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Momentum• Read Your Textbook: Introduction to Physical Science
– Chapter 3.5– Chapter 4
• Practice Homework Exercises
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….
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.
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
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
Impulse and Momentumacceleration = acceleration
a = a
F = v F t = m v
m t
Impulse Momentum
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
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
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
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’
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’
v
M
m
Total Momentum Before:
M V + m v
60 kg ( 0 km/hr) + 20 kg (10 km/hr) = 200
Ice Ball Toss
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
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
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
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
Rifle ShotIf momentum is conserved, why doesn’t a rifle kill you upon
recoil after firing a bullet?
Before: mbulletvbullet + MrifleVrifle = 0
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
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
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
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
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?
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
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
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
Precession and the Earth
• 1 complete cycle takes 26,000 years
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.
Faster, CloserConservation of Angular Momentum:
L = L
m V r m v R
Summary• Impulse and Momentum
– F t = m v
• Conservation of Momentum– Total Momentum (P = M V)
• Angular Momentum– L = m v r