Download Unit Lesson Plan – Atomic Structure

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Basics
1D Mot.
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2D Mot.
     
Forces
Energy
Moment.
Rotation
Circ/Grav
SHM
Waves
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Circuits
AP Exam
AP Unit 8: Uniform Circular Motion and Gravity – HW
Knowledge & Skills
(What skills are needed to achieve the desired results?)
By the end of this unit, students will know:
 Newton’s Law of Universal Gravitation
 That the motion of an object in orbit is under the influence of gravitational forces
 How an object’s gravitational field is determined by its size and its mass
 How to relate the radius of the circle and the speed or rate of revolution of the particle to the magnitude
of the centripetal acceleration.
 How to analyze situation in which an object moves with specified acceleration under the influence of
one or more forces so they can determine the magnitude and direction of the net force, or of one of the
forces that makes up the net force, in situations such as the following:
(1)Motion in a horizontal circle (e.g., mass on a rotating merry-go-round, or car rounding a banked
curve).
(2) Motion in a vertical circle (e.g., mass swinging on the end of a string, cart rolling down a curved
track, rider on a Ferris wheel).
(What is the sequence of activities, learning experiences, etc, that will lead to desired results (the plan)?
Day
In Class Work
Homework
Due that day
Notes: Uniform Circular Motion
1-5
Notes: Dynamics of UCM
6-9
Notes: Universal Law of
Gravitation
Lab: Law of universal gravitation
(PHET)
Notes: Satellites and
“Weightlessness”
Lab: Inertial and Gravitational
Mass
Practice:
Ranking Task
Practice:
Practice Test
10-13
14-18
MP: UCM Due Online 11pm
19-24
PhET Lab Due on MP by 8am
MP: Law of Universal
Gravitation Due Online 11pm
Lab: Inertial & Grav. Mass
Due
MC Test
FR Test
Textbook Chapters: 6.1-6.6
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8 – UCM and Gravity
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Uniform Circular Motion
1. 6.1 A 5.0-m-diameter merry-go-round is turning with a 3.8s period. What is the speed of a child on
the rim?
2. 6.3 An old-fashioned LP record rotates at 33⅓ rpm.
a. What is its frequency in rev/s?
b. What is its period, in seconds?
3. 6.7. A CD-ROM drive in a computer spins the 12-cm-diameter disks at 8400 rpm.
a. What is a disk's period (in s) ?
b. What is a disk's frequency (in rev/s)?
c. What would be the speed of a speck of dust on the outside edge of this disk?
d. What is the acceleration in units of g that this speck of dust experiences?
4. 6.7 The radius of the earth's very nearly circular orbit around the sun is 1.50×1011m. Assume a year of
365 days.
a. Find the magnitude of the earth's velocity as it travels around the sun.
b. Find the magnitude of the earth's centripetal acceleration as it travels around the sun.
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5. Linearization of Data: It is much easier to analyze data when the graph of the data is a line. Curves
are often too difficult for drawing conclusions. This section deals with the technique called
“linearization”, in which data that yields a curve can be converted to yielding a line.
A penny dropped from rest at time t = 0 falls next to a meterstick while being recorded by a camera. The
resulting video analysis yields the data of time t and distance fallen d shown below. The purpose of the
experiment is to measure the acceleration of gravity.
Original Data
t (sec)
d (m)
0.133
0.11
0.167
0.16
0.200
0.23
0.234
0.30
0.267
0.39
Linearized Data
xyvariable variable


Step 1: Write an equation appropriate to the situation that relates the two variables. The equation cannot
have + or – symbols in it.
Step 2: Get the two variables on one side of the equal sign, and all constants on the other side of the equal
sign.
Step 3: Your “variables side” should be a fraction. Think “rise over run”, and choose your x-variable and
y-variable. Then fill in the new table.
Step 4: Graph the linearized data from the new table. Write the linear regression equation below.
Step 5: Use the slope of the linearized data to answer the purpose of the lab.
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Dynamics of UCM
6. 6.19 A baseball pitching machine works by rotating a light and stiff rigid rod about a horizontal axis
until the ball is moving toward the target. Suppose a 144g baseball is held 81cm from the axis of
rotation and released at the major league pitching speed of 85 mph.
a. What is the ball's centripetal acceleration just before it is released?
b. What is the magnitude of the net force that is acting on the ball just before it is released?
7. 6.23 Gibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to
the next handhold. A 8.8kg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its
motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point
of its swing, the gibbon is moving at3.5m/s . What upward force must a branch provide to support the
swinging gibbon?
8. 6.17 A 1500kg car drives around a flat 230-m-diameter circular track at 26 m/s. What is the
magnitude of the net force on the car?
9. 6.18 A fast pitch softball player does a "windmill" pitch, moving her hand through a vertical circular
arc to pitch a ball at 73 mph. The 0.18kg ball is 55cmfrom the pivot point at her shoulder.
a. Just before the ball leaves her hand, what is its centripetal acceleration?
b. At the lowest point of the circle the ball has reached its maximum speed. What is the magnitude
of the force her hand exerts on the ball at this point?
c. At the lowest point of the circle the ball has reached its maximum speed. What is the direction
of the force her hand exerts on the ball at this point?
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Apparent Forces in CM
10. 6.24 The passengers in a roller coaster car feel 50%heavier than their true weight as the car goes
through a dip with a 40m radius of curvature. What is the car's speed at the bottom of the dip?
11. 6.25 You hold a bucket in one hand, and in the bucket is a 500g rock. You swing the bucket so the
rock moves in a vertical circle 2.2m in diameter. What is the minimum speed the rock must have at
the top of the circle if it is to always stay in contact with the bottom of the bucket?
12. 6.27 As a roller coaster car crosses the top of a 60-m-diameter loop-the-loop, its apparent weight is the
same as its true weight. What is the car's speed at the top?
13. 6.28 An 80-ft-diameter Ferris wheel rotates once every 25s .
a. What is the apparent weight of a 76kg passenger at the lowest point of the circle? Express your
answer in SI units.
b. What is the apparent weight of a 76kg passenger at the highest point of the circle? Express your
answer in SI units.
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Weightlessness and Gravity
14. 6.30 A satellite orbiting the moon very near the surface has a period of 110 min. Use this information,
together with the radius of the moon r=1.74×106m, to calculate the free-fall acceleration on the
moon’s surface. What is the moon's acceleration due to gravity?
15. 6.31 Spacecraft have been sent to Mars in recent years. Mars is smaller than Earth and has
correspondingly weaker surface gravity. On Mars, the free-fall acceleration is only 3.8m/s2 . What is
the orbital period of a spacecraft in a low orbit near the surface of Mars? Assume the radius of the
satellite's orbit is about the same as the radius of Mars itself, rMars = 3.37×106m .
16. 6.37 In recent years, astronomers have found planets orbiting nearby stars that are quite different from
planets in our solar system. Kepler-12b, has a diameter that is 1.7 times that of Jupiter(RJupiter =
6.99 × 107 m), but a mass that is only 0.43 that of Jupiter(MJupiter = 1.90 × 1027 kg ). What is the value
of g on this large, but low-density, world?
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AP Physics 1: 2015-2016
17. Linearization of Data: It is much easier to analyze data when the graph of the data is a line. Curves
are often too difficult for drawing conclusions. This section deals with the technique called
“linearization”, in which data that yields a curve can be converted to yielding a line. The first two
examples walk you through the steps of the process.
The Texas Driver's Handbook (page 8-1) illustrates a table of stopping distances d. The distance required
for a car to stop depends on the car’s speed v when the brakes were applied. For this exercise, the initial
speeds v and braking distances d were converted to m/s and meters (from mph and ft). You are to
determine the acceleration of the car as it brakes to rest.
Original Data
Linearized Data
x-variable
v (m/s)
d (m)
8.94
5.79
13.41
13.11
17.88
23.16
22.35
36.27
26.82
52.12
31.29
71.02

y-variable

Step 1: Write an equation appropriate to the situation that relates the two variables. The equation cannot
have + or – symbols in it.
Step 2: Get the two variables on one side of the equal sign, and all constants on the other side of the equal
sign.
Step 3: Your “variables side” should be a fraction. Think “rise over run”, and choose your x-variable and
y-variable. Then fill in the new table.
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Step 4: Graph the linearized data from the new table. Write the linear regression equation below.
Step 5: Use the slope of the linearized data to answer the purpose of the lab.
18. 6.41 What is the free-fall acceleration at the surface of the moon?
b. What is the free-fall acceleration at the surface of the Jupiter?
Gravity and Orbits
19. 6.45 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period
of 5.0 earth years. Assume a 365.25-days year and MSun = 1.99 × 1030 kg.
a. What is the asteroid's orbital radius?
b. What is the asteroid's orbital speed?
20. 6.42 Planet X orbits the star Omega with a "year" that is 400 earth days long. Planet Y circles Omega
at four times the distance of Planet X. How long is a year on Planet Y?
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21. 6.43 Satellite A orbits a planet with a speed of 20000m/s . Satellite B is twice as massive as satellite A
and orbits at twice the distance from the center of the planet. What is the speed of satellite B? Assume
that both orbits are circular.
22. 6.44 The International Space Station is in a 280-mile-high orbit.
a. What is the station's orbital speed? The radius of Earth is 6.37×106m, its mass is5.98×1024kg.
b. What is the station's orbital period?
23. 6.46 An earth satellite moves in a circular orbit at a speed of 7000 m/s. What is its orbital period?
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24. 6.49 In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these
planets are in orbits that are similar to that of earth, which orbits the sun(Msun = 1.99 × 1030 kg) at a
distance of1.50 × 1011 m, called 1 astronomical unit (1 au).Others have extreme orbits that are much
different from anything in our solar system. The following problem relates to one of these planets that
follows circular orbit around its star. Kepler-42c orbits at a very close 0.0058au from a small star with
a mass that is 0.13 that of the sun. How long is a "year" on this world? Assume the orbital period of
earth is 365 days.
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Mastering Physics: Law of
Universal Gravitation
Name:
Period:
Due Online: Monday, February 15, 2016 11pm
Due Work: (next school day) Tuesday, February 16, 2016
6.34 The free-fall acceleration at the surface of planet 1 is _____. The radius and the mass of planet 2 are
twice those of planet 1. What is the free-fall acceleration on planet 2?
6.39 The mass of the sun is ___________ and its distance to the Earth is ___________ .
a. What is the gravitational force of the sun on the earth?
b. The mass of the moon is ___________ and its distance to the Earth is ___________ . What is
the gravitational force of the moon on the earth?
c. The moon's force is what percent of the sun's force?
6.32 The centers of a _____ lead ball and a _____ lead ball are separated by _____.
a. What gravitational force does each exert on the other?
b. What is the ratio of this gravitational force to the weight of the _____?
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Mastering Physics: Uniform
Circular Motion (UCM)
Name:
Period:
Due Online: Tuesday, February 9, 2016 11pm
Due Work: (next school day) Wednesday, February 10, 2016
6.6 The horse on a carousel is _____from the central axis.
a. If the carousel rotates at _____, how long does it take the horse to go around twice?
b. How fast is a child on the horse going (in m/s)?
6.8 Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed
of the blades tips can be quite high-many times higher than the wind speed. A turbine has
blades _____long that spin at _____.
c. At the tip of a blade, what is the speed?
d. At the tip of a blade, what is the centripetal acceleration?
6.20 A wind turbine has ___________ blades that are36m long. The blades spin at _____. If we model a
blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each
blade's centripetal acceleration?
6.26 A roller coaster car is going over the top of a _____-radius circular rise. At the top of the hill, the
passengers "feel light," with an apparent weight only _______ of their true weight. How fast is the coaster
moving?
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AP Physics 1: 2015-2016