identical car traveling
toward you at the same speed
(c) Neither - the same amount of damage
(d)Not enough information given
Answer: (c)
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(c): Both cases are
equivalent, because either
way, your car rapidly
decelerates to a dead stop.
The dead stop is easy to
see when hitting the wall,
and identical cars at equal
speeds means equal
momenta—zero before,
zero after collision.
Example #9
Strictly speaking, when a gun is fired,
compared with the momentum of the recoiling
gun, the opposite momentum of the bullet is
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(a) less
(b) more
(c) the same
(d) no way to determine
(Neglect the effect of the hand.)
Answer: (a)
(a) Why? Because more than just a bullet comes out of
the barrel when a gun is fired. The gas, formed when
the powder in the cartridge burns, pushes the bullet
along the barrel and this gas too has appreciable mass
and exits at high speed. So, Momentum of recoiling
gun = momentum of bullet + momentum of gases.
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The End...