

Essential Question:
Do force fields really exist and
are they similar to the force fields on Star Trek or Star Wars? 
 1. Mathematically define gravity field.
(gravity field) =

(gravity force) 
(unit of mass) 
 2. State that gravity field is a vector.
 3. Draw a ray diagram of a constant gravity
field.
 4. State the meaning of the space between rays
in a force field diagram.
 5. State the two assumptions implicit in
modeling the Earth's gravity field as constant.
 The Earth is flat
 The Earth's surface is infinitely large
 6. List 3 types of force fields.
Field Type 
Symbol 
Definition 
gravity 
g 
( force ) / ( unit
of mass ) 
electrical 
E 
( force ) / ( unit
of charge ) 
magnetic 
B 
( force ) / [ (
unit of charge )( velocity ) ] 
Relevance: Air resistance is a basic characteristic that
determines all kinds of important issues including fuel efficiency
of vehicles and terminal velocities of falling objects. 


Lesson 1
Key Concept: Falling
in Uniform
Gravity Fields
Purpose:
Introduce the concept of force fields using the most common force
field gravity. Show how a velocity dependent force like air
resistance interacts with a constant gravity field.
Interactive Discussion:
Star Wars vs. real life
In Class Problem Solving:
 Derive an expression for calculating terminal
velocity.


 MiniLab
Physics Investigation (Requires only Purpose,
data, and conclusion)

Title 
Analysis of Low velocity Air Resistance for a streamlined
and nonstreamlined object 
Purpose 
Determine if air resistance is directly proportional to velocity
for a streamlined and non streamlined object/ 
Overview 
Air resistance is often modeled as being directly proportional
to velocity when included in mathematical models using Newton's
second Law. 
Data,
Calculations 
Perform regression analysis on the the data for each object
using Minitab and plot the residuals. 
Questions,
Conclusions 
Was a linear relationship between air resistance and velocity
appropriate? How did the streamlined object differ from the
non streamlined one. 
Resources/Materials: 
Wind Tunnel and associated equipment. 

Essential Question:
What causes non uniform force
fields? 
Gravity Fields Around Planets
Section 13.1, 14.2

7. Correctly use the universal
gravitational force equation.

yields an action reaction pair

r = distance between centers of mass

G = universal gravitational constant

the equation does not work inside a planet

force is directly proportional to mass

force is inversely proportional to r squared

8. Draw a ray diagram of the gravity field
around a planet (see red lines in figure at right). Note that the spacing of the
lines is directly proportional to the gfield strength, if the drawing is made
to scale.

9. Calculate the
gravity field strength = g
(or acceleration due to gravity) using the universal gravitational force equation.
F = (G∙M∙m)
/ r^{2}
g = (G∙M)
/ r^{2}

10. Note that the gravity field above a planet's
surface acts as though it came from a point source located at the planet's
center of mass. Remember, the universal gravitational
force equation is only valid on a planet's exterior.

11. Explain why the equation for gravity force
vs. distance from a planet (a point source of gravity) is only valid above the
planet's surface. (The
amount of mass attracting an object toward the planet's center of mass changes
as the object approaches the center of the planet. Outside the planet's surface,
the amount of mass is constant)
Homefun: Read 13.1 to 13.3;
Problems 1, 3, 11, 23

Read:
Insultingly Stupid Movie Physics
 Chapter 14, Scenes With Real Gravity:
Celebrating Disasters With Happy Hollywood Endings, pp 213  229


Lesson 2 Key Concept:
NonUniform
Gravity Fields
Purpose:
Introduce the concept of force fields and show how it can be used in
problem solving.
Interactive Discussion:
Objectives
Demo
1: Demonstrate the
inverse square law with a flashlight.
Video Clip:
Show a video clip of Armageddon when the asteroid is split in half
and travels around the Earth. Estimate the tidal forces casued by
the asteroid as it travels within 300 miles of Earth's surface.
(teams of 2)
In Class Problem Solving:
 Calculate g for planet Earth.
 Calculate g for Zorg.
Resources/Materials: Flashlight 

Essential Question:
How can the force of gravity be
calculated inside a planet? 
The Ultimate Transportation System

a Tunnel Through the Center of a Planet.
Relevance: Worm
holes are a major yet unproven form of space travel in science fiction. In many
ways, the holeintheplanet transportation system is analogous to a worm hole.
 12. Define scaling factor.
The number every dimension of an object is multiplied by
in order to create a different sized version of the object that looks
identical to the original except for its size.

13. Derive an expression for the gravity field vs. radius inside a planet,
using the following:
 the gravity field inside a hollow planet is zero
 if an object's center of mass (CM) is at a distance r from the
planet's CM, only mass in the sphere of radius r will create a net
gravitational force.
 the gravitational force is calculated using the universal gravity
equation using the above sphere
 mass scales with the cube of the scaling factor.
 14. Using the displacement equation for simple
harmonic motion as show below, derive the velocity and acceleration equations
for simple harmonic motion.
x = (x_{max})cos (ωt)
 15. Derive
the time it would take to fall through a tunnel bored through the center of
the Earth.
 radius =
6.371 x
10^{6} meters,
 mass = 5.9736×10^{24}
kg,
 G =
6.754 × 10^{−11} m^{3}/kg/s^{2}

 16. Plot a graph of gfield vs, distance from the center of a planet.
Homefun: Serway


Lesson 3 Key
Concept: Gravity Field Inside a Planet
Purpose:
Introduce scaling factors and show how scaling factors in
combination with simple harmonic motion and the universal
gravitational equation can be used to analyze the gfield inside a
planet.
 Interactive Discussion:

Describe the gravity field inside a hollow planet.
 Describe the ultimate transportation system.
In Class Problem Solving:
 Derive an equation for the gravity field inside
a planet.
 Give the displacement vs. time equation for
simple harmonic motion, derive the velocity and acceleration vs.
time equations.
 Calculate the time required to fall completely
through a tunnel from one side of Earth to the other.


Essential Question:
How is gravitational Potential
energy calculated when the gfield is not constant? 


Gravitational
Potential Energy From a Planet

17. Note that that by convention the gravitational
potential energy is considered to be zero at a distance of infinity from
a planet.
 18. Using the definition of gravitational potential
energy, derive an expression for gravitational potential energy vs.
distance from the center of a planet, above the planet's surface.
(Note
blue dashed lines at right are constant potential energy lines.)


Equations 
Comments 
ΔU =  
∫

^{r} 
(force
function) (dr) 
_{∞} 

The force will have a negative sign because it is an
attractive force. 
U_{r}  U_{∞}
=  
∫

^{r} 
([G(Mm)] / r^{2})
(dr) 
_{∞} 

∞ is typically used as
the location of zero gravitational potential energy 
U_{r }
=  m [G(M) / r] 
U_{f }has to be negative in order to
be lower than U_{∞.} 
 19. Explain why the equation for potential energy vs.
distance from a planet (a point source of gravity) is only valid above
the planet's surface. (The amount of mass
attracting an object toward the planet's center of mass changes as the
object approaches the center of the planet, so the force as a function
of r equation is different.)
Homefun: Read 13.4 to 13.6, Problem
27
Relevance: Gravitational
potential energy is a key concept in space exploration. The energy required for
getting off a planet's surface is a critical problem
that could limit the exploration of planets by humans.

Lesson 4 Key
Concept: Potential Energy Around a Planet
Purpose: Relate
gravitational potential energy to gravity force.
 Interactive Discussion: How are
gravity field lines related to constant potential energy lines?
In Class Problem Solving:
 Derive an expression for potential energy vs
distance from the center of a planet.


Essential Question:
How can a spacecraft escape from a
planet's gravity? 
Gravity
and Orbits

20. Circular Orbit: Calculate the velocity or radius (depending
on what is given) for circular orbits by combining circular motion
equations with the universal gravity equation.
(Note: r is the distance from the center of the planet to the
spacecraft, M = mass of planet)
v = [(GM) / r]^0.5
 21. Elliptical Orbit (speed lowered at P): Describe what happens to a
satellite in circular
orbit if it's tangential velocity is decreased.
 22. Eliptical Orbit (speed increased at P): Describe what happens to a
satellite in circular orbit if it's tangential velocity is increased.
 23. Escape from Orbit: Calculate escape speed from the surface of a
planet. (p. 407, note: r is the distance from the center of the planet
to the spacecraft, M = mass of planet)
v = [(2GM) / r]^0.5
 24. State the two critical speeds for orbits.
 25. Calculate the radius and velocity required for a geosynchronous
or geostationary orbit.
 geosynchronousthe
orbit returns the satellite to the same location in the in the sky at
the same time every day.
 geostationarya
special case of geosynchronous orbit in which the satellite remains
above a fixed point on the equator.
Note that an orbiting object can
only remain in a fixed position above a point on the equator and then
only if the radius and speed are correct.
Relevance: Orbit knowledge is key to an understanding of space
travel, communication satellites, science fiction movies etc. Orbiting
spacecraft are frequently incorrectly portrayed in science fiction movies.
Homefun: Read 13.4 to 13.7,
Questions 110 ; Problems 41

Lesson 3 Key
Concept: Orbiting and Escaping from a Planet
Purpose: Derive
the key equations associated with orbits.
 Interactive Discussion:
Objective s
Video Clip:
Show a video clip of the Space Shuttle taking off from the surface
of the asteroid in Armageddon. Calculate the escape velocity needed.
How fast would the ship have to be moving to take off?
Work in groups of two


Essential Question:
How can the effects of
air resistance be derived mathematically for a falling object? 

Falling With Air Resistance

 26. Explain where air
resistance comes from and why it should not be called air
friction. For an object to move forward, it has to push air out of
the way. The change in momentum of the
air creates a force that resists the motion. This is sometimes
referred to as an inertial force. There is friction between the
air air molecules "rubbing" past the surface of the moving object
but this force is very low except at supersonic velocities.

 27. Derive a differential equation that
accounts for the air resistance of a falling object, assuming the
air resistance force is directly proportional to velocity.
bv  mg = ma
bv  mg = m(dv/dt)
m(dv/dt)  bv + mg = 0
 28. using the above equation, derive an
expression for the velocity of a falling object vs. time.
 29. Calculate terminal velocity for a falling
object with air resistance and compare it to a falling object
without air resistance. (see page 162)
Relevance: Air resistance is a basic characteristic that
determines all kinds of important issues including fuel efficiency
of vehicles and terminal velocities of falling objects.


