lec momentum.notebook
January 23, 2013
Momentum & Impulse
Chapter 7
Can you give examples of things that might have a lot of momentum?
The Hush Sound
So Sudden
lec momentum.notebook
The larger an object, the more momentum it has.
Smaller objects have less momentum.
January 23, 2013
lec momentum.notebook
January 23, 2013
Smaller objects have less momentum.
But with enough velocity, they still deliver a punch!
Momentum
is a product
of mass
and velocity!
When one object with momentum strikes another,
some momentum is transferred.
The original object may or may not retain some of its momentum.
lec momentum.notebook
January 23, 2013
The Big Mo
p = mv
• (p) is momentum, (m) is mass, and (v) is velocity
(note: Velocity is a vector, mass is a scalar)
The Big Mo
p = mv
• (p) is momentum, (m) is mass, and (v) is velocity
• Momentum is also referred to as Moving Inertia
lec momentum.notebook
January 23, 2013
The Big Mo
p = mv
• (p) is momentum, (m) is mass, and (v) is velocity
• Momentum is also referred to as Moving Inertia
• Momentum is always conserved (it has to go somewhere)
The Big Mo
p = mv
•
•
•
•
(p) is momentum, (m) is mass, and (v) is velocity
Momentum is also referred to as Moving Inertia
Momentum is always conserved (it has to go somewhere)
Momentum can be added as vectors as well
lec momentum.notebook
January 23, 2013
So, now we know how to calculate the momentum of something. What should we test?
So, now we know how to calculate the momentum of something. What should we test?
If the velocity of the Ping­Pong Ball Bazooka is 300m/s, and its mass is 2.7g, what's its momentum?
lec momentum.notebook
January 23, 2013
Energy of the Ping Pong Ball Bazooka...
m = 2.7 g = 0.0027kg
v ≈ 300m/s
p = mv = 0.0027kg * 300m/s
p = 0.81 kg m/s (or a 1kg mass moving 0.81 m/s)
How about Energy?
Energy of the Ping Pong Ball Bazooka...
m = 2.7 g = 0.0027kg
v ≈ 300m/s
p = mv = 0.0027kg * 300m/s
p = 0.81 kg m/s (or a 1kg mass moving 0.81 m/s)
How about Energy?
KE = 1/2 mv2
KE = 0.00135kg*(300m/s)2
KE = 121.5 J (or about the same as dropping a 1kg mass 12m onto your foot)
lec momentum.notebook
Momentum is conserved
in a collision or explosion.
Though you must treat it
like a vector to properly
understand it.
Given:
F = ma
Because of Action­Reaction:
F1 = ­F2
(the forces are equal, but opposite in direction)
F = ma
F1 = ­F2
m1a = ­m2a
m1(vf­vi)/t = ­m2(vf­vi)/t
January 23, 2013
lec momentum.notebook
F = ma
F1 = ­F2
m1a = ­m2a
m1(vf­vi)/t = ­m2(vf­vi)/t
m1vf ­ m1vi = ­m2vf + m2vi
F = ma
F1 = ­F2
m1a = ­m2a
m1(vf­vi)/t = ­m2(vf­vi)/t
m1vf ­ m1vi = ­m2vf + m2vi
m1vf + m2vf = m1vi + m2vi
January 23, 2013
lec momentum.notebook
January 23, 2013
F = ma
F1 = ­F2
m1a = ­m2a
m1(vf­vi)/t = ­m2(vf­vi)/t
m1vf ­ m1vi = ­m2vf + m2vi
m1vf + m2vf = m1vi + m2vi
Final Momentum = Initial Momentum
ALWAYS!! *
p1f + p2f = p1i + p2i
Final Momentum = Initial Momentum
ALWAYS!! *
* If there are no outside forces.
Imagine pushing a car's bumper, vs pushing the dashboard.
Friction would be an outside force, so we don't consider the conservation of momentum AFTER the collision, just during it.
lec momentum.notebook
January 23, 2013
Witness the conservation of momentum!
Shoot the ping pong ball into the coffee can. Let the can & ball fly off the table horizontally.
Where will the coffee can & ping pong ball land?
First we CALCULATE...then we TEST!!!
Ping Pong Ball:
mp = 2.7 g = 0.0027kg
vp ≈ 300m/s
pp = mv = 0.0027kg * 300m/s
pp = 0.81 kg m/s
Coffee Can Catch:
mc = 282g = 0.282kg
Table:
dy = 0.91 m (table height)
t = 0.43s
(from freefall)
Where does it land...huh?
dx = lec momentum.notebook
How does Force relate to Momentum?
F = ma
How does Force relate to Momentum?
F = ma
F = m(Δv/t)
Ft = mΔv
January 23, 2013
lec momentum.notebook
January 23, 2013
How does Force relate to Momentum?
F = ma
F = m(Δv/t)
Ft = mΔv
mΔv = Δp This change in momentum is called IMPULSE
I = Ft = mΔv
I
e
s
l
u
p
m Impulse is the change in momentum: it is equal to Force multiplied by the time
I = Ft = mΔv
Increasing the time of impact decreases the force of impact.
Decreasing the time of impact increases the force of impact.
lec momentum.notebook
January 23, 2013
The brakes go out on your car, and you need to stop. Given the following two choices, in which situation would you rather be in?
2
1
a) 1
b) 2
c) neither
The brakes go out on your car, and you need to stop. Given the following two choices, in which situation would you rather be in?
1
2
a) 1
b) 2
c) neither
Hopefully you said 1. I would have picked neither if that were an option!!!
lec momentum.notebook
January 23, 2013
The airbag in this picture increases the
time of impact, whereas the wall
causes an impulse for the car that
happens very quickly.
Assuming both the hay and the wall stop you, in which scenario do we have the greatest impulse? 1
2
a) 1
b) 2
c) same
d) no impulse here dude
lec momentum.notebook
January 23, 2013
Assuming both the hay and the wall stop you, in which scenario do we have the greatest impulse? 1
2
a) 1
b) 2
c) same
d) no impulse here dude
Assuming both the hay and the wall stop you, in which scenario do we have the greatest impulse? 1
F
t
2
F
a) 1
b) 2
t
c) same
d) no impulse here dude
lec momentum.notebook
January 23, 2013
lec momentum.notebook
January 23, 2013
lec momentum.notebook
January 23, 2013
Longer tube means more time for the force (breath) to act on the projectile.
Longer tube means more time for the force (breath) to act on the projectile.
More time means more Impulse
(I = Ft)
lec momentum.notebook
January 23, 2013
Longer tube means more time for the force (breath) to act on the projectile.
More time means more Impulse
(I = Ft)
Impulse means greater change in momentum. (Ft = Δmv)
Longer tube means more time for the force (breath) to act on the projectile.
Ft
F
More time means more Impulse
(I = Ft)
t
t
F
Impulse means greater change in momentum. (Ft = Δmv)
lec momentum.notebook
January 23, 2013
Ft = mΔv
Longer tube means more time for the force (breath) to act on the projectile.
Δv
More time means more Impulse
(I = Ft)
t Δv
Impulse means greater change in momentum. (Ft = Δmv)
t
F = m
F
= m
How does this relate to energy?
F = ­F
For two interacting objects, F*t is the same.
Is F*d?
lec momentum.notebook
How does this relate to energy?
F = ­F
For two interacting objects, F*t is the same.
Is F*d?
No! when they push off each other, the smaller object has greater acceleration, so covers more distance. More work is done on the smaller object.
So ENERGY is NOT conserved.
Bouncing, Sticking, Passing Through (Impulse)
January 23, 2013
lec momentum.notebook
January 23, 2013
Catch vs. Play Catch?
The Pelton Water Wheel
Water bouncing vs striking
lec momentum.notebook
January 23, 2013
PING­PONG BALL BAZOOKA
Remember What
happens?
Click for 1 can
Click for 2
cans