Objective - Lesson 1: Motion Characteristics for Circular Motion

1
Objective - Lesson 1 Motion Characteristics for
Circular Motion

• Speed and Velocity
• Acceleration
• The Centripetal Force Requirement
• Mathematics of Circular Motion

2
Uniform circular motion

• Uniform circular motion is the motion of an
  object in a circle with a ___________ or uniform
  speed. The velocity is changing because the
  direction of motion is ______________.

• Speed _____________
• Direction of motion _____________ of the path
• Velocity
• magnitude ___________
• Direction _____________

3
Speed and velocity

• Calculation of the Average Speed
• vavg _________
• The distance of one complete cycle around the
  perimeter of a circle is known as the
  ____________.
• Circumference ____ (R is the radius of the
  circle)
• The time (T) to make one cycle around the circle
  is called one _________.
• The average speed of an object in uniform
  circular motion is

vavg ____________
4

• The average speed and the Radius of the circle
  are _____________________.
• The average speed and the Period of the circle
  are _____________________.

5
The Direction of the Velocity Vector
The best word that can be used to describe the
direction of the velocity vector is the word
____________________. The direction of the
velocity vector at any instant is in the
direction of a tangent line drawn to the circle
at the object's location.
6

• To summarize, an object moving in uniform
  circular motion is moving around the perimeter of
  the circle with a __________speed. While the
  speed of the object is constant, its velocity is
  changing. Velocity, being a vector, has a
  constant magnitude but a changing direction. The
  direction is always directed _________ to the
  circle and as the object turns the circle, the
  tangent line is always pointing in a new
  direction.

The average speed is directly proportional to the
____________ and inversely proportional to the
_____________.
7
Check Your Understanding

• A tube is been placed upon the table and shaped
  into a three-quarters circle. A golf ball is
  pushed into the tube at one end at high speed.
  The ball rolls through the tube and exits at the
  opposite end. Describe the path of the golf ball
  as it exits the tube.

8
example

• A vehicle travels at a constant speed of 6.0
  meters per second around a horizontal circular
  curve with a radius of 24 meters. The mass of the
  vehicle is 4.4 103 kilograms. An icy patch is
  located at P on the curve. On the icy patch of
  pavement, the frictional force of the vehicle is
  zero.  Which arrow best represents the direction
  of the vehicle's velocity when it reaches icy
  patch P?

a
b
c
d
9
Acceleration

• An object moving in uniform circular motion is
  moving in a circle with a uniform or constant
  speed. The velocity vector is constant in
  magnitude but changing in direction.
• Since the velocity is changing. The object is
  __________________.

where vi represents the initial velocity and vf
represents the final velocity after some time of
t
10
Direction of the Acceleration Vector

• The velocity change is directed towards point C -
  the ________ of the circle.
• The acceleration of the object is dependent upon
  this velocity change and is in the same direction
  as this ____________. The acceleration is
  directed towards point C as well - the
  ___________________________.

11
example

• The initial and final speed of a ball at two
  different points in time is shown below. The
  direction of the ball is indicated by the arrow.
  For each case, indicate if there is an
  acceleration. Explain why or why not. Indicate
  the direction of the acceleration.
• a.

b.
c.
d.
12
example

• Explain why an object moving in a circle at
  constant speed can be said to experience an
  acceleration.

13
example
An object is moving in a clockwise direction
around a circle at constant speed.

1. Which vector below represents the direction of
   the velocity vector when the object is located at
   point B on the circle?
2. Which vector below represents the direction of
   the acceleration vector when the object is
   located at point C on the circle?
3. Which vector below represents the direction of
   the velocity vector when the object is located at
   point C on the circle?
4. Which vector below represents the direction of
   the acceleration vector when the object is
   located at point A on the circle?

14
The Centripetal Force Requirement

• According to Newton's second law of motion, an
  object which experiences an acceleration requires
  a __________________.
• The direction of the net force is in the same
  direction as the ______________. So for an object
  moving in a circle, there must be an inward force
  acting upon it in order to cause its inward
  acceleration. This is sometimes referred to as
  the ________________ force requirement.
• The word centripetal means _______________. For
  object's moving in circular motion, there is a
  net force acting towards the center which causes
  the object to seek the center.

15
Centrifugal force is a fictitious force

• centrifugal (center fleeing) force
• A fictitious or inertial force that is
  experienced from INSIDE a circular motion system
• centripetal (center seeking) force
• A true force that pushes or pulls an object
  toward the center of a circular path

16
The Centripetal Force is Net Force

• Any object moving in a circle (or along a
  circular path) experiences a _______________
  force. This is the centripetal force requirement.
  
• The word centripetal is merely an adjective used
  to describe the direction of the force. We are
  not introducing a new type of force but rather
  describing the direction of the ________ force
  acting upon the object that moves in the circle.

17
examples of centripetal force
As the moon orbits the Earth, the force of
____________ acting upon the moon provides the
centripetal force required for circular motion.
As a car makes a turn, the force of _____________
acting upon the turned wheels of the car provides
centripetal force required for circular motion.
As a bucket of water is tied to a string and spun
in a circle, the _____________ force acting upon
the bucket provides the centripetal force
required for circular motion.
18

• To summarize, an object in uniform circular
  motion experiences an __________ net force. This
  inward force is sometimes referred to as a
  _______________ force, where centripetal
  describes its direction. Without this centripetal
  force, an object could never alter its direction.
  The fact that the centripetal force is directed
  ___________________ to the tangential velocity
  means that the force can alter the direction of
  the object's velocity vector without altering its
  magnitude.

19
Check your understanding

• An object is moving in a clockwise direction
  around a circle at constant speed

1. Which vector below represents the direction of
   the force vector when the object is located at
   point A on the circle?
2. Which vector below represents the direction of
   the force vector when the object is located at
   point C on the circle?
3. Which vector below represents the direction of
   the velocity vector when the object is located at
   point B on the circle?
4.  Which vector below represents the direction of
   the velocity vector when the object is located at
   point C on the circle?
5. Which vector below represents the direction of
   the acceleration vector when the object is
   located at point B on the circle?

20
Mathematics of Circular Motion
21
Relationship between quantities
This equation shows for a constant mass and
radius, both Fnet and a is directly proportional
to the v2.
F _____
a ______
If the speed of the object is doubled, the net
force required for that object's circular motion
and its acceleration are ____________. And if the
speed of the object is halved (decreased by a
factor of 2), the net force required and its
acceleration are decreased by a factor of
________.
22
example

• A car going around a curve is acted upon by a
  centripetal force, F. If the speed of the car
  were twice as great, the centripetal force
  necessary to keep it moving in the same path
  would be
• F
• 2F           
• F/2
• 4F  

23

• Centripetal force and mass of the object

This equation shows for a constant speed and
radius, the Fnet is _________________________ to
the mass.
If the mass of the object is doubled, the net
force required for that object's circular motion
is ____________. And if the mass of the object is
halved (decreased by a factor of 2), the net
force required is decreased by a factor of
______.

• Centripetal acceleration and mass of the object

Centripetal acceleration is ________________ by
the mass of the object
24
example

• Anna Litical is practicing a centripetal force
  demonstration at home. She fills a bucket with
  water, ties it to a strong rope, and spins it in
  a circle. Anna spins the bucket when it is
  half-full of water and when it is quarter-full of
  water. In which case is more force required to
  spin the bucket in a circle? Explain using an
  equation.

25
example

• The diagram shows a 5.0-kilogram cart traveling
  clockwise in a horizontal circle of radius 2.0
  meters at a constant speed of 4.0 meters per
  second. If the mass of the cart was doubled, the
  magnitude of the centripetal acceleration of the
  cart would be
• doubled
• halved
• unchanged
• quadrupled

26

• Centripetal Force, acceleration and the radius

This equation shows for a constant speed and
mass, the Fnet and acceleration a is
______________________ to the radius
If the radius of the object is doubled, the net
force required for that object's circular motion
and its acceleration are both ____________. And
if the radius of the object is halved (decreased
by a factor of 2), the net force required and its
acceleration are both increased by a factor of
_______________.
27
example

• Two masses, A and B, move in circular paths as
  shown in the diagram. The centripetal
  acceleration of mass A, compared to that of mass
  B, is
• the same
• twice as great
• one-half as great
• four times as great

28
Equations as a Recipe for Problem-Solving

• A 900-kg car moving at 10 m/s takes a turn around
  a circle with a radius of 25.0 m. Determine the
  acceleration and the net force acting upon the
  car.

29
example

• A 95-kg halfback makes a turn on the football
  field. The halfback sweeps out a path which is a
  portion of a circle with a radius of 12-meters.
  The halfback makes a quarter of a turn around the
  circle in 2.1 seconds. Determine the speed,
  acceleration and net force acting upon the
  halfback.

30
example

• Determine the centripetal force acting upon a
  40-kg child who makes 10 revolutions around the
  Cliffhanger in 29.3 seconds. The radius of the
  barrel is 2.90 meters.

31
Lesson 2 Applications of Circular Motion

• Newton's Second law - Revisited
• Amusement Park Physics

32
Applications of Circular Motion

• Newton's Second Law - Revisited

Where Fnet is the sum (the resultant) of all
forces acting on the object.
Newton's second law was used in combination of
circular motion equations to analyze a variety of
physical situations. Note centripetal force is
the _____ force!
33
Steps in solving problems involving forces

• Drawing Free-Body Diagrams
• Determining the Net Force from Knowledge of
  Individual Force Values
• Determining Acceleration from Knowledge of
  Individual Force Values
• Or Determining Individual Force Values from
  Knowledge of the Acceleration

34
example

• A 945-kg car makes a 180-degree turn with a speed
  of 10.0 m/s. The radius of the circle through
  which the car is turning is 25.0 m. Determine the
  force of friction and the coefficient of friction
  acting upon the car.

35
example

• The coefficient of friction acting upon a 945-kg
  car is 0.850. The car is making a 180-degree turn
  around a curve with a radius of 35.0 m. Determine
  the maximum speed with which the car can make the
  turn.

36

• A 1.50-kg bucket of water is tied by a rope and
  whirled in a circle with a radius of 1.00 m. At
  the top of the circular loop, the speed of the
  bucket is 4.00 m/s. Determine the acceleration,
  the net force and the individual force values
  when the bucket is at the top of the circular
  loop.

m 1.5 kg a ________ m/s/s Fnet  _________
N  
37

• A 1.50-kg bucket of water is tied by a rope and
  whirled in a circle with a radius of 1.00 m. At
  the bottom of the circular loop, the speed of the
  bucket is 6.00 m/s. Determine the acceleration,
  the net force and the individual force values
  when the bucket is at the bottom of the circular
  loop.

m 1.5 kg a ________ m/s/s Fnet  _________
N  
38
Roller Coasters and Amusement Park Physics
In a roller coaster, the centripetal force is
provided by the combination of ___________________
_________.
39
example

• Anna Litical is riding on The Demon at Great
  America. Anna experiences a downwards
  acceleration of 15.6 m/s2 at the top of the loop
  and an upwards acceleration of 26.3 m/s2 at the
  bottom of the loop. Use Newton's second law to
  determine the normal force acting upon Anna's 864
  kg roller coaster car.

40
example

• Anna Litical is riding on The American Eagle at
  Great America. Anna is moving at 18.9 m/s over
  the top of a hill which has a radius of curvature
  of 12.7 m. Use Newton's second law to determine
  the magnitude of the applied force of the track
  pulling down upon Anna's 621 kg roller coaster
  car.

41
Lesson 3 Universal Gravitation

1. Gravity is More than a Name
2. The Apple, the Moon, and the Inverse Square Law
3. Newton's Law of Universal Gravitation
4. Cavendish and the Value of G
5. The Value of g

42
Gravity is More Than a Name

• We know that gravity is a force and we represent
  it by the symbol Fgrav. It causes an acceleration
  of all objects around it. The acceleration is
  referred as the acceleration of gravity. On and
  near Earth's surface, the value for the
  acceleration of gravity is approximately 9.81
  m/s/s. It is the same acceleration value for all
  objects, regardless of their mass (and assuming
  that the only significant force is gravity).
• but
• How and by whom was gravity discovered?
• What is the cause of this force of gravity?
• What variables affect the actual value of the
  force of gravity?
• Is the force of gravity that attracts my body to
  the Earth related to the force of gravity between
  the planets and the Sun?

43
The Apple, the Moon, and the Inverse Square Law

• In the early 1600's, German mathematician and
  astronomer Johannes ________________ developed
  three laws to describe the motion of planets
  about the sun. However, there was no accepted
  explanation for why such paths existed.

• Newton was troubled by the lack of explanation
  for the planet's orbits. Newton knew that for the
  motion of the moon in a circular path required
  that there be an inward component of __________.
  However, the nature of such a force - its cause
  and its origin - bothered Newton for some time.

44
And according to legend, a breakthrough came at
age 24 in an apple orchard in England.
Clearly, it was Newton's ability to relate the
cause for heavenly motion (the orbit of the moon
about the earth) to the cause for Earthly motion
(the falling of an apple to the Earth) that led
him to his notion of __________________________
45
Newton's reasoning
Suppose a cannonball is fired horizontally from a
very high mountain in a region devoid of air
resistance. In the presence of gravity, the
cannonball would ___________________
Now suppose that the cannonball is fired
horizontally again with a greater speed. In this
case, the cannonball would _______________________
___________.
Now suppose that there is a speed at which the
cannonball could be fired such that the
trajectory of the falling cannonball matched the
curvature of the earth, then the cannonball would
_________________________________________________
______
46
And then at even greater launch speeds, a
cannonball would once more orbit the earth, but
in an ____________ path, like the planets
The motion of the cannonball orbiting to the
earth under the influence of gravity is similar
to the motion of the moon orbiting the Earth. And
if the orbiting moon can be compared to the
falling cannonball, it can even be compared to a
falling apple. The same force that causes objects
on Earth to fall to the earth also causes objects
in the heavens to move along their circular and
elliptical paths.
47

• It was known at the time, that the force of
  gravity causes earthbound objects (such as
  falling apples) to accelerate towards the earth
  at a rate of 9.81 m/s2. And it was also known
  that the moon accelerated towards the earth at a
  rate of 0.00272 m/s2.
• If the same force that causes the acceleration of
  the apple to the earth also causes the
  acceleration of the moon towards the earth, then
  there must be a plausible explanation for why the
  acceleration of the moon is so much smaller than
  the acceleration of the apple. What is it about
  the force of gravity that causes the more distant
  moon to accelerate at a rate of acceleration that
  is approximately 1/3600-th the acceleration of
  the apple?

48

• Newton knew that the force of gravity must
  somehow be ____________" by distance.
• The riddle is solved by a comparison of the
  _____________ from the apple to the center of the
  earth with the __________ from the moon to the
  center of the earth. The moon in its orbit about
  the earth is approximately _____________ further
  from the earth's center than the apple is. The
  mathematical relationship becomes clear. The
  force of gravity between the earth and any object
  is inversely proportional to the square of the
  distance that separates that object from the
  earth's center. The moon, being 60 times further
  away than the apple, experiences a force of
  gravity that is 1/(60)2 times that of the apple.
  The force of gravity follows an
  _____________________.

49
Inverse square law.

• The relationship between the force of gravity
  (Fgrav) between the earth and any other object
  and the distance that separates their centers (d)
  can be expressed by the following relationship

The force of gravity is inversely related to the
square of the distance. This mathematical
relationship is sometimes referred to as an
inverse square law.
50
Relationships in the equation

• The inverse square law suggests that the force of
  gravity acting between any two objects is
  ___________________________ to the ___________ of
  the separation __________________ between the
  object's centers.
• If the separation distance is increased by a
  factor of 2, then the force of gravity is
  decreased by a factor of four (______). And if
  the separation distance is increased by a factor
  of 3, then the force of gravity is decreased by a
  factor of nine (_______).

Fg
r
51
Check Your Understanding

• 1 . Suppose that two objects attract each other
  with a gravitational force of 16 units. If the
  distance between the two objects is doubled, what
  is the new force of attraction between the two
  objects?
•  
•   
• 2. Suppose that two objects attract each other
  with a gravitational force of 16 units. If the
  distance between the two objects is tripled, then
  what is the new force of attraction between the
  two objects?
•  
•   
• 3. Suppose that two objects attract each other
  with a gravitational force of 16 units. If the
  distance between the two objects is reduced in
  half, then what is the new force of attraction
  between the two objects?
•  
•   
• 4. Suppose that two objects attract each other
  with a gravitational force of 16 units. If the
  distance between the two objects is reduced by a
  factor of 5, then what is the new force of
  attraction between the two objects?

52
example

• An astronaut weighs 8.00 102 newtons on the
  surface of Earth. What is the weight of the
  astronaut 6.37 106 meters above the surface of
  Earth?
• 0.00 N
• 2.00 102 N
• 1.60 103 N
• 3.20 103 N

53
Newton's Law of Universal Gravitation

• Consider Newton's famous equation Fnet m a
• Newton knew that the force that caused the
  apple's acceleration (gravity) must be dependent
  upon the mass of the __________. And since the
  force acting to cause the apple's downward
  acceleration also causes the earth's upward
  acceleration (Newton's third law), that force
  must also depend upon the mass of the ________.
• So for Newton, the force of gravity acting
  between the earth and any other object is
  directly proportional to the mass of the _______,
  directly proportional to the mass of the
  ________, and inversely proportional to the
  _______________________ that separates the
  centers of the earth and the object.
• Newton's law of universal gravitation is about
  the _______________ of gravity. _________ objects
  attract each other with a force of gravitational
  attraction.

54
Examples

• What happens to Fg in the following cases?

• Double one mass
• Double both masses
• Triple one mass
• Triple both masses
• Halve one mass
• Halve one mass and double the other

55
Examples

• What happens to Fg in the following cases?

• Double the distance
• Triple the distance
• Halve the distance
• Quarter the distance

56
Examples

• What happens to Fg in the following cases?

• Double one mass and double the distance
• Double both masses and double the distance
• Halve one mass and halve the distance
• Triple one mass and quarter the distance

57
Newton's Law of Universal Gravitation

• Another means of representing the
  proportionalities is to express the relationships
  in the form of an equation using a constant of
  proportionality.

G represent Gravitational Constant G
____________________
58
Example

• Determine the force of gravitational attraction
  between the earth (m 5.98 x 1024 kg) and a
  70-kg physics student if the student is standing
  at sea level, a distance of 6.38 x 106 m from
  earth's center.

59
The Universality of Gravity
Mass of Object 1 (kg) Mass of Object 2 (kg) Separation Distance (m) Force of Gravity (N)
Student 70 kg Earth 5.98 x1024 kg 6.60 x 106 m (low-height orbit)
Student 70 kg Physics Student 70 kg 1 m
Student 70 kg Physics Book 1 kg 1 m
Student 70 kg Jupiter 1.901 x 1027 kg 6.98 x 107 m (on surface)
 
60
Cavendish and the Value of G

• The value of G was not experimentally determined
  until nearly a century later (1798) by Lord Henry
  Cavendish using a torsion balance.

Lord Henry Cavendish - English chemist and
physicist
61
The Value of g
Fgrav mg

• We can use the two equations above to derive an
  equation for the value of g.

The acceleration of gravity is dependent upon the
mass of the earth (approx. 5.98x1024 kg) and the
distance (d) that an object is from the center of
the earth.
The acceleration of gravity is location dependent.
62
Note that g is inversely proportional to the
distance squared inverse square law.
63
The table below shows the value of g at various
locations from Earth's center.
The table below shows the value of g at various
locations from Earth's center.
Location Distance from Earth's center (m) Value of g m/s2
Earth's surface 6.38 x 106 m 9.8
1000 km above surface 7.38 x 106 m
5000 km above surface 1.14 x 107 m
10000 km above surface 1.64 x 107 m
50000 km above surface 5.64 x 107 m

64
Using this equation, the following acceleration
of gravity values can be calculated for the
various planets.
Planet Radius (m) Mass (kg) g (m/s2)
Mars 3.38 x 106 6.42 x 1023
Jupiter 6.98 x 107 1.901 x 1027
Neptune 2.27 x 107 1.03 x 1026
Pluto 1.15 x 106 1.2 x 1022

65
Example - Calculating the mass of the Earth

• Knowing G, and the radius of the Earth, RE
  6.37 x 106 m, we can now actually calculate the
  mass of the Earth.

66
Gravity is a field force

• Gravitational field a ________________ where an
  object would experience a gravitational force.
  Every mass is surrounded by a gravitational
  field.
• As the distance from the Earth increases, the
  strength of gravitational ___________________.
• As the distance from the Earth increases, the
  arrows are further apart and the length of arrows
  are _________, indicating the strength of the
  gravitational force _______________.

67
The gravitational field around Earth
Gravitational field strength is a vector
quantity. Its direction is directed
_____________________ of Earth, or normal to
Earths surface. Its magnitude at a point equals
the force per unit mass at that point.

• The concentration of the field lines increases as
  the distance from Earth decreases.

68
example

• The weight of an object was determined at five
  different distances from the center of Earth. The
  results are shown in the table below. Position A
  represents results for the object at the surface
  of Earth. What is the approximate mass of the
  object?

69
Lesson 4 Satellite Motion

• Circular Motion Principles for Satellites
• Mathematics of Satellite Motion
• Weightlessness in Orbit

70
Circular Motion Principles for Satellites

• A satellite is any object that is orbiting the
  earth, sun or other massive body. Satellites can
  be categorized as ____________ satellites or
  _____________ satellites.
• The ___________, the _______________ and comets
  are examples of natural satellites.
• ________________ launched from earth for purposes
  of communication, scientific research, weather
  forecasting, intelligence, etc. are man-made
  satellites.
• Every satellite's motion is governed by the same
  physics principles and described by the same
  mathematical equations.

71
Velocity, Acceleration and Force Vectors

• The motion of an orbiting satellite can be
  described by the same motion characteristics as
  any object in circular motion.
• The ______________ of the satellite would be
  directed tangent to the circle at every point
  along its path.
• The _______________ of the satellite would be
  directed towards the center of the circle -
  towards the central body that it is orbiting.
• And this acceleration is caused by a ____________
  that is directed inwards in the same direction as
  the acceleration. This centripetal force is
  supplied by _________________ - the force that
  universally acts at a distance between any two
  objects that have mass.

72
(No Transcript)
73
Mathematics of Satellite Motion

• If the satellite moves in circular motion, then
  the net centripetal force acting upon this
  orbiting satellite is given by the relationship
• Fnet ____________________
• This net centripetal force is the result of the
  gravitational force that attracts the satellite
  towards the central body and can be represented
  as
• Fgrav ____________________

74

• Since Fgrav Fnet,
• _________________________________
• v2 _______________
• v _______________

where G is 6.673 x 10-11 Nm2/kg2, Mcentral
is the mass of the central body about which
the satellite orbits, and R is the radius of
orbit for the satellite.
The speed of satellite is determined by its
location ___ and mass of the central body
__________.
75
Check your understanding

• A satellite is orbiting the earth. Which of the
  following variables will affect the speed of the
  satellite?
• a. mass of the satellite
• b. height above the earth's surface
• c. mass of the earth

76
Weightlessness in Orbit

• Astronauts who are orbiting the Earth often
  experience sensations of weightlessness. These
  sensations experienced by orbiting astronauts are
  the __________ sensations experienced by anyone
  who has been temporarily suspended above the seat
  on an amusement park ride.
• Not only are the sensations the same (for
  astronauts and roller coaster riders), but the
  __________ of those sensations of weightlessness
  are also the ________. Unfortunately however,
  many people have difficulty understanding the
  causes of weightlessness.

77
Test your preconceived notions about
weightlessness

• Astronauts on the orbiting space station are
  weightless because...
• there is no gravity in space and they do not
  weigh anything.
• space is a vacuum and there is no gravity in a
  vacuum.
• c. space is a vacuum and there is no air
  resistance in a vacuum.
• d. the astronauts are far from Earth's surface
  at a location where gravitation has a minimal
  affect.

78
Contact versus Non-Contact Forces
79
Contact versus Non-Contact Forces

• As you sit in a chair, you experience two forces
  ________
• The normal force and results from the
  _______________ between the chair and you. You
  can feel this force because of the contact you
  have with the chair.
• The force of gravity acting upon your body is a
  field force, which is the result of your center
  of mass and the Earth's center of mass exerting a
  mutual pull on each other this force would even
  exist if you were not in contact with the Earth.
• The force of gravity ___________________. Forces
  that result from contact ____________. And in the
  case of sitting in your chair, you can feel the
  chair force and it is this force that provides
  you with a sensation of weight. Without the
  contact force (the normal force), there is no
  means of feeling the non-contact force (the force
  of gravity).

80
Scale Readings and Weight
Now consider Otis L. Evaderz who is conducting
one of his famous elevator experiments. He stands
on a bathroom scale and rides an elevator up and
down. As he is accelerating upward and downward,
the scale reading is __________________ than when
he is at rest and traveling at constant speed.
81
Fnet ma Fnet 0 N Fnet ma Fnet 400 N, up Fnet ma Fnet 400 N, down Fnet ma Fnet 784 N, down
Fnorm equals Fgrav Fnorm ____N Fnorm gt Fgrav by 400 N Fnorm ____ N Fnorm lt Fgrav by 400 N Fnorm _____ N Fnorm lt Fgrav by 784 N Fnorm __ N
82
Weightlessness in Orbit

• Earth-orbiting astronauts are weightless for the
  same reasons that riders of a free-falling
  amusement park ride or a free-falling elevator
  are weightless. They are weightless because there
  is ______________________ force pushing or
  pulling upon their body.
• In each case, gravity is the _____________ acting
  upon their body. Being an action-at-a-distance
  force, it cannot be felt and therefore would not
  provide any sensation of their weight. But for
  certain, the orbiting astronauts weigh something
  that is, there is a force of gravity acting upon
  their body.
• In fact, if it were not for the force of gravity,
  the astronauts would not be orbiting in circular
  motion. It is the force of gravity that supplies
  the ____________________ requirement to allow the
  __________________ acceleration that is
  characteristic of circular motion.
• The astronauts and their surroundings are falling
  towards the Earth under the sole influence of
  _______________.

83

• 1. Otis stands on a bathroom scale and reads the
  scale while ascending and descending the John
  Hancock building. Otis' mass is 80 kg.. Use a
  free-body diagram and Newton's second law of
  motion to solve the following problems.
• a. What is the scale reading when Otis
  accelerates upward at 0.40 m/s2?
•  
• b. What is the scale reading when Otis is
  traveling upward at a constant velocity of at 2.0
  m/s?
•  
• c. As Otis approaches the top of the building,
  the elevator slows down at a rate of 0.40 m/s2.
  Be cautious of the direction of the acceleration.
  What does the scale read?
•  
• d. Otis stops at the top floor and then
  accelerates downward at a rate of 0.40 m/s2. What
  does the scale read?
•  
• e. As Otis approaches the ground floor, the
  elevator slows down (an upward acceleration) at a
  rate of 0.40 m/s2. Be cautious of the direction
  of the acceleration. What does the scale read?
•  
• Use the results of your calculations above to
  explain why Otis fells less weighty when
  accelerating downward on the elevator and why he
  feels heavy when accelerating upward on the
  elevator.
•