momentum read your textbook: introduction to physical science –chapter 3.5 –chapter 4 practice...
TRANSCRIPT
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Momentum• Read Your Textbook: Introduction to Physical Science
– Chapter 3.5– Chapter 4
• Practice Homework Exercises
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Motion ReviewVelocity = change in displacement = x Speed
change in time t
Acceleration = change in velocity = v How fast are you
change in time t getting faster.
Force = mass x acceleration = m v a = F/m
t
A look at the two definitions of acceleration….
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Force and Acceleration F = m v = m a
t
If a Force acts occurs over a short time,
a small acceleration results.
If a Force acts over a long time,
a large acceleration results.
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Cannon Ball!
F t = m v
For the same Force (amount of powder), why is the speed of
a cannon ball greater when fired from a longer cannon barrel?
F = m v
t
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Interaction Time
F t = m v
The longer cannon barrel gives the cannon ball a larger
impulse and therefore more momentum. The Force (F) is
allowed to act for a longer time t to build up velocity (v).
F t = m v
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Impulse and Momentumacceleration = acceleration
a = a
F = v F t = m v
m t
Impulse Momentum
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Impulse and Momentum F = v F t = m v
m t
Impulse Momentum
If a change in velocity (momentum) occurs over a short time,
a large force must act.
If the change in velocity (momentum) occurs over an extended
time, a small force is acting. • Recall the Egg Toss Game
• A Boxer Bobs and Weaves His Head
• Bending Legs Upon a Parachute Landing
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Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
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Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
Consider the following collision:
Before After
mMV
v
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Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
Consider the following collision:
Before After
m M mMV
v
v’
V’
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Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
Consider the following collision:
Before After
Total Momentum
MV + mv = total momentum = MV’ + mv’
m M mMV
v
v’
V’
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v
M
m
Total Momentum Before:
M V + m v
60 kg ( 0 km/hr) + 20 kg (10 km/hr) = 200
Ice Ball Toss
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Momentum After (must be identical to momentum before)
= 200
= (M+m) v’
200 = (M+m) v’
200 = (60+20) v’
v’ = 200/80 = 2.5 km/hr
Ice Toss
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What is the total momentum of the debris from a firecracker?
Before After
M V = 0 = total momentum before
Total Momentum After = m1v1 + m2v2 + m3v3 + …
Conservation of Momentum
m1
m2
m4
m3
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What is the total momentum of the debris from a firecracker?
Before After
M V = 0 = total momentum before
Total Momentum After = m1v1 + m2v2 + m3v3 + …
= 0
Conservation of Momentum
m1
m2
m4
m3
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Rifle ShotLet mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle
0 = 0.3 kg (370 m/s) + 5kgVrifle
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Rifle ShotIf momentum is conserved, why doesn’t a rifle kill you upon
recoil after firing a bullet?
Before: mbulletvbullet + MrifleVrifle = 0
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Rifle ShotIf momentum is conserved, why doesn’t a rifle kill you upon
recoil after firing a bullet?
Before: mbulletvbullet + MrifleVrifle = 0
After: = 0
Let mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
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Rifle ShotLet mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle
0 = 0.3 kg (370 m/s) + 5kgVrifle
-0.3(370) = 5 kg Vrifle
Vrifle = - 0.3(370)/5 = - 2.2 m/s
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Rifle ShotLet mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle
0 = 0.3 kg (370 m/s) + 5kgVrifle
-0.3(370) = 5 kg Vrifle
Vrifle = - 0.3(370)/5 = - 2.2 m/s
Shoulder aches, BUT your alive!
Mriflevrecoil = mbulletVbullet
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Now you try:• What is the velocity of a bullet (m = 0.15 kg) after being fired from a 10 kg rifle (NOTE: rifle recoils with a velocity of 3 m/s).
A. 30 m/sB. 1.5 m/sC. 200 m/sD. 310 m/sE. none of these
mbulletvbullet + MrifleVrifle = 0.15 kg (vbullet) + 10kg (3 m/s)
0 = 0.15 kg (vbullet) + 30 kg m/s
-30 kg m/s = 0.15 kg vbullet
vbullet = - 30 kg m/s /(0.15 kg) = - 200 m/s
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Train LinkAn train engine runs into a stationary box car
weighing 4x more than itself to link up. If the engine
was traveling 10 mph before link up, how fast does
the train move after?
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Train LinkAn train engine runs into a stationary box car
weighing 4x more than itself to link up. If the engine
was traveling 10 mph before link up, how fast does
the train move after?
MOMENTUM BEFORE = MOMENTUM AFTER
MVBC + 0 = (M + 4M) VAC
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Train LinkAn train engine runs into a stationary box car
weighing 4x more than itself to link up. If the engine
was traveling 10 mph before link up, how fast does
the train move after?
MOMENTUM BEFORE = MOMENTUM AFTER
MVBC + 0 = (M + 4M) VAC
M(10) = (5M) VAC
10 = 5 VAC
2 = VAC
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Angular MomentumL Angular Momentum: A combination of...
m Mass
v Speed of Rotation
r Mass Position (with respect to rotational axis)
L = m v r
• Conservation Examples:– Spins of Dancers or Ice Skaters– Those Funky Coin Vortexes in Stores– Tops and Gyroscopes– Riding a Bicycle
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Precession and the Earth
• 1 complete cycle takes 26,000 years
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Orbit ApplicationAngular Momentum L,
is the product of a planet's mass (m),
orbital velocity (v)
and distance from the Sun (R).
The formula is simple: L = m v R,
where R = a function of e the eccentricity.
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Faster, CloserConservation of Angular Momentum:
L = L
m V r m v R
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Summary• Impulse and Momentum
– F t = m v
• Conservation of Momentum– Total Momentum (P = M V)
• Angular Momentum– L = m v r