D1a - Newton's Law of Gravity

D1a - Newton's Law of Gravity
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Slide 1: Slide
PhysicsSecondary Education

This lesson contains 27 slides, with interactive quizzes, text slides and 1 video.

Items in this lesson

D1a - Newton's Law of Gravity

Slide 1 - Slide

Learning Objectives:
  1. What is gravity?
  2. Newton's equation
  3. Assumptions in Newton's equation
  4.  gravitational field strength
  5. Representing gravity.

Slide 2 - Slide

What do you know about gravity?

Slide 3 - Mind map

What is gravity?
If you were to strip the universe back to the most basic components you would find that it contains stuff (matter etc) and forces.
As far as we know there are four fundamental forces of nature. They are the strong nuclear force, the weak nuclear force, the electromagnetic force and gravity.

Gravity is the force that we are probably most familiar with as it governs the stars and planets.
The truth about gravity
Gravity was later discovered by Einstein to not really be a force but instead a curvature of spacetime.

Slide 4 - Slide

Newton
In 1687 Newton published his law of gravitation which was said to be inspired by an apple falling.

Slide 5 - Slide

Slide 6 - Slide

Slide 7 - Slide

What is the formula for the law of gravitation?
A
F=m1m2r2G
B
F=r2Gm1m2
C
F=rG(m1+m2)
D
F=Gr2M

Slide 8 - Quiz

What does 'G' represent in the law of gravitation formula?
A
Acceleration due to gravity
B
Mass of the object
C
Gravitational constant
D
Distance between the objects

Slide 9 - Quiz

What happens to the gravitational force if the distance between two objects doubles?
A
It becomes one-fourth of the original force
B
It becomes half of the original force
C
It remains the same
D
It doubles

Slide 10 - Quiz

The gravitational force between a star of mass M and a planet of mass m is F. What would the force (F_2) be between the star and a planet of mass 3m and 4 times the distance?

Slide 11 - Open question

Newton's law of gravitation assumes all bodies to be point masses i.e. they have no size. What are the correct conditions under which an extended body can be assumed to be a point mass?
A
The distance separating the masses is significantly large.
B
The masses have a similar magnitude.
C
The density of each mass is the same
D
The masses are spherically symmetric.

Slide 12 - Quiz

Point Masses
In physics we ALWAYS start with the simplest case. To do this we need to make some assumptions. In the case of Newton's law of gravity we simplify any extended body into a point mass. This works very well as long as:
  1. The distance between the two masses is very large
  2. the masses are spherically symmetric.

Slide 13 - Slide

Gravitational Field

Slide 14 - Slide

What are fields?
on the left we have a field of wheat.
This is a region where wheat is grown

Slide 15 - Slide

What are fields?
On the right we have a soccer field.
This is a region where people play soccer.

Slide 16 - Slide

Gravitational field
Following this logic a gravitational field is simply a region where gravity exerts an influence (force) on other masses
more information
We will encounter other fields in physics (e.g. electric and magnetic fields) that are defined in similar ways. Fields are a better way of describing non-contact forces as they remove the necessity of considering 'action at a distance' forces which violate Einstein's principles in relativity .

Slide 17 - Slide

Field lines
The black arrows here represent field lines. A field line is an imaginary line which points in the direction a 'test mass' would experience a force. Gravity is ALWAYS attractive and so the field lines always point towards the mass we are interested in.
equipotential lines
The red circles here represent equipotential lines. These are lines that are perpendicular to the field lines at each point and trace out a line where the potential energy is the same. If you travel along one of these lines gravity will do no work as you would not be losing or gaining energy.
Field strength
Notice that as you get closer to the mass the field line density increases (the field lines are closer together along single equipotential). This signifies that the gravitational field is stronger where the field density increases.

Slide 18 - Slide

zooming in
Note that close to the surface of the earth the field lines can be assumed to be parallel (uniform) as the curvature of the earth is not evident locally.

Slide 19 - Slide

What do gravitational field lines around a spherical mass represent?
A
lines where gravitational potential energy is the same
B
The force of gravity
C
The distance between different points in space
D
The direction of the force experienced by a mass

Slide 20 - Quiz

What do equipotential surfaces for gravity indicate?
A
Areas of maximum gravity
B
Points with different gravitational forces
C
Points with the same gravitational potential
D
Locations of zero gravity

Slide 21 - Quiz

How is gravitational field strength related to distance from a spherical mass?
A
It increases with increasing distance from the mass
B
It is unrelated to distance from the mass
C
It remains constant at all distances
D
It decreases with increasing distance from the mass

Slide 22 - Quiz

Slide 23 - Video

Given that the radius of the earth is
m, and g=9.81 N/kg . What is the mass of the Earth?
6.4106
point mass
Remember that Newton's law of gravity works for point masses. So technically we imagine that all of the mass is located at the origin (r=0). When working out the field strength at the surface of a planet we can still use the equation and the answer is accurate.

Slide 24 - Open question

Learning Objectives:
  1. What is gravity?
  2. Newton's equation
  3. Assumptions in Newton's equation
  4.  gravitational field strength
  5. Representing gravity.

Slide 25 - Slide

How do you feel about the content of this lesson?

😒🙁😐🙂😃

Slide 26 - Poll

Is there anything you found particularly challenging you would like to go over in class?

Slide 27 - Open question