Lecture
8: Newton's Laws
FORCE
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Force is a vector quantity, it has both magnitude
and direction.
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It has standard SI units called NEWTONS (N),
where 1 N = kg m/s2
Newton's First Law
We start with the concept of Inertia. Inertia is the tendency of a body
to maintain it's state of rest or state of uniform motion in a straight
line. Newton's first law is sometimes called the law of inertia.
Newton's first law states that:
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Every body or object continues in it's state
of rest or of uniform speed in a straight line, unless acted on by a nonzero
net force.
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mathematically speaking:
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Note that the SF
refers to the sum of all forces acting on the object: SF
= F1 + F2 + F3 + ...
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The first law states that if a body is moving
with constant velocity or if an object is at rest, then that means that
there are no net forces acting on that object.
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Hence, the absence of acceleration means the
absence of net forces.
Newton's Second Law
Newton's second law makes use of mass, specifically, inertial mass. The
concept of mass has never been really defined, just presented to the students
as something that exists. Basically, mass is the measure of the inertia
of a body, the greater the mass a body has, the harder it is to change
the state of the motion of the body. This brings us to Newton's second
law:
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The acceleration of an object is directly proportional
to the net force acting on a body. The constant of proportionality is the
mass of the object.
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Mathematically, SF=
ma , the net force acting on a body is equal to the mass times the
acceleration.
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Force, being a vector quantity, can be decomposed
into it's components. For instance in 2 dimensional motion:
F=
Fx + Fy
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Going back to mass, the greater the mass of an
object, the greater the force needed to change it's motion, hence the harder
it is to accelerate the object. This is a consequence of Newton's
second law.
Newton's Third Law
The third law has to do with action and reaction. The third law can be
summarized as follows:
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When object 1 exerts a force,F12
on object 2, then object 2 exerts a force, F21 on the
first object of equal magnitude, but opposite direction.
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Mathematically: F12 = - F21
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Basically, for every action, there is an equal
but opposite reaction.
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The forces involved are called action-reaction
pairs and these pairs always act along a straight line.
Equilibrium
The last thing to discuss is equilibrium.
An object is said to be in equilibrium if the net force acting on the object
is equal to zero. That means that any object at rest (v = ) or moving
with constant velocity (a = 0) is in equilibrium, therefore SF=
0.
Weight and Normal Force
Weight
Neglecting air resistance, all objects dropped
near the surface of the Earth will fall with the same acceleration, g,
the acceleration due to gravity = 9.80 m/s2. Applying
Newton's law to gravitational force, we obtain the weight of any object
acted on by gravity :
w = Fg = mg
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Weight is the force of gravity acting on an object.
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Weight is always directed downward since acceleration
due to gravity is directed down toward the center of the Earth.
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This acceleration is different for every planet
or any celestial body, for instance acceleration due to gravity on the
Moon is 1/6 that of the earth, and the acceleration due to gravity on Jupiter
is about 2.6 time that of the Earth.
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The reaction pair of weight is just the force
that the object exerts on the Earth.
Normal Force
Normal force is the force exerted by a surface
on an object that sits on the surface. For example, consider a book
on a table. The table exerts a force on the book, the normal force denoted
by N or FN. The normal force is always at
right
angles or perpendicular to the surface as illustrated in the figures
below.
Note: Weight and Normal Force are NOT
action and reaction pairs. So, what are the action-reaction pairs
associated with Normal forces? Normal force is the force that a surface
exerts on an object, the reaction pair is the force that the object exerts
on the table.
Tension
Tension is the magnitude of the force exerted
by a rope (or string, cable, or wire) on the object that it is attached
to. It is directed along the rope or cable, but away from the object.
Frictional Forces
Frictional forces come in many forms: an
object sliding on a surface experiences frictional forces associated with
the degree of roughness of the surface, or an object falling from a building
experiences friction in the form of air resistance, or an object sinking
to the bottom of a lake experience friction in the form of viscosity of
the fluid. Basically, frictional forces are resistive forces. They resist
the motion of the object.
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Frictional forces will be denoted by a lower
case f
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Frictional forces act in the opposite direction
of the motion, for example, a block sliding to the left on a rough surface,
experiences a frictional force directed to the right.
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However, even objects at rest experience friction.
This type of friction is called static friction.
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The type of friction involved with moving objects
is called kinetic friction.
The following is a list of laws and properties
involving friction:
The direction of the force of static friction
between any 2 surfaces in contact is opposite the direction of the applied
force.
The force of static friction can have values
fs
< msFN
where ms
is the coefficient of static friction (a dimensionless constant), and FN
is the normal force.
When the block is on the verge of slipping,
then fs = msFN
The direction of the force of kinetic
friction is opposite the direction of motion.
The force of kinetic friction is given by
fk
= mkFN
where
mk
is the coefficient of kinetic friction.
The values of the coefficients of friction
depend on the properties of the surface. In general mk
is less than ms