AP Physics
Monday 13.09.30
Standards: 1)a. Students should
understand the general relationships
between position velocity & acceleration for a
particle along a straight line.
Objective: SWBAT understand
where the equations of motion
come from and WBAT employ
them to solve problems
involving falling objects.
Agenda
1. Warm Up
2. Galileo Video
3. 3 equations of motion applied to
falling objects Notes
4. Falling Objects Problems
Warm Up
The graph below is a plot of
position versus time. For
which labeled region is the
velocity positive and the
acceleration negative?
(A) A (B) B (C) C (D) D (E) E
Homework
Make up Quiz Today After School
Falling Objects HW p.15 1-5,8
AP Physics
Tuesday 13.10.01
Standards:
Warm Up
Relate to two particles that start at x = 0 at t = 0 and move in
one dimension independently of one another. Graphs, of the
velocity of each particle versus time are shown below.
Use the three equations of motion for
1D constant acceleration
Objective: SWBAT verify the
acceleration due to gravity and the
properties of gravity using the
equations of motion.
Agenda
1. Warm Up
2. Correct & Turn in HW
Wednesday
3. Falling Objects
Stations
A
B
#1. Which particle is farthest from the origin at t = 2 seconds.
(A) A (B) B (C) they are in the same location at t = 2 seconds (D)
They are the same distance from the origin, but in opposite
directions (E) It is not possible to determine
#2. Which particle moves with constant non-zero acceleration?
(A) A (B) B (C) both A and B (D) neither A nor B (E) It is not
possible to determine
#3. Which particle is in its initial position at t = 2 seconds?
(A) A (B) B (C) both A and B (D) neither A nor B (E) It is not
possible to determine
Homework
Finish Monday’s HW 1-5,8
Finish Lab Write Up
I will be gone right after school today. Retakes Extended 1 Week
AP Physics
Wednesday 13.10.02
Standards:
2. Motion in 2D, including
projectiles: a,b vectors
Objective: SWBAT resolve
displacement and velocity
vectors.
Agenda
1. Warm Up
2. Correct HW 1-5,8
3. Stations #2 15 min
4. Stations #3 15 min
Warm Up
An object is dropped from rest from the
top of a 400 m cliff on Earth. If air
resistance is negligible, what is the
distance the object travels during the
first 6s of its fall?
a) 30 m b) 60 m c) 120 m d) 180 m e)
360m
Homework
Finish Data and Conclusions for
Station 1,2, and 3
AP Physics
Thursday 13.10.03
Standards: 2. Motion in 2D,
including projectiles: a,b vectors
Objective: SWBAT be able to find
resultant vectors of
displacement, velocity, &
acceleration and break them into
components.
Agenda
1. Warm Up
2. AP Problems
Warm Up
Linearization Graph done on the
board
Homework
Finish AP Problems
AP Physics
Friday 13.10.04
Standards: Standards: Use the
three equations of motion for
1D constant acceleration
Objective:
Warm Up
At a certain time, an object in free fall has a
velocity of 4.0 m/s in the upward direction.
What is the approximate velocity of the
object one second later?
a) 14m/s up b) 10 m/s up c) 4.0 m/s up
d) 6.0m/s down e) 10 m/s down
Agenda
1. Warm Up
2. Review AP Questions
3. Work on 2 more AP questions
Homework
Finish Today’s Classwork
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 & Equations of Motion
- When objects fall they accelerate. There are only slight differences
between the motion of falling objects and the motion of objects on
the ground that speed up and slow down.
- If we assume that gravity is the only force acting on an object then
our acceleration becomes a given and a constant called g.
g=9.8m/s2
- In general when an object is falling towards the ground acceleration
in the motion equations is written a=-g.
- Also the displacement is no longer horizontal x but vertical y.
- From there we have the option of rewriting the equations of motion
to apply specifically to falling objects.
v = v0 - gt
v = v0 - gt
1
Dx = v0t - gt 2
2
v 2 = v02 - 2gDx
1
Dy = v0 t - gt 2
2
v 2 = v02 - 2gDy
Falling Objects Example
#6 p.15 – The Westin Stanford Hotel in Detroit is 228 m tall. If
a worker on the roof drops a sandwich, how long does it take
the sandwich to hit the ground, assuming there is no air
resistance? How would air resistance affect the answer?
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