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A-level Physics



  Unit G484:
  The Newtonian
  World


  Newton’s law of gravitation



Circular motion
Gravitation – lesson 1 recall                         LOs



   To do/answer

   1. Complete the following:

           ‘a field is a region of space in which a particular type of
            object experiences a … ‘

   2. Name the type of object needed to detect the following:

      a. a magnetic field      b. an electric field   c. a gravitational field

   3. Sketch a diagram to show the gravitational field in this lab.. Be ready to
      explain what you are attempting to show.

   4. Sketch a diagram to show the Earth’s gravitational field. How do we
      describe this field? Where do the field lines i) come from, ii) go to?
      What have you assumed about the Earth?

   5. Define ‘gravitational field strength’.


Circular motion
Lesson focus
  • Newton’s law of universal gravitation


  Learning objectives
  At the end of the lesson you will be able to:

  • state Newton’s law of gravitation;
  • select and use the equation for centripetal force F = -GMm/r2 for the
    force between two point or spherical objects.




Circular motion
Learning outcomes
  All of you should be able to
  • state Newton’s law of gravitation in words;
  • state this law as an equation and define the symbols used;
  • use this equation to solve simple problems.


  Most of you will be able to
  • use Newton’s law of gravitation to solve more complex problems.




Circular motion
The gravitational force between objects                                  LOs




    Imagine two masses




                           m1                       m2

    We know that masses give rise to gravitational fields. Each mass will,
    therefore, be in the gravitational field of the other.

    1. Sketch the situation and show the forces on each mass.

    2. List the factors that determine the size of the forces on the
       masses.

                                                                   Isaac Newton and gravity: video


Circular motion
Newton’s law of universal gravitation                            LOs




      This law states that the

         ‘gravitational force between two point masses is proportional to the
      product of the two masses and inversely proportional to the square of
      the distance between them’.



                 G m1 m 2
       F = -
                     r2

                                                       G - universal gravitational
      Notes:                                               constant (‘big G’)
      • a point mass has no spatial extent
      • the minus sign in the equation shows that the force is attractive



Circular motion
Newton’s law of universal gravitation                           LOs




                               G m1 m2              where,
                       F = -                        G - universal gravitational
                                   r2
                                                        constant (‘big G’)


2/3   Newton conceived of this force extending (instantaneously)
      throughout the entire Universe (hence universal). He did not
      attempt to explain the origin of the force.



Circular motion
Newton’s law of universal gravitation                      LOs




      To do

      Using the data given
      find a value for G.

      Data:                                                        G m 1 m2
      • your mass                                          F = -
      • the mass of the Earth (5.97 x 1024 kg)
                                                                        r2
      • radius of the Earth (6.37 x 103 km)

3/3   G is one of the least well defined constants of nature (hw: why is this?).
      The accepted value is 6.674×10−11 N m2 kg−2 .

      To do
      Calculate the percentage difference between this and your value.


 Circular motion

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Cm 6 newton's law of gravitation (shared)

  • 1. A-level Physics Unit G484: The Newtonian World Newton’s law of gravitation Circular motion
  • 2. Gravitation – lesson 1 recall LOs To do/answer 1. Complete the following: ‘a field is a region of space in which a particular type of object experiences a … ‘ 2. Name the type of object needed to detect the following: a. a magnetic field b. an electric field c. a gravitational field 3. Sketch a diagram to show the gravitational field in this lab.. Be ready to explain what you are attempting to show. 4. Sketch a diagram to show the Earth’s gravitational field. How do we describe this field? Where do the field lines i) come from, ii) go to? What have you assumed about the Earth? 5. Define ‘gravitational field strength’. Circular motion
  • 3. Lesson focus • Newton’s law of universal gravitation Learning objectives At the end of the lesson you will be able to: • state Newton’s law of gravitation; • select and use the equation for centripetal force F = -GMm/r2 for the force between two point or spherical objects. Circular motion
  • 4. Learning outcomes All of you should be able to • state Newton’s law of gravitation in words; • state this law as an equation and define the symbols used; • use this equation to solve simple problems. Most of you will be able to • use Newton’s law of gravitation to solve more complex problems. Circular motion
  • 5. The gravitational force between objects LOs Imagine two masses m1 m2 We know that masses give rise to gravitational fields. Each mass will, therefore, be in the gravitational field of the other. 1. Sketch the situation and show the forces on each mass. 2. List the factors that determine the size of the forces on the masses. Isaac Newton and gravity: video Circular motion
  • 6. Newton’s law of universal gravitation LOs This law states that the ‘gravitational force between two point masses is proportional to the product of the two masses and inversely proportional to the square of the distance between them’. G m1 m 2 F = - r2 G - universal gravitational Notes: constant (‘big G’) • a point mass has no spatial extent • the minus sign in the equation shows that the force is attractive Circular motion
  • 7. Newton’s law of universal gravitation LOs G m1 m2 where, F = - G - universal gravitational r2 constant (‘big G’) 2/3 Newton conceived of this force extending (instantaneously) throughout the entire Universe (hence universal). He did not attempt to explain the origin of the force. Circular motion
  • 8. Newton’s law of universal gravitation LOs To do Using the data given find a value for G. Data: G m 1 m2 • your mass F = - • the mass of the Earth (5.97 x 1024 kg) r2 • radius of the Earth (6.37 x 103 km) 3/3 G is one of the least well defined constants of nature (hw: why is this?). The accepted value is 6.674×10−11 N m2 kg−2 . To do Calculate the percentage difference between this and your value. Circular motion