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Linfield Christian High School
AP Physics 1
Dr. Botros
Email:[email protected]
AP Physics Summer Work
June 2020
Kinematics
Name:
Due date: July 31st.2020
Text Book: College Physics –Serway.VUILLE/ELEVENTH EDITION
ISBN-13:978-1305952300, ISBN-10: 9781305952300
Submit your work on my Linfield or by Email (due July 31st.at 3:30 PM)
Please email or contact me if you have any questions
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NEWTONIAN MECHANICS (KINEMATICS) - Objectives
Learning Objective (3.A.1.1): The student is able to express the motion of an object using narrative, mathematical, and graphical representations. Learning Objective (3.A.1.2): The student is able to design an experimental investigation of the motion of an object. Learning Objective (3.A.1.3): The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. Learning Objective (4.A.1.1): The student is able to use representations of the center of mass of an isolated two-object system to analyze the motion of the system qualitatively and semi quantitatively. Learning Objective (4.A.2.1): The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time. Learning Objective (4.A.2.3): The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. Learning Objective (5.D.3.2):
The student is able to make predictions about the velocity of the center of mass for interactions within a defined one-
dimensional system.
Learning Objective (5.D.3.3):
The student is able to make predictions about the velocity of the center of mass for interactions within a defined two-
dimensional system.
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VOCABULARY
Read Chapters 2 and 3 (Kinematics) in your textbook. Define the following vocabulary words:
Kinematics –
Scalar –
Vector –
Resultant –
Distance –
Displacement –
Speed –
Velocity –
Acceleration –
Free Fall –
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TEXTBOOK NOTES
Read Chapter 2 and 3 (Kinematics) in your textbook. Fill in the following graphic organizer:
Main Ideas: Important Examples: Find the following examples in your
text. Describe and understand the example, include the
page number to refer back.
1.) Solving for velocity after a ball has fallen a given
distance.
2.) Finding the maximum height of a ball thrown
upwards
3.) Solving for the horizontal distance of a horizontal
projectile
4.) Solving for the horizontal distance of an angled
projectile
Equations:
Find these on your reference table!
Important Graphs/Pictures:
Draw and explain Figure 3.16 and Figure 3.17:
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Text Book NOTES – Velocity and Acceleration
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Text Book NOTES – Graphing Relationships
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PRACTICE - Linear Motion
Calculations
1. A car traveling at 40 m/s came to a halt in 8 seconds after the brakes were applied with uniform pressure. The
speed of the car 5 seconds after the brakes were applied was
a. 25 m/s b. 10 m/s c. 15 m/s d. 20 m/s
2. A ball starts from rest and rolls down an incline. After 1.0 second the ball has traveled 1.0 meters. Assuming no
friction, how fast is the ball moving after 5.0 seconds?
a. 5.0 m/s b. 8.0 m/s c. 10 m/s d. 15 m/s
3. A high-speed train in Japan travels a distance of 300. Kilometers in 3.60 x 103 seconds. What is the average
speed of this train?
4. A bullet traveling at 300 m/s enters a wooden block that is 10 cm wide and emerges from the other side with a
velocity of 100 m/s. What is the magnitude and direction of the bullets’ average acceleration while it is passing
through the block?
5. The speed of an object undergoing constant acceleration increases from 8 m/sec to 16 m/sec in 10 seconds.
How far does the object travel?
6. A bullet traveling at 400 m/s enters a wooden block emerges from the other side 0.0008s later with a velocity of
200 m/s. What is the magnitude and direction of the bullet’s average acceleration while it is passing through the
block?
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Conceptual
1. If an object stars from rest and travels with uniform accelerated motion, the acceleration rate compared to the
displacement of the object during the first second is
a. Equal b. ½ as great c. Twice as great d. Four times as great
2. A ball is thrown vertically upwards with an initial velocity of 20 m/s. The acceleration due to gravity on Earth is
rounded to 10 m/s2. On Mars the acceleration due to gravity is 3.7 m/s2.
a. Fill in the following data tables:
Earth
Time Acceleration Velocity Distance
0 s 20 m/s 0 m
1 s
2 s
3 s
4 s
b. Discuss the differences in distance values between 0-1 seconds and 1-2 seconds on Earth. Why is the
ball not increasing at a constant rate?
c. Explain how and why the above scenarios are different:
d. How long will it take the ball on Mars to fall back to its original position?
e. Sketch a graph of velocity vs. time for each planet for 11 seconds:
Earth Mars
f. Describe all of the differences of the above graphs and the rationale behind these differences:
Mars
Time Acceleration Velocity Distance
0 s 20 m/s 0 m
1 s
2 s
3 s
4 s
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PRACTICE - Graphing Relationships
Write the number of the graph, below, that best illustrates the relationship described with respect to time
1. The speed of a freely falling object _______
2. The distance from an observer to a stationary object _______
3. The velocity of an object moving with no acceleration _______
4. The distance an object has moved as it rolls down an incline _______
5. The height above the ground of a ball thrown upward _______
6. Sketch a distance vs. time graph with following separate segments:
a. Traveling forward at a constant speed 3 seconds
b. Traveling forward at a greater constant speed 2 seconds
c. Not moving for 2 seconds
d. Accelerating for 3 seconds
e. Traveling backwards to the “start” position at a constant speed for 4 seconds
7. Then sketch the corresponding velocity vs. time graph
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EXAMPLE – Horizontal Projectiles
Base your answers on the information below and the diagram at the right.
Arrow 1 is dropped straight down at while Arrow 2 is fired horizontally with
an initial speed of 20 m/s. Both are initially at a height of 45 meters above
the ground.
1. Which arrow (ball) will hit the ground first? Why?
Predict: Actual:
2. What do you know about the horizontal direction? The vertical direction? How does that help simplify the
equations above?
3. How long will it take arrow 1 to strike the ground?
4. How long will it take for arrow 2 to strike the ground? Look familiar?? Why?
5. What is the velocity of arrow 1 just as it hits the ground?
6. What is the resultant velocity of arrow 2 just as it hits the ground?
7. What will be the horizontal distance traveled by arrow 2?
45 meters
20 m/s Arrow 2
Arrow 1
2
00
0f
at2
1tvxx
atvv
2
00 at2
1tvxx
directionx
2
00 at2
1tvyy
directiony
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EXAMPLE – Angled Projectiles
Using the following information, answer the questions below:
A soccer ball is kicked with an initial speed of 5 m/s at an angle of 30⁰ relative to the horizontal
1. Determine the horizontal component of velocity of the soccer ball.
2. Determine the vertical component of velocity of the soccer ball.
3. How long will it take for the soccer ball to reach its maximum height?
4. What will be the maximum height reached by the soccer ball?
5. How long will the soccer ball be in the air?
6. What will be the horizontal distance traveled by the soccer ball?
5.0 m/s
30⁰ 2
00
0f
at2
1tvxx
atvv
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Text Book NOTES – Angled Projectiles
1.) Fill out the chart below for the following two scenarios:
Scenario:
Suppose a golf ball is hit off the tee with an initial velocity of 30.0 m/s at an angle of 35⁰ to the horizontal. If the green is at the same elevation, how far must the golf ball be hit?
Neglecting air resistance, what is the maximum height obtained by the ball?
A 0.5 kg rock is thrown off the edge of a cliff at 30 m/s at an angle of 35⁰ above
the horizontal. If the height of the cliff is 200 meters, find the maximum height and the horizontal range of the rock.
Picture:
Similarities:
Differences:
2.) Calculate the time in the air, maximum height obtained, and horizontal range for the second scenario.
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PRACTICE – Conceptual Angled Projectiles
Jim and Sara stand at the edge of a 50 m high cliff on the moon. Jim extends his arm over the cliff edge and throws a ball straight up with an initial speed of 20 m/s. Sara throws an identical ball with the same initial speed, but she throws the ball at a 30 degree angle above the horizontal. a.) Consider each ball at the highest point in its flight. At this point:
i.) Which ball has the greater vertical velocity? Circle your answer and explain briefly.
Sara’s Jim’s Both are the same
ii.) Which ball has the greater horizontal velocity? Circle your answer and explain briefly.
Sara’s Jim’s Both are the same
iii.) Which ball's velocity vector has greater magnitude? Circle your answer and explain briefly.
Sara’s Jim’s Both are the same iv.) Which ball reaches the peak of its flight more quickly after being thrown? Circle your answer and explain briefly.
Sara’s Jim’s Both are the same
b.) Now consider each ball just before it hits the ground, 50 m below where the balls were initially released. At this point: i.) Which ball has the greater vertical velocity? Circle your answer and explain briefly.
Sara’s Jim’s Both are the same
ii.) Which ball's velocity vector has greater magnitude? Circle your answer and explain briefly.
Sara’s Jim’s Both are the same
c.) Below is a velocity-time graph representing the vertical velocity of Sara's ball. On the same axes, sketch a velocity-time graph representing the vertical velocity of Jim's ball.
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PRACTICE QUIZ - Kinematics
1. A boy rolls his 3 kg toy truck at 2 m/s off the edge of a horizontal 25 m high bridge. How far away from the
bridge will it land?
2. A baseball player hits a foul ball straight up into the air at 30 m/s.
a. How long will it take to land?
b. What is its maximum height?
c. Sketch a graph of the velocity vs. time and the height vs. time for the object and state what the slope of
each graph represents
3. An arrow is show at 20 m/s at 30⁰ from the horizontal.
a. What maximum height will it reach?
b. How far away will it land?
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Use the following graph and to answer questions 4-7.
4. Arrange each section (A-B, B-C, etc) in increasing magnitude of acceleration.
5. Identify the point or section in which the car has returned to its original starting location. If it does not return to
original location, explain how far it is away and how you know.
6. Describe, in words, the motion of the car throughout each section.
A
B C
D
E
F
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7. Draw the corresponding acceleration vs. time graph:
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TEXTBOOK PROBLEMS – p. 91-97
Re-read your textbook. Use the examples provided and answers in the back of the book to help answer the following
questions. Try them to the best of your ability. Show all work.
18.) Two vectors, of magnitudes 3 and 4, respectively, are added. Determine how the magnitude changes as the vector
direction changes.
29.) An airplane flies northwest (exactly 45⁰ north of west) for 250 mi and then west for 150 mi. Find the resultant (or
sum) displacement vector by (a) graphical method and (b) the component method
81.) An arrow has an initial launch speed of 18 m/s. If it must hit a target 31 meters away at the same elevation, what
should be the projection angle? (You will need to use the trig function: 2sinθcosθ = sin2θ)
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83.) A stone thrown off a bridge 20 meters above a river has an initial velocity of 12 m/s at an angle of 45⁰
Fill in the data table below until the stone hits the water
(use any needed rows, adding more if necessary):
Go back and draw the horizontal velocity and vertical velocity vectors in the above picture.
Identify all the possible changes to this stone-throw that would decrease the horizontal range. Explain why
these modifications decrease the range.
Time (s) Horizontal Velocity (m/s) Vertical Velocity (m/s)
0
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85.) William Tell is shooting at an apple that hangs on a tree. The apple is a horizontal distance of 20.0 m away and a
height of 4.00 m above the ground. If the arrow is released from a height of 1.00 m above the ground and this the
apple 0.500 s later, what is its initial velocity?
Outline all of the necessary steps needed to solve this
problem. It is not necessary to perform all the calculations,
just set up the steps that you would take:
86.) A ditch 2.5 m wide crosses a trail-bike path. An upward incline of 15⁰ has been built up on the approach so that the
top of the incline is level with the top of the other side of the ditch. With what minimum speed must a trail-bike be
moving to clear the ditch? (Add 1.4 m to the rand for the back of the bike to clear the ditch safely.)
Set up the x- and y- directions, filling in all of the information that you
know and leaving the rest as variables (we will actually solve together):
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NOTES – Center of Mass
Equation:
Examples: A dumbbell has a connecting bar of negligible mass.
1.) Find the location of the center of mass if m1 and m2 are each
5.0 kg.
2.) Find the location of the center of mass if m1 is 5.0 kg and m2 is 10.0 kg.
Demo: You can lean
over and touch your
toes without toppling
only if your center of
gravity (center of
mass) is above the
area bounded by your
feet
Concept: Average position of all the
particles of mass that make up an
object. The point at which all of the
mass of an object of system may be
considered to be concentrated.
Important Note:
The center of mass
of the total system
does not move!
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