AP Physics
Monday 13.10.07
Standards:
2a1,2,3 add, subtract, and resolve
displacement and velocity vectors
Objective: SWBAT apply basic
mathematical operations to the
displacement and velocity vectors and
represent them graphically.
Agenda
1.
Warm Up
2.
Review Falling Objects Lab & collect Analysis
3.
Collect First 3 AP Problems. & Q&A Sheets
4.
Hand out Solutions to next 2 AP Problems.
5.
Adding & Subtracting & Graphing Vectors
Notes
6.
Practice
Warm Up
What is A+B, what is B+A,
what is A-B, what is B-A?
A
B
Homework
Correct #2 AP Problems
Practice adding & subtracting
displacement & velocity vectors
AP Physics
Tuesday 13.10.08
Standards: 2c1 Students
should understand the motion
of projectiles in a uniform
gravitational field.
Objective: SWBAT break
displacement vectors in
components and graph them.
Agenda
1. Warm Up
2. Review Vector HW
3. Component vectors and
their graphs notes
4. More Practice breaking
vectors into components
Warm Up
Break the following vector into
components.
vo = 7
m
at 30° N of E
s
Homework
Vector Component Worksheet
AP Physics
Wednesday 13.10.09
Standards: 2c2
Students should understand the motion
of projectiles in a uniform gravitational
field.
Warm Up
a = 2.7
m
s2
at 20° S of E
Objective: SWBAT will master finding
resultant vectors and breaking vectors
into components.
Agenda
1. Warm Up
2. Review Component Vector HW
3. Projectile Motion Notes
3. Practice Analyzing Projectile Motion
Homework
Finding Resultant Vectors &
Resolving Vectors p. 18 1,2,3
p.20 1,2,5
AP Physics
Thursday 13.10.10
Standards: Students should
understand the motion of projectiles in a
uniform gravitational field.
Warm Up
Mr. A is playing a game of pool, he
will win the game if he sinks the final
shot. If the pocket is 1.6 m away at
an angle of 30°, how much horizontal
and vertical distance will Mr. A’s shot
cover in order to sink the shot?
Objective: SWBAT solve projectile
motion problems based on an object
falling from a high place.
CCS.ELA-Literacy.RST11-12.10 By the end of grade 12, read
and comprehend science/technical texts in the grades 11CCR text complexity band independently and proficiently
Agenda
1. Warm Up
2. Review HW
3. Projectile Motion Reading
4. The Basics of Projectile Motion
5. Practice
Homework
D.24 Projectiles launched
horizontally
1,2,3,7,8
AP Physics
Friday 13.10.11
Standards: Students should
understand the motion of projectiles
in a uniform gravitational field.
Objective: SWBAT score 80% on the
quiz
Agenda
1. Warm Up
2. Projectile Reading 2
3. Projectile Motion Sample
Problem
4. Projectile Motion Problems.
Warm Up
A ball is kicked horizontally out of
the back of an airplane at 20m/s.
If the airplane is 3000m in the air,
how far will the ball travel before
it hits the ground?
Homework
p.26,27 #1-6
3 equations of Motion
There are three equations of motion that we use. I will derive
1&3
v = v0 + at
1 is created by combining a=Δv/Δt & Δv=v-v0
No Δx
2.
1
Dx = v0t + at 2
2
2 can be found by graphing the motion of an
accelerating object on a v vs t graph and finding its
area. It can be derived using calculus.
No v
3.
v 2 = v02 + 2aDx
3 is created by substituting equation 1 into equation 2
1.
Though you will not need to derive these, these illustrate a very
important practice we undertake in Physics. There are situations where
we can combine multiple equations in order solve problems that don’t
seem to have a solution.
No t
How to Use the 3 equations of motion
1. The # 1 rule is to use the givens to decide which equation to use.
v = v0 + at
This equation can’t find an x, so don’t use it if you are given
displacement or it is an unknown
1
Dx = v0t + at 2 This equation can’t find v, so don’t use it if you are given final velocity
2
or it is an unknown.
v 2 = v02 + 2aDx
This equation can’t find t, so don’t use it if you are given t or it is an
unknown.
We will call this equation of motion #1
v = v0 + at
We will call this equation of motion #2
1
Dx = v0t + at 2
2
We will call this equation of motion #3
v 2 = v02 + 2aDx
How to use the equations of motion day 2?
2. The # 2 rule is avoid quadratics! If one of your givens is a v0 and your unknown is t
then equation 2 is going to be messy.
2a.Right now try to solve for t using:
Δx=10m,Vo=20m/s,a=-9.8m/s2
1
Dx = v0t + at 2
2
2b.You can avoid this process by using equation 3 then equation 1. Now try solving
the same problem using equation 1 & 3.
3. Remember what they are useful for. These equations work within the context of
uniformly accelerated motion or constant acceleration. This includes no acceleration
Falling Objects Lab Stations
Be sure to collect all data in class. You may analyze the data and calculate at
home if necessary. Justify all of your conclusions with actual data.
Station 1: A falling Marble. You will first make the appropriate calculation to
predict the time it will take for the marble to fall. Then you will actually time it
and find the % error between your calculation and your measurement.
Station 2: What is gravity? By measuring the the time it takes for a golf ball to fall
at different heights make a linear graph and find the slope of the graph for an
accurate value of g. Find the % error. g=9.807m/s2 use significant figures
Station 3: How does gravity work? Directions: Drop the following objects and
time how long it takes them to fall to the ground. Does shape matter? Does size
matter? Use what you know about gravity to make sense of what you observe.
Once you have collected data write a paragraph explaining the physics of falling
objects to the best of your ability.
a. How does gravity affect a marble and a golf ball?
b. How does gravity affect a piece of paper vs. a book?
Can you find a way to make paper and a book fall at the same rate?
c. Compare a large cylinder and a small cylinder.
Does the orientation of the cylinder affect your result?
Kinematic Vector Practice
®
s =10mi + 5mj
Classwork 3: Resultant Vectors
x = 4miˆ + 6mĵ
1.
2.
m
m
v = -2.7 i + 0.5 j
s
s
3.
4.
5.
®
®
v = -3 2
m
m
i- j
s
s
®
a =1.2x10 4
km
4 km
i
+1.1x10
ĵ
hr 2
hr 2
Breaking Vectors into
Components
• x component = horizontal component (left to right)
• y component = vertical component (up and down)
• If you have a vector, you have a quantity that has a magnitude
(size) and a direction. s is a general way to right length or
s=4m
displacement.
θ=30°
• In order to solve problems involving vectors, we benefit
greatly by breaking them into components.
• In 2 dimensional physics the components are x and y
• In 3 dimensional physics the components are x, y, and z.
• We will use 2 dimensions x and y.
Breaking vectors into
Components
When you break vectors into
components they are written
using the following form:
s=4m
θ=30°
x
s = xiˆ + yĵ
ˆand ĵ are called unit vector.
iThey
have a magnitude of 1 and
their sole purpose is to denote
direction.
iˆ means the vector
component is in the horizontal
direction
ĵ means the vector
component is in the vertical
direction.
cos30=x/4m
x=cos30(4m)Î
x=3.46mÎ
sin30=y/4m
y=sin30(4m)Ĵ
y=2mĴ
y
Adding & Subtracting
Displacement Vectors
First show the derivation
for Δx on the board. Then
clarify…
Lets take a look at the vector
relationship that creates Δx:
The x0 vector is shown to your
right. Then x changes by the
amount of Δx
x0
Dx
so xo + Δx = x
x0
Dx
x
but xo + Δx = x solved
for Δx = x-xo
x0
x - x0
x
Adding & Subtracting
Displacement Vectors
Lets take a look at the vector
relationship that creates Δx:
The x0 vector is shown to your
right. Then x changes by the
amount of Δx
x0
Dx
so xo + Δx = x
x0
Dx
x
but xo + Δx = x solved
for Δx = x-xo
The same derivation works for
the Δv vector.
x0
x - x0
x
Resolving Displacement &
Velocity Vectors
For each of the following, find the displacement and
velocity vectors graphically and then find the
displacement using vector components.
1. x = 5cm,30°NW xo =10cm , 45°NW
2. x = 2m ,30°SW xo = 5m , 10°NW
3. x =10m ,30°NE
xo = 7m , 60°NE
4. v = 4m / s ,20°NE
vo = 7
m , 40°NE
s
5. v = 2 m ,10°SW v = 6 m , 70°SE
o
s
s
Breaking vectors into Components
1. x = 5cm
2.
3.
4.
m
v =8
s
30 degrees
45degrees
m 45degrees
s
m
vo = -8
60 degrees
s
v = -4
5. r = -4.2cmiˆ + 7.5cmĵ
6.
7.
r =12.3kmiˆ + 4.9kmĵ
v =12
mˆ
m
i - 4 ĵ
s
s
m
s
8. a = -2.7 2 iˆ - 7.9
m
ĵ
2
s
The Basics of Projectile Motion
1. Read the 2 pages in the handout, focusing on the question:
“What info/knowledge do they want us to take away from this
reading?” 5 min
2. Break into table groups, discuss the main points of the
paragraph, and come to a consensus on the main idea of the
test - 4 min
3. Write a concise paragraph together as a group explaining
your conclusions you reached in #2 5 min
4. This will be a lab grade.
Projectile Motion Reading 2
Read pages 82 – 83, 5 minutes
Focus on: What are differences between the motion of horizontal
projections and todays motion at arbitrary angles? What are the
points of interest in projectile motion? Finally, What is the central
idea that the writer would like you to understand?
Discuss the reading in groups and answer the questions, 7 minutes
Extra Credit: Worth 1 HW assignment, Derive the Range Equation on
p. 85, but do not copy it from the book. You will need to explain each
step you take in words in order to receive extra credit.