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SP1. Students will analyze the relationships between force, mass, gravity, and the
motion of objects.
d. Measure and calculate the magnitude of frictional forces and Newton’s three
Laws of Motion.
e. Measure and calculate the magnitude of gravitational forces.
g. Measure and calculate centripetal force.
SP6. The student will describe the corrections to Newtonian physics given by
quantum mechanics and relativity when matter is very small, moving fast
compared to the speed of light, or very large.
d. Describe the gravitational field surrounding a large mass and its effect on a ray of
light.
What is a force?
• A force is a push or pull upon an object resulting
from the object's interaction with another object.
• Whenever there is an interaction between two
objects, there is a force upon each of the objects.
• When the interaction ceases, the two objects no
longer experience the force. Forces only exist as a
result of an interaction.
• Examples?
Do the interacting objects have to
touch?
• Contact forces are those types of forces that result
when the two interacting objects are perceived to
be physically contacting each other.
• Examples?
• Field forces are those types of forces that result
even when the two interacting objects are not in
physical contact with each other, yet are able to
exert a push or pull despite their physical
separation.
• Examples?
Types and Descriptions of Forces
• Applied Force – FA
• A force that is applied to an object by a person or
another object.
• If a person is pushing a desk across the room, then there
is an applied force acting upon the object.
• The applied force is the force exerted on the desk by the
person.
Types and Descriptions of Forces
• Gravitational Force – FG or FW
• The force with which the earth, moon, or other
massively large object attracts another object towards
itself.
• By definition, this is the weight of the object.
• All objects upon earth experience
a force of gravity that is directed
"downward" towards the center
of the earth.
• The force of gravity on earth is
always equal to the weight of the
object as found by the equation
FG = mg
Types and Descriptions of Forces
• Normal Force – FN
• The support force exerted upon an object that is in
contact with another stable object.
• If a book is resting upon a surface, then the surface is
exerting an upward force upon the book in order to
support the weight of the book.
• Normal forces are always
PERPENDICULAR to the plane
in which the objects are touching
Types and Descriptions of Forces
• Friction Force – FF
• The force exerted by a surface as an object moves across
it or makes an effort to move across it.
• Friction depends upon the nature of the two surfaces
and the degree to which they are pressed together.
• Friction force OPPOSES the motion of an object.
• If a book slides across the surface of a desk, then the
desk exerts a friction force in the opposite direction of
its motion.
• Air resistance, or drag, is a special kind of friction that
has greater effects at high speeds.
Types and Descriptions of Forces
• Tension Force – FT
• The tension force is the force that is transmitted through
a string, rope, cable or wire when it is pulled tight by
forces acting from opposite ends.
• The tension force is directed along the length of the wire
and pulls equally on the objects on the opposite ends of
the wire.
Types and Descriptions of Forces
• Spring Force – FSP
• The spring force is the force exerted by a compressed or
stretched spring upon any object that is attached to it.
• An object that compresses or stretches a spring is always
acted upon by a force that restores the object to its rest
or equilibrium position.
How do we measure forces?
• Force is a quantity that is measured using the
standard metric unit known as the Newton.
• A Newton is abbreviated by an "N." To say "10.0 N"
means 10.0 Newtons of force.
• One Newton is the amount of force required to give
a 1-kg mass an acceleration of 1 m/s2.
• So, 1 N = 1 kgm/s2
• Weight is the measurement of force – specifically
that of Earth’s gravity – on a mass.
• 1 Newton is about the weight of an apple.
How do we indicate forces?
• A force is a vector quantity, so it has both
magnitude and direction.
• To fully describe the force acting upon an object,
you must describe both the magnitude (size or
numerical value) and the direction, usually just a
sign (+/-) or a physical description (up/down or
left/right).
• Balanced forces cause no change
in motion
• Unbalanced forces do result in a
change in motion
How do we show how forces interact?
• Free-body diagrams are diagrams used to show the relative
magnitude and direction of all forces acting upon an object
in a given situation.
• A free-body diagram is a special example of the vector
diagrams that we used earlier. The size of the arrow in a
free-body diagram reflects the magnitude of the force. The
direction of the arrow shows the direction that the force is
acting.
• Each force arrow in the diagram is labeled to indicate the
exact type of force.
• It is generally customary in a free-body diagram to represent
the object by a box and to draw the force arrow from the
center of the box outward in the direction that the force is
acting.
Examples: Draw FBDs for each situation
1. A textbook sits motionless on a table.
2. A coconut falls from a tree (no drag).
3. A puck slides along frictionless ice.
4. A dragster accelerates from rest.
5. A car drives at a constant velocity.
6. A block of wood slides down an incline.
In 1665 Sir Isaac Newton formulated several laws
that dictate the motion of objects. These laws are
universal and apply to all forces in the universe.
First Law of Motion – “The Law of Inertia”
Second Law of Motion – “F=ma”
Third Law of Motion – “The Law of Action and Reaction”
Universal Law of Gravitation – “The Law of Gravity”
Newton’s First Law of Motion
• This law is referred to as “The Law of Inertia”
because it explains how inertia is responsible for an
object’s movement, or lack thereof.
• Inertia is the property of matter that maintains its
current status. Inertia keeps a still object still and a
moving object moving.
• Inertia is directly proportional to an object’s mass
• This is why it is way harder to move (or stop) a heavy
object.
Newton’s First Law of Motion
• An object at rest remains at rest, or if in motion,
remains in motion at a constant velocity unless
acted on by a net external force.
• Net force is the sum of all forces acting on an
object. Direction matters!
Newton’s Second Law of Motion
• This law is referred to as “F=ma” because the law is
typically expressed as that formula, where:
Force = mass x acceleration
(N)
(kg)
(m/s2)
• There are several relationships implied in this law:
• The harder the force, the faster it will move (F ∝ a)
• The bigger the object, the harder you have to push (F ∝ m)
• The bigger the object, the slower it gets moving (m ∝ 1/a)
Newton’s Third Law of Motion
• This law is referred to as “The Law of Action and
Reaction” because the law explains the interactive
nature of forces.
• For every action (force), there is an equal (in size)
and opposite (in direction) reaction (force).
• Forces are always in pairs and involve the same
objects (A on B; B on A)
Basic Problems and the
nd
2
Law
1. What is the force on a 1000 kg elevator that is
falling freely at 9.8 m/s2?
2. A net force of 16 N causes a mass to accelerate at
a rate of 5 m/s2. Determine the mass.
3. What acceleration will result when a 12 N net
force applied to a 3 kg object?
Advanced Problems and the 2nd Law
1. A 1200kg car accelerates at 5.85 m/s2. If the force
of friction acting on the car is 2800 N, how much
force does the engine exert?
2. You exert a 2.45 N rightward force on a 0.500-kg
cart to accelerate it across a track. If the total
resistance force is 0.72 N, then what is the cart's
acceleration?
Advanced Problems and the 2nd Law
3. An applied force of 50 N is
used to accelerate an
object to the right across a
frictional surface. The
object encounters 10 N of
friction. Use the diagram
to determine the normal
force, the net force, the
mass, and the acceleration
of the object. (Neglect air
resistance.)
More about friction…
• There are 2 categories of friction forces –
Static (FS) and Kinetic (FK)
• Static friction exists while the objects are
attempting to move, reaches its maximum amount
right before it moves, and is then converted to
kinetic friction once it moves
More about friction…
• Friction forces are proportional to normal forces
• Greater contact forces produce more molecular
interaction
• Friction forces are (generally) independent of
contact area
• Static friction forces are ALWAYS LARGER than
kinetic friction forces
• Friction forces are dependent on surface texture
More about friction…
• The coefficient of friction is specific to the surfaces
in contact, is represented by μ, and is different for
static friction (μS) and kinetic friction (μK).
• Typically the value ranges from 0 (frictionless) to 1,
it has no unit, and it is scalar (so direction doesn’t
matter)
• Examples:
• ice on ice – 0.02
• glass on glass – 0.9
• rubber on concrete – 0.6
More about friction…
• The mathematical relationship that exists between
friction forces, normal forces, and coefficients of
friction is this:
FF = μ FN
Basic Problems with Friction
1. How much force would be required to get a 15000 N
car to roll across dry concrete (μS=0.6) ?
2. If the car can be kept moving at a constant speed by
applying 19000 N, what is the coefficient of kinetic
friction?
Advanced Problems with Friction
3.
Advanced Problems with Friction
4.
Newton’s Universal Law of Gravitation
•
•
Every object with mass attracts every other object
with mass.
Newton realized that the force of attraction
between two massive objects…
• Increases as the mass of the objects
increases.
• Decreases as the distance between the
objects increases.
Newton’s Universal Law of Gravitation
M1M2
•
FG = G
•
G = Gravitational Constant
•
•
•
r2
G = 6.67x10-11 N*m2/kg2
M1 and M2 = the mass of two bodies (kg)
r = the distance between them (m)
Newton’s Universal Law of Gravitation
•
The ULoG is an inverse-square law:
•
•
•
•
If the distance doubles, the force drops to 1/4.
If the distance triples, the force drops to 1/9.
Distance x 10 = FG / 100
There is a gravitational force between you and the
person next to you, but it is dwarfed by the force
between you and the earth. Why?
Newton’s Universal Law of Gravitation
■
Jimmy is attracted to Betty. Jimmy’s mass is 90.0 kg and Betty’s
mass is 57.0 kg. If Jim is standing 10.0 meters away from Betty,
what is the gravitational force between them?
■ FG = GM1M2 / r2
■ FG = (6.67x10-11 Nm2/kg2)(90.0 kg)(57.0 kg) / (10.0 m)2
■ FG = (3.42x10-7 Nm2) / (100. m2)
■ FG = 3.42x10-9 N = 3.42 nN
■
In standard terms, that’s 7.6 ten-billionths of a pound of force.
Newton’s Universal Law of Gravitation
■
The Moon is attracted to the Earth. The mass of
the Earth is 6.0x1024 kg and the mass of the Moon
is 7.4x1022 kg. If the Earth and Moon are 345,000
km apart, what is the gravitational force between
them?
Newton’s Universal Law of Gravitation
■
Gravitational field – an area of influence
surrounding a massive body.
■
■
g = GM / r2
■
■
■
Field strength = acceleration due to gravity (g).
Notice that field strength does not depend on the mass
of a second object.
GM1M2/r2 = M2g = FG = Fw
So gravity causes mass to have weight.
Variations in Gravitational Field Strength
Things Newton didn’t know…
■
■
■
Newton didn’t know what caused gravity, although
he knew that all objects with mass have gravity
and respond to gravity.
To Newton, gravity was simply a property of
objects with mass.
Newton also couldn’t explain how gravity was able
to span between objects that weren’t touching.
■
He didn’t like the idea of “action-at-a-distance”.
Other things Newton didn’t know…
■
Newton didn’t know that gravity bends light.
■
■
This was verified by a solar eclipse in 1919.
He also didn’t know that gravity slows down time.
■
■
Clocks near the surface of Earth run slightly slower than
clocks higher up.
This effect must be accounted for by GPS satellites,
which rely on accurate time measurements to calculate
your position.
Einstein and Relativity
■
■
■
■
Einstein’s Theory of General Relativity explains
many of the things that Newtonian mechanics
cannot explain.
According to Einstein, massive bodies cause a
curvature in space-time.
Objects moving through this curvature move in
locally straight paths through curved space-time.
To any observer inside this curved space-time, the
object’s motion would appear to be curved by
gravity.
Curvature of Space-Time
Curvature of Space-Time
Gravity…it’s not so simple anymore
■
According to Einstein, gravity isn’t technically a force.
■
■
It’s an effect caused by the curvature of space-time by
massive bodies.
Why treat it as a force if it isn’t one?
■
■
■
Because in normal situations, Newton’s ULoG provides an
excellent approximation of the behavior of massive bodies.
And besides, using the ULoG is a lot simpler than using the
theory of relativity, and provides results that are almost as
good in most cases.
So there.