NEWTON’S LAW OF UNIVERSAL GRAVITATION
26 FEBRUARY 2013
Lesson Description
In this lesson, we
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Describe and explain Newton’s Law of Universal Gravitation
Demonstrate the acceleration due to gravity is independent of the mass of the object
Solve problems involving Newton’s Law of Universal Gravitation
Key Concepts
All objects are attracted to the Earth, irrespective of their shape, size or mass. If an object is thrown
up into the air, it will move upwards for a period of time it will then change direction and move towards
the Earth. This is due to the force of gravity acting on the object, which is the force of attraction
between the Earth and an object. This force is described in Newton’s Law of Universal Gravitation.
Newton’s Law of Universal Gravitation
The force of attraction between two objects is directly proportional to the product of their masses and
inversely proportional to the square of the distance between their centres.
As an equation:
Where: F = force of attraction (N)
G = Universal Gravitational constant = 6,67 x 10
-11
2
-2
N.m .kg
= mass of objects (kg)
r = distance between their centres (m)
Demonstration
Is the acceleration due to the force of gravity that a body experiences determined by the mass of the
object?
Apparatus
Retort Stand
Length of string
Mass pieces
Clamp
Rubber stopper
Stop watch
Met
Method
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Set up the apparatus as shown in the diagram.
Pull up the pendulum and then allow it swing freely.
Note the time it takes to complete 5 swings.
Repeat the above steps but increase the mass of the bob.
Conclusion
The acceleration experienced by an object when falling under the influence of gravity is independent
of the mass of the object.
Mathematical Proof
Weight of an object is given by:
m = mass of object
g = acceleration due to gravity
Force of attraction between
object and the Earth:
F = force of attraction between Earth and object
G = Universal Gravitation constant
m = mass of object
Mp = mass of planet
rp = radius of planet
But:
Questions
Question 1
Calculate the magnitude of the force between a box of mass 100 kg and a person of mass 75 kg if
they are 0,5 m apart.
Question 2
(Adapted from National Final Exam, Paper 1, 2001, Higher Grade)
The distance between two similar mass pieces is r and the magnitude of the force which they exert on
each other is F. If the distance between them is halved and the masses of both objects is also halved,
what is the magnitude of the force they now exert on other?
Met
Question 3
(Adapted from Gauteng Province, Paper 1, 2000, Higher Grade)
A large planet has a radius of 10 times that of the Earth and a mass of 300 times that of the Earth. If
the weight of a body is 500N on the Earth, calculate the weight of the object on the planet.
Question 4
(Adapted from Western Cape Province, Paper 1, 1999, Higher Grade)
8
24
The radius of the Earth is 6,4 x 10 m and its mass, M is 6,00 x 10 kg. Use Newton’s Law of
Universal Gravitation to calculate the acceleration of a 10 kg object near the surface of the Earth.
Question 5
(Adapted from Western Cape Province, Paper 1, 1999, Higher Grade)
“A falling object falls towards the Earth because the force exerted by the Earth on the object is greater
than the force exerted by the object on the Earth.” Is this statement true or false? Explain.
Links
1. Newton’s Law of Universal Gravitation briefly explained:
http://www.youtube.com/watch?v=Jk5E-CrE1zg
2. Explanation of Newton’s Law of Universal Gravitation, including a simulation:
http://www.youtube.com/watch?v=Y50HeIUS4tk
3. Misconceptions about falling objects: http://www.youtube.com/watch?v=_mCC-68LyZM
Met