Gravity

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• Gravity

3/31/2009 Version
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Consent for Participation in Research

• Construct Centered Design Approach to Developing
  Undergraduate Curriculum in Nanoscience Education
• Why am I being asked?You are being asked to
  participate in a research study focused on
  improving methods to teach students about
  3-dimensional force interactions by allowing us
  to evaluate your in class responses to lecture
  questions. Your instructor is collecting your
  responses electronically. We will anonymously
  evaluate your responses to evaluate the
  effectiveness of the lecture material. This study
  is being conducted by Carmen Lilley and Robert
  Klie at the University of Illinois at Chicago.

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Consent for Participation in Research

• Why is this research being done?The concept of
  3-dimensional force interactions are relevant to
  understanding how object move at many length
  scales. In the case of the macroscale, concepts
  of gravity and electromagnetic forces are
  foundational knowledge to students in
  introductory physics. At the nanoscale,
  3-dimensional electrostatic force interactions
  will result in what is called self-assembly,
  where environments are designed such that
  elements in those environments organize
  themselves into useful patterns. These concepts
  are difficult to teach with conventional
  white-board/black-board lectures. Using modern
  interactive, 3D computer graphics it may be
  possible to improve the learning of these
  concepts. 

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Consent for Participation in Research

• YES - I give my consent to allow my responses to
  be anonymously evaluated for research purposes
  and also certify that I am 18 years or older in
  age. Please press A
• or
• NO - I decline to allow my responses to be
  anonymously evaluated and understand that by
  doing so, there is no impact to my course grade
  or relationship with the University of Illinois
  at Chicago. Please press B

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Question 1

• Which of the following statements is correct
• A - There is a gravitational field between the
  Earth and the person
• B - There is a gravitational field between the
  person and the dog
• C - Both A and B
• D - Neither of the above

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Question 2

• What is the direction of the gravitational force
  on the Earths surface?
• A - Gravity does not have direction
• B - Towards the Earths center of mass
• C - Away from the Earths center of mass
• D - Tangent to the Earths surface

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Question 3

• Given the following two objects, which of the
  following will increase the force on object B
• A Increasing the radius of object A
• B Increasing the mass of object B
• C Increasing the distance between objects A
  and B
• D None of these will affect the force on
  object B

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Question 4

• Which of the following images correctly
  represents the gravitational field for the Earth
  and Moon?
• A
  B
• C
  D

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Body Forces

• Body forces are forces that act on an object (for
  example a mass such as solid sphere or a charged
  spherical particle.)
• These forces permeate through the body of the
  object and thus the body force acts on the
  material throughout its volume.
• Imagine a mass, a body force acts on all points
  that describe that mass. Thus, the units of force
  for a body force are Force/Volume.

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Gravity

• We are most commonly aware of gravity.
• We typically imagine gravity as being one
  dimensional when we consider gravity acting on an
  object on the Earths surface. For example here
  we see a person and a dog on the Earths surface.

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Gravity

• We typically think of gravity on earth as being
  one dimensional where gravity acts downward
  towards the Earths center of mass.
• This is because we typically model the Earth as a
  sphere with a uniform density and therefore, its
  center of mass is located at the center of the
  sphere.
• The arrows shown in the figure are called field
  lines.
• These field lines indicatethe direction in which
  theforce is acting.

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Gravity

• However, gravitational force is a force that acts
  between masses. This force is an attractive
  force.
• Thus, in addition to a gravitational force
  existing between the person and Earth or the dog
  and the Earth which is attractive, there is also
  an attractive gravitational force acting between
  the person and the dog.
• The gravitational force between the person and
  the dog is much smaller than the gravitational
  force between the person and Earth or the dog and
  Earth.

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Gravity

• The magnitude of the gravitational force between
  two objects can be calculated with Newtons Law
  of Gravity and is expressed in this equation
• where
• G is called the universal gravitation constant
  and is equal to 6.67 x 10-11 Nm2/kg
• m1 is the mass of object one
• m2 is the mass of object two
• r is the distance between the two objects

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Gravity

• If we consider m1 to be the mass of the Earth
  (m1 6 x 1024 kg) and r to be the radius of the
  earth (r 6.4 x 106 m), then the magnitude of
  force between an object on the Earths surface
  and the Earth is given by
• Where
• g is gravity on the Earths surface and is equal
  to 9.8 m/s2
• m2 is the mass of the
• g is the gravitational acceleration that acts on
  an object when the object is located on the
  Earths surface and it will face downwards
  towards the center of mass of the Earth.

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Gravity

• If we compare the force interaction between the
  person and the dog we can see that the force is
  much smaller, even though the distance between
  them is much smaller. This is because the mass of
  the person and the dog are much smaller that the
  mass of the Earth.
• A typical man weighs 70 kilograms. A typical dog
  weighs 15 kilograms. If we assume they are
  standing 1 meter apart then the force exerted on
  the man by the dog (and vice-versa) is 7 x 10-8
  N.
• The force exerted on the man from the Earth is
  686 N or 10,000,000,000 times larger than the
  force on the man by the dog.
• On the Earths surface, the force that dominates
  is gravity because of the mass of the Earth. We
  call this the dominant force for this special
  case.

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Gravitation Acceleration Fieldaround the Earth

• Lets look at the gravitational acceleration field
  that exists around the Earth by zooming out our
  view so that we can see the entire planet.
• To draw the field lines we can imagine a test
  object that has some mass m. Lets call this
  object particle P. If we move this particle
  around the Earth and sketch arrows that show the
  direction of the force, these arrows will face
  the Earth because the force between particle P
  and the Earth is an attractive force.

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Gravitation Acceleration Fieldaround the Earth

• There is a single force vector tangent to the
  gravitational field at all points in the
  gravitational field. If field lines were to
  intersect, this implies that there would be
  multiple directions for that force vector which
  is inaccurate.

• If we imagine that the arrows color changes with
  magnitude of the force, then we can see that
  these arrows become brighter as we move towards
  the Earth and darker as we move away.
• This is because the magnitude of the force
  decreases at a rate of 1/r2 with increasing
  distance away from Earth.

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Gravitation Acceleration Fieldaround the Earth

• We should also note that the field is continuous,
  meaning it occupies all space around the Earth
  and exists at an infinite distance.

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Gravitation Acceleration Fieldaround the Earth

• If we draw a line that connects the arrows, then
  we get continuous lines which again are called
  field lines. These field lines are used to
  represent the gravitational acceleration and
  direction exerted on an object at a distance r.
• Assuming Earth is a perfectsphere then the field
  lines areradial lines normal to theEarths
  surface.

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Gravitation Acceleration Fieldaround the Earth

• We can also illustrate the shape of the
  gravitational field that exists around the Earth
  by using a cloud to represent the field shape.
  The edge of the cloud shows a constant value or
  magnitude of the gravitational field - these
  lines are called isolines.
• If we sketch the isolines aroundthe Earth, then
  we see that wehave a series of concentric
  circles.

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Gravitation Acceleration Fieldaround the Earth

• Remember that the field lines indicate the
  direction and shape of the gravitational
  acceleration as it varies throughout space. An
  isoline shows the shape of the region where the
  gravitational acceleration field is constant.

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Gravitation Acceleration Fieldaround the Earth

• We have been drawing these diagrams in two
  dimensions, but the forces exist in three
  dimensions as shown in these animations below.

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Gravitation Acceleration Fieldaround the Moon

• Now lets look at the Moon in isolation. We can
  carry out the same procedure of moving particle P
  around the Moon to determine its gravitational
  acceleration field.
• We can see that the shape of the field is similar
  to that of the Earth because we model both the
  Earth and the Moon as spheres.

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Gravitation Acceleration Fieldaround the Moon

• Notice also that the magnitudes of the fields are
  different because the Moon has much less mass
  than the Earth.
• The mass of the Moon is 7.4x1022 kg and the mass
  of the Earth is 600x1022 kg so the mass of the
  Moon is approximately 81 times smaller than the
  mass of the Earth.

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Gravitation Acceleration Fieldaround the Earth
and Moon

• To study the gravitational field that exists when
  we consider the Moon and the Earth together, we
  use what is called linear superposition where we
  directly add the gravitational acceleration
  fields that we have previously seen.
• Note then that the gravitational fields lines are
  no longer spherical, but vary with position
  around the Earth and Moon.

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Gravitation Acceleration Fieldaround the Earth
and Moon

• We have been drawing these diagrams in two
  dimensions, but the forces exist in three
  dimensions as shown in these animations below.

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Gravitation Acceleration Fieldaround the Earth
and Moon

• Imagine then the other planets, stars, meteors,
  objects with a mass that exist in space. We can
  draw gravitational field lines around all these
  objects and these gravitational fields lines
  would all overlap since they exist at infinite
  distances.
• However, since the magnitude of the gravitational
  field decreases with distance at a rate of 1/r2,
  their influence decreases as we move further away
  from them.
• Thus, the gravitational force acting on any
  object, even on the Earths surface, is a sum of
  all objects that exist in space, but the dominant
  force or forces acting on the object will depend
  on distance between objects and the mass of the
  interacting objects.

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Question 5

• Which of the following statements is correct
• A - There is a gravitational between the Earth
  and the person
• B - There is a gravitational field between the
  person and the dog
• C - Both A and B
• D - Neither of the above

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Question 6

• What is the direction of the gravitational force
  on the Earths surface?
• A - Gravity does not have direction
• B - Towards the Earths center of mass
• C - Away from the Earths center of mass
• D - Tangent to the Earths surface

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Question 7

• Why do Gravitational Field Lines never cross?
• A - The are radial to the center of mass of an
  object
• B - They are parallel
• C - Gravitational field lines are vectors, so at
  a point the field vectors add to a single vector.
• D - Field lines are concentric circles

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Question 8

• Given the following two objects, which of the
  following will increase the force on object B
• A Increasing the radius of object A
• B Increasing the mass of object B
• C Increasing the distance between objects A
  and B
• D None of these will affect the force on
  object B

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Question 9

• There are three equal masses placed at each
  corner of an equilateral triangle with sides
  length d. Point A is located at the midpoint of
  one side of the triangle. Point B is located at
  the center of the triangle

Which statement below best describes the
magnitude of the gravitational field at point B
A - It is greater than at point A B - It is
the same as at point A and both are greater than
zero C - It is less than at point A D - The
magnitude at A and B are both zero
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Question 10

• Which of the following images correctly
  represents the gravitational field for the Earth
  and Moon?
• A
  B
• C
  D

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Question 11

• Which of the following images correctly
  represents the gravitational field for three
  identical masses?
• A B
• C D