Transcript Newton`s Laws

Newton’s Laws
Forces and Motion
Laws of Motion
formulated by Issac Newton in the
late 17th century
 written as a way to relate force and
motion
 Newton used them to describe his
observations of planetary motion.
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History
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Aristotle was an ancient Greek philosopher
Based on his observations the common
belief was that in order for an object to
continue moving, a force must be exerted
in the direction of the motion
This lasted until Issac Newton proposed
his “Laws of Motion” based on
observations made of bodies free from
earth’s atmosphere.
Newton’s 1st Law
Inertia
An object at rest will stay at rest, and
an object in motion will stay in
motion at constant velocity unless
acted on by an unbalanced force.
This statement contradicted Aristotle’s teaching and was
considered a radical idea at the time. However, Newton
proposed that there was, in fact, an unrecognized force of
resistance between objects that was causing them to stop
in the absence of an applied force to keep them moving.
This new unseen resistance force became known as
“friction”.
Newton’s 2nd Law
Fnet = ma
If an unbalanced force acts on a
mass, that mass will accelerate in the
direction of the force.
2N
8N
a
Since 8N is greater than 2N,
the unbalanced force is to the
right so the acceleration is to
the right.
Newton’s 1st Law says that without an unbalanced
force objects will remain at constant velocity
(a=0)…so it seems logical to say that if we apply a
force we will see an acceleration.
Newton’s 3rd Law
Action - Reaction
For every action force there is an
equal and opposite reaction force.
Example: If you punch a wall with your fist in anger,
the wall hits your fist with the same force.
That’s why it hurts!
Action-reaction forces cannot balance each other
out because they are acting on different objects.
A Force is…
A “push” or “pull”
 Measured in Newtons (N) in the
metric (SI) system and pounds (lbs)
in the English system
 A vector quantity requiring magnitude
and direction to describe it
 Represented by drawing arrows on a
diagram
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Types of Forces
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Weight - force of gravity
Normal force – surface pushing back
Friction - resistance force
Applied force - force you exert
Tension - applied through a rope or chain
Centripetal Force – any force that causes circular motion
Elastic Forces – applied force due to the stretch or
compression of a rubberband, bungee, or spring
Drag Forces – any resistance force caused by fluids (i.e.
air resistance)
Net force – total vector sum of all forces
Balanced forces – equal and opposite
Unbalanced forces – not equal and opposite
Weight
The force of gravity acting on a mass.
Weight always acts down!
Weight = mass (kg) * acceleration due to gravity
Fg  W  m * g
Weight is a force…so this is a special case
of F=ma and the unit is a Newton.
Mass is…
The amount of matter an object is
made up of.
 Measured in kilograms.
 A universal value, independent of the
influences of gravity.
 NOT a force.
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Normal Force (FN)
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Defined as the force of a surface pushing
back on an object.
Always directed perpendicular to the
surface.
This is a contact force. No contact…no
normal force.
NOT always equal to weight.
Examples:
FN
FN
Table
W
a
l
l
Friction
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A resistance force usually caused by two
surfaces moving past each other.
Always in a direction that opposes the
motion.
Measured in Newtons
Depends on surface texture and how hard
the surfaces are pressed together.
Surface texture determines the coefficient
of friction (μ) which has no units.
Normal force measures how hard the
surfaces are pressed together.
Types of friction
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Static friction is the force an object must
overcome to start moving.
Kinetic friction is the force an object must
overcome to keep moving.
Static friction is always greater
than kinetic friction!
Calculating the Force of Friction
f   FN
Where f is the force of friction, μ is the
coefficient of friction, and FN is the normal force
For kinetic friction:
f k  k FN
For static friction:
f s  s FN
Drag Forces
Deriving expressions for drag forces such as
air resistance will be the topic of an entire
powerpoint of its own.
Stay tuned for more to come to an AP
Physics class near you.
May the
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Net Force be with you
Total force acting on an object
Vector sum of all the forces
The unbalanced force referred to in Newton’s
Law of Motion
Net force is equal to the mass of an object times
the acceleration of that object.
Fnet   F  ma
Force Diagrams
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Force diagrams must include the object
and all forces acting on it.
The forces must be attached to the object.
No other vectors may be attached to the
object.
Components of forces, axis systems,
motion vectors and other objects or
surfaces may be included in force
diagrams.
Force Diagram
Problem: A 10 kg crate with an applied force of 100 N slides across a
warehouse floor where the coefficient of static friction is 0.3 between
the crate and the floor. What is the acceleration of the crate.
FN
f = μFN
10 kg
Fapplied = 100 N
Weight = Fg = (10 kg)*(9.81m/s2)
To Solve the Problem
Now that you have the force diagram!
Problem: A 10 kg crate with an applied force of 100 N slides across a
warehouse floor where the coefficient of static friction is 0.3 between
the crate and the floor. What is the acceleration of the crate.
FN
f = μFN
10 kg
Fapplied = 100 N
a
Weight = Fg = (10 kg)*(9.81m/s2)
Write the Newton’s 2nd Law equation for the x- and y- directions.
Fnet , x   Fx  Fapplied  friction  max
Fnet , y   Fy  Fn  Fg  may
Now plug in what you know and solve for what you don’t. Algebra…YUK!!
Centripetal Force
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Any force that causes an object to travel in a
circular path
Always toward the center of the circular path
Any of the forces we have identified could be
the centripetal force, most commonly… gravity
(weight), tension, friction, & elastic forces
v
r
Fc
m
mv
Fc 
r
2
Note: an object’s
velocity is tangent
to the curved path
it takes, so
perpendicular to
the centripetal
force, acceleration
and radius
Centripetal Forces in horizontal
circles with tension
Top view
When the plane of the circle traced out by the
object is horizontal, gravity is perpendicular to the
motion so the velocity remains constant.
However, since the object will always hang below
the point of support, only the component of the
tension that is parallel to the plane of the circle
can be considered as the centripetal force.
v
m
Fc
Side view
L
θ
T
r
m
Fc
mv
T sin  
r
T cos   mg
Fg=mg
2
Centripetal forces
in vertical circles
At the top of the circle: Fc  FT  Fg
-velocity is the lowest
-centripetal force is a combination of
the tension and gravitational forces
v
Fc
FT
Fg
Fg
v
Fc
Fc
FT
FT
Fc
FT
v
Fg
In a vertical circle, gravity does
have an effect on the speed at
different points on the circular
path.
Fc  FT
At the sides:
v -velocity is vertical and
changing with the acceleration due
to gravity
-centripetal force is supplied by the
Fg tension alone since the gravitational
force is perpendicular.
At the bottom: Fc  FT  Fg
-velocity is the maximum
-centripetal force is a combination of
the tension and gravitational forces
Gravity as the Centripetal Force
Satellite Motion (assuming circular orbits)
v
m
H
Fg
RE
ME
r
In the case of a satellite orbiting a planet, the
centripetal force (net force required to keep the
object moving in the circular path) is provided
by the gravitational force (weight). Of course
at orbital altitudes we can no longer use Fg=mg
to calculate weight of the satellite, so…
Fc  Fg
m ME
mv 2
G
r
r2
We can solve this for v to get the orbital
velocity associated with that particular radius.
GM E
v
r
Note the orbital radius is measured to the center of the circular path of the orbit
so … r = RE + H
Friction as the centripetal force
A car going around a curve
v
Fc
m
For a car going around a curve on a road, the
force that keeps the car in the circular path
(Centripetal force) is the friction of the road
pushing the tires in toward the center of the
circle.
Fc  f
mv2
 FN
r
Note: This is for a flat curve. If the curve is banked, the problem is a little
trickier. Draw the force diagram and be careful about the components. It
combines the best of Centripetal Motion and Inclined Planes…lots of vectors!
Normal Force as the centripetal force
Amusement Park Rides
Top view
v
Fc
r
fs
FN
Fg
m
In a ride where the rider is stuck to the wall due to
the spinning motion while the floor drops away the
Normal force provides the Centripetal Force to keep
the rider moving in circular path. Meanwhile, static
friction between the wall and the rider is the force that
balances gravity allowing the rider to “hang” on the
wall.
f s  Fg
Fc  FN
Elastic Forces and Hooke’s Law
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When a spring is
stretched or compressed
x
it exerts a restoring force.
k
m
That force depends on
the stiffness of the spring
m
and the amount of
deformation (stretch or
compression)
Hooke’s Law states:
The direction of the force
is always opposite to the
Where:
F is the restoring force,
direction of deformation.
k=spring constant (stiffness),
F  kx
x=stretch (or compression)
Spring force as centripetal force