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WEEKLIES ISSUE
2012-2013
Science—Forces and Newton’s Three Laws
Have you ever wondered how the physical world around you works? How it is possible to walk,
to lift a book off the table, or throw a baseball? These—and most of the universe that you see
around you—are due to the effects of forces.
Forces
A force is a push or a pull on an object that can cause changes in the object’s state of motion.
You encounter forces every day—each movement you make, each object you see—everything is
subject to forces. The basic nature of forces can be summed up into three laws, first recorded by
Sir Isaac Newton.
Sir Isaac Newton
Sir Isaac Newton was an English polymath—he was a
mathematician, an alchemist, a physicist, a philosopher, and many
others. Born on Christmas of 1642, Newton had a difficult
childhood in which he had little of his mother’s attention and hated
his stepfather (his biological father died before he was born).
Though accounts of his undergraduate schooling would seem to
indicate that he was an average student, studies of his notebooks
indicate that he rapidly mastered several topics in advanced
mathematics in self-study. Newton graduated the University of
Cambridge without distinction.
Shortly following his graduation from the University of Cambridge,
Newton had several years of incredibly productive and inventive work in which he discovered a
whole field of mathematics (Calculus) and studied the forces of nature, which he published in his
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pivotal 1687 Philosophiæ Naturalis Principia Mathematica (often just The Principia). The
Principia is considered to be one of the most important works of scientific literature ever written.
Newton was faced with a mathematical curiosity when studying the
motion of celestial objects; while the moon was definitely held in place
near the earth, it was difficult to figure out what held it in place.
Historically, Newton witnessed a falling apple in his orchard—it didn’t
necessarily strike him on the head—that brought him to realize that the
same force that causes objects to fall on earth is the same force that holds
the moon around the earth: gravity. Newton’s theory of Gravitational
Attraction was the most accurate and widely regarded gravity theory for
over two hundred years, and is still used today for simpler, low-accuracy
calculations.
Newton died in 1727 having completed astounding advances in science and mathematics.
Of his study of the forces of nature, Newton began by defining three axioms that are today
collectively known as “Newton’s Three Laws of Motion.” These laws are the basis of almost all
modern mechanical physics—important enough for physicists to name the unit of force the
newton in Sir Isaac’s honor. Let us take a look at these three laws and study why they are so
important.
Newton’s First Law
An object at rest will remain at rest, and an object in motion will remain in
motion, unless acted upon by an unbalanced force
This law may seem slightly obvious at first glance. After all, if you have a desk
sitting in the middle of a room, it is not going to suddenly start moving towards
you unless something pushes it towards you; this is simply part of everyday
observation.
The key observation in this law comes from the second part “an object in motion
will remain in motion.” Counterintuitive? After all, even if that desk were
moving towards you, it would eventually stop…right? Are there outside forces
acting on the desk?
There are outside forces: friction between the desk and the ground and air
resistance act on the desk to slow it down to a stop. What Newton’s law tells us,
then, is that if the desk were in a perfect environment where no forces acted on it,
then the original state of motion of the desk would be the state it would be
in…forever.
If the desk were moving and no forces acted on it, then it would move forever. If
the desk were at rest (not moving), then it would remain at rest forever.
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What’s more is that this law tells us that objects resist changes in their state of
motion—an attribute called inertia. You’ve probably noticed that it can be hard
to change the direction of moving objects, or to get objects to move from
rest—this is due to the inertia of the object. Further, the more mass that an object
has (the more matter in an object), the more inertia it has; this is why it is harder
to change the motion of heavy objects than it is of light objects.
So this law tells us that all motion is due to the action of forces.
Example: Inertia and Newton’s First Law
Say that you have two bowling balls sitting in a bowling lane. One
bowling ball has a mass of 2 kilograms (~4.5 pounds) and the other has a
mass of 7 kilograms (~15.5 pounds). Both bowling balls are at rest—they
are not moving.
Bart pushes both bowling balls with the same amount of force and
recognizes that the heavier bowling ball is harder to move than the lighter
bowling ball. This shows both that once an outside force (Bart) acts upon
the bowling balls, the state of motion changes; also, because the second
bowling ball has more mass, it has more inertia and is harder to move.
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Newton’s Second Law
The acceleration of an object is directly proportional to the net force acting on
the object, and inversely proportional to its mass.
This law is rarely seen in sentence form because it is so much more useful in its
equation form. The equation form most often associated to Second Law is:
ΣF=m∙a
Where ΣF is the total force acting on an object, m is the mass of the object, and a
is the acceleration of the object. This reads much easier; we can see that the total
force acting on an object is equal to the product of the mass of the object and its
acceleration. This equation is very important to physics because it allows us to
derive complex relationships between physical motion and force, as well as
determine the magnitude of forces acting on an object (see example below).
Further, if we use the SI units for force (newton), mass (kilogram), and
acceleration (meters per second squared), we can see that the newton is defined as
a kilogram meter per second squared (kg∙ms2).
Example: Newton’s Second Law with One Force
Maggie is sitting on a sled that sits on frictionless ice—they have a
combined mass of 9 kilograms. A dog starts pulling the sled with a force
of 45 newtons. What is the acceleration of the Maggie-sled system?
We can proceed directly by applying Newton’s Second Law because we
know the mass (9 kilograms) and the force (45 newtons). Using algebra,
we can solve for the acceleration:
ΣF=m∙a
45N=9kg∙a
a=5m/s2
The sled and Maggie start accelerating at 5 m/s2.
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Example: Newton’s Second Law with More than One Force
Lisa starts pushing a 10-kilogram box horizontally with a force of 30
newtons. The box starts to accelerate at 2 meters per second squared.
What is the magnitude of the frictional force acting on the box?
We can solve this problem by using Newton’s Second Law. We know the
acceleration (2 m/s2), the mass (10kg) and one of the two forces acting on
the box (30N, the other being friction). If we call the force of friction Ff,
then we have:
ΣF=m∙a
30N+Ff=10kg∙2m/s2
If we rearrange and solve for Ff, we find that the frictional force is -10
newtons.
Newton’s Third Law
For every action force, there is an equal and opposite reaction force.
At first glance, this law can be rather difficult to understand—at least until you
realize that this law is constantly around. It can be best illustrated with an
example.
Example: Newton’s Third Law
When you stand on the floor, the earth exerts a force of gravity upon you
that pulls you towards the center of the earth. In order to keep you from
accelerating through the floor, miles of dirt, stone, and liquid metal, the
floor exerts a force back on you that is exactly equal (but in the opposite
direction) to the force of gravity that the earth exerts on you.
In the image on the left, a ball experiences both the force of gravity and
the corresponding normal force that opposes the force of gravity. Almost
all phenomena have to do with this ever-present balance of forces.
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Example: Newton’s Third Law
Elaine stands in a canoe next to the
dock. She tries to jump from the
canoe onto the dock, but the canoe
moves backwards while she jumps,
causing her to come up short and fall
into the water. Why did this occur?
Because of Newton’s Third Law, we
know that the force that Elaine
applies to the canoe in order to try to jump to shore is matched by an equal
and opposite force. Thus, the canoe moves backwards while Elaine moves
forwards.
Now that we have discussed the Three Laws of Motion, let’s talk about two of the most
common forces—gravity and friction. Note: these two topics are a bit more advanced.
Gravity
Ever wondered why it is that you don’t get flung off the earth into the dusty voids
of space? It’s because of the force of gravity. Gravity is one of the four
fundamental forces of nature—it actually is the weakest of the four. Despite that,
however, gravity is one of the forces that we experience on a macroscopic scale
every day.
Objects that have mass attract each-other due to gravity, directly related to the
distance between the objects. That is to say that the earth exerts a gravitational
attraction on you and you exert an equal and opposite attraction on the earth.
Why does it seem like the earth is the only thing exerting a gravitational
attraction? It has to do with the size of the mass. The earth, after all, has a mass
of about 6x1024 kilograms, whereas the average human mass is about 70
kilograms.
Sir Isaac Newton realized the connection between gravitational attraction and the
masses of the objects involved. He formulated a Universal Theory of Gravitation
that is still used today—nearly 400 years later—for applications where speed and
relative accuracy are required. Newton formulated the force of the gravitational
attraction between two bodies as:
Fg=Gm1m2r2
Where Fg is the force of gravitational attraction, m1 is the mass of one body, m2
is the mass of the second body, r is the distance between the centers of the bodies,
and G is the Universal Gravitation Constant.
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Using this equation, along with Newton’s Second Law, we can see that while the
average human accelerates towards the earth at about 9.8 meters per second
squared, the earth essentially does not accelerate towards the human.
Because the acceleration of the earth is miniscule for almost all bodies that we
encounter on a daily basis (excepting the moon, sun, and other celestial bodies),
we can treat the earth as essentially stationary with respect to everything on it.
This lets us treat the force of the earth on everything as a constant downwards
acceleration—the acceleration due to gravity (g), which is about equal to 9.8
meters per second squared, or 32 feet per second squared. We can then say that
the force of gravity can be calculated as:
Fg=m∙g
Where m is the mass of the object we’re working with, and the other terms are as
noted above. Notice that this is almost exactly the same as our formulation of
Newton’s Second Law above.
Example: Gravity
Jerry, an average human with a mass of about 70 kilograms, jumps off a
high dive. What is the force of gravity that Jerry experiences?
Remembering that the acceleration due to gravity on
earth is about 9.8m/s2, we can proceed straight
forward with the equation above.
Fg=m∙g
Fg=70kg∙9.8m/s2
Fg=686N
The force of gravity that Jerry experiences is 686
newtons.
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Friction
Friction is another everyday force for us. Without friction, things would be
sliding everywhere, and it would be almost impossible to go anywhere. So what
causes the force of friction?
For things like mud or sandpaper, that is an easy question to answer. We know
that the lumps in the mud and the sand of the sandpaper rub against things moving
on them, turning their motion energy into heat energy while slowing them down.
The force of friction is actually what allows us to create fire with matches or by
rubbing two sticks together; the heat from friction ignites the fuel in the match
head or ignites the wood, causing fire.
What about surfaces that seem smooth? If you roll a stainless steel ball bearing
on a non-stick surface, it will still stop eventually due to friction. We find the
answer on a microscopic scale. On tiny scales, all surfaces are slightly
irregular—bumpy, ridged, etc.—and those irregular surfaces rub against eachother just like the macroscopic mud or sandpaper.
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