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Work and Mechanics
Lesson 13: Newton’s Law of Motion
Isaac Newton’s Laws of Motion
To really understand the significance of the work of Isaac Newton, you have to know a little
bit about the common beliefs of the scientists of the time (or “natural philosophers” as they
were called then). The prevalent perception at the time was that the natural state of all
objects was to be at rest; that to maintain motion, there had to be a “mover” (something
that applies force to a body). This model had its roots from the philosopher Aristotle.
Newton’s first law of motion gave concise wording to another idea that was growing among
independent thinkers in Newton’s time.
Newton’s First Law of Motion: Inertia
Every body will persevere in its state of rest or uniform motion
in a straight line unless a net external force acts upon it.
Imagine trying to send a probe into space if the model Aristotle had proposed was correct.
A continuing force would be needed for the whole journey. Remember that force times
distance is work (energy). You would have to store enough energy on board to complete
the whole journey, and it is unlikely that this would be possible. With Newton’s law of
inertia, once a space probe breaks out of the gravitational fields of planets and stars, it does
not need a continuing source of energy to keep moving. Instead it maintains a “uniform
motion in a straight line” since there are no significant external forces acting upon it.
Newton’s first law of motion is a foundation on which his second law can be better
understood. (The first law corrected some prevalent fundamental misconceptions so that
the people of his day would be more able to grasp the second law.) The second law is the
real heart of his laws of motion.
Newton’s Second Law of Motion: F = m∙a
For a body with constant mass, a net force applied to the body
equals the mass of the body times the rate of change of the
body’s velocity.*
The mass of a body is simply a measure of how much matter comprises the body. This is a
physical quantity that does not change if the body is taken to different gravitational fields.
We often measure mass by weighing things, but the weight of an object (which is a force)
changes if there are changes in gravity. Mass, on the other hand is a pure measure of how
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Work and Mechanics
Lesson 13: Newton’s Law of Motion
much matter is present in a body. If we could count the number of protons, neutrons, and
electrons that make up a body, we could determine its mass.
The units of force, mass and acceleration must be consistent for the equation F = m∙a to
hold. In the metric system, the unit for force is a Newton, which is defined in terms of other
units:
𝑁𝑒𝑤𝑡𝑜𝑛 = 𝑁 =
𝑘𝑔 ∙ 𝑚
𝑠2
A Newton is the amount of force it takes to accelerate a kilogram of mass at a rate of 1m/s2.
Just for reference, a Newton is approximately how much an apple weighs (this is just a
coincidence).
Other unit systems also have units that allow the equation F = m∙a to hold. In the US
customary system, pounds, slugs and feet per second per second are related.
𝑠𝑙𝑢𝑔 ∙ 𝑓𝑡
𝑝𝑜𝑢𝑛𝑑 = 𝑙𝑏 =
𝑠2
A slug is the amount of mass that weighs 32.2 lb (a force) on earth. You may have also seen
people use pounds to describe mass. This is one of the confusing things about the US
customary system. The same unit name can be given to both force and mass, even though
they are different types of physical quantities. Sometimes people use the denotations lbf for
“pounds force” or lbm for “pounds mass”. On earth, one pound mass weighs one pound
force. We will be dealing nearly exclusively with the metric system in this course, but it is
good to know about the other system since we deal with it fairly regularly (e.g. we never
tell people how much we weigh in Newtons).
CLASS PROBLEM: A space probe with a mass of 24 kg has main thrusters that
produce 800 N of force. How long will the thrusters have to burn to increase the
velocity of the probe by 110 m/s?
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Work and Mechanics
Lesson 13: Newton’s Law of Motion
Newton’s third law has to do with how bodies interact with one another.
Newton’s Third Law of Motion: Forces come in Pairs
Any force placed on a body comes from some other body. The force
exerted on the first body by the second is equal in magnitude and
opposite in direction to the force exerted on the second body by the
first.
Examples:
Consider an apple resting on a table:
The apple places a downward force on the table:
The table places an upward force on the apple,
equal and opposite!
Now think about gravitational force. The gravity
between the apple and the earth draws the apple
toward the earth…
…and the earth toward the apple!
(Since the earth is so massive
compared to the apple, the force from
the apple has little effect on the earth,
but it is there nonetheless)
As a matter of fact, every force in nature actually has two sides to it – two bodies that are
affected. The magnitudes of the two parts of the force are always equal, and the directions
are always opposite.
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Work and Mechanics
Lesson 13: Newton’s Law of Motion
CLASS PROBLEM: Draw a diagram of an accelerating automobile. Show all of the forces
that the earth places on the automobile as arrows. Label each arrow with a name you could
call that force. Then show a diagram of the surface of the earth with arrows indicating the
forces that the automobile places on the earth.