Download Physics 7B - AB Lecture 3 April 24 Vectors

Physics 7B - AB
Lecture 4
April 24
Chapter 6
Galilean Space-Time Model, lots of
Vectors, Intro. to Force, Momentum
Lecture slides available at
http://physics.ucdavis.edu/physics7
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Course Website
http://physics.ucdavis.edu/physics7
Click on Physics 7B-A/B
Today
Quiz 2!
May is a busy month.
There will be four Quizzes.
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What is Galilean Space-Time model about?
The Galilean Space-Time Model
In our ordinary experience, three spatial dimensions and
one time dimensions are all independent of each other.
z
Ex. You walk on a moving bus,
y
what is your V
?
w.r.t.the ground
x
What if the bus was moving really fast? Like
close to the speed of light? (i.e., C = 3 x 108
m/s)
3
What is Galilean Space-Time model about?
The Galilean Space-Time Model
In our ordinary experience, three spatial dimensions and
one time dimensions are all independent of each other.
z
Ex. You walk on a moving bus,
y
what is your V
?
w.r.t.the ground
x
If the speed of the bus was close to the speed of
light…
The Special Relativity Model of Space-Time
The three spatial dimensions are NOT independent of time.
i.e. Someone on the moving bus and someone on the ground
will measure different velocity.
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Models in 7B are based on Galilean SpaceTime model.
Good news is,
The predictions of special relativity agree well with Galilean SpaceTime model in their common realm of applicability, specifically in
experiments in which all velocities are small compared to the speed of
light. z
y
x
What are the forces exerted
on the airplane for it to accelerate?
Why does she start spinning
much faster when she
pulls her arms and legs in?5
To describe the motion of objects, we use
several vector quantities such as…
• Position vector R
e.g. Rinitial, Rfinal
• Displacement vector ∆R = Rfinal – Rinitial
• Velocity vector v = dr/dt
• Acceleration vector a = dv/dt
• Force vector F
•Linear momentum vector p = mv
New physical
quantities!
• Angular momentum vector L = rptangential
Ok… What were vectors again??
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Example #1
I take four steps right and three steps up,
what is my displacement?
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Example #2
If I take a different path from point A to point
B, would my displacement be different as
well?
B
∆RAB
A completely
different path
A
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vave = ∆R/ ∆t,
v = dR/ dt
Therefore, velocity (vector) points in the same
direction as the displacement (vector)
The magnitude of velocity is a positive
number called speed
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Introduction to
Conservation of
Momentum
Momentum is another (vector) quantity
Nature chooses to conserve (for a closed
system).
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Momentum
For a particle: Defined by p = mv
Is a vector, points in the same direction as v
(see above equation)
For a system: Defined by adding together the
momentum vectors of everything that makes
up the system, I.e. ptotal = ∑pi = p1+ p2+ p3+…
Is conserved for a system if nothing external
pushes or pulls on it
Has units of kg m/s
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Conservation of Momentum
Example Rifle recoil
Before shooting (at rest)
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Conservation of Momentum
Example Rifle recoil
Before shooting (at rest)
vbullet
After shooting
pbullet
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Conservation of Momentum
Example Rifle recoil
Before shooting (at rest)
vbullet
pbullet
After shooting
vRifle
pRifle
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Conservation of Momentum
Railroad cars collide
A 10,000kg railroad car A, traveling at a speed of
24m/s strikes an identical car B, at rest. If the car
lock together as a result of the collision, what is
their common speed afterward?
vAi
i =0
v
B
Before
collision
After
collision
A
B
pAi
A+B
At rest
vA+Bf
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Conservation of Momentum
Railroad cars collide
A 10,000kg railroad car A, traveling at a speed of
24m/s strikes an identical car B, at rest. If the car
lock together as a result of the collision, what is
their common speed afterward?
vAi
i =0
v
B
Before
collision
After
collision
A
B
pAi
A+B
At rest
vA+Bf
pA+Bf
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•
•
When does momentum of something
change??
… when a force F acts on the something
during a time interval
e.g. A bat hits a baseball
change in momentum is called: Impulse
Impulse Is related to the net external force in
the following way:
Net Impulseext = ∆ p = ∫ ∑ Fext(t)dt
Approximate a varying force as an average force acting
during a time interval ∆t
Net Impulseext = ∆ p = ∑ Fave.ext x ∆ t
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DLM8&9 : Use of vectors, Force Model,
Some new ideas: Force diagram, Momentum
chart
Next week
May1 Quiz3(20min) will cover:
Today’s lecture (exclude momentum, force,
Impulse)
Activities and FNTs from DLM7 and Activities
from DLM8
Bring Calculator!
Closed-book, formulas will be provided.
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Be sure to write your name, ID number & DL section!!!!!
1
MR 10:30-12:50
Dan Phillips
2
TR 2:10-4:30
Abby Shockley
3
TR 4:40-7:00
John Mahoney
4
TR 7:10-9:30
Ryan James
5
TF 8:00-10:20
Ryan James
6
TF 10:30-12:50
John Mahoney
7
W 10:30-12:50
Brandon Bozek
7
F 2:10-4:30
Brandon Bozek
8
MW 8:00-10:20
Brandon Bozek
9
MW 2:10-4:30
Chris Miller
10 MW 4:40-7:00
Marshall Van Zijll
11 MW 7:10-9:30
Marshall Van Zijll
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