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Newton’s Laws
Physics Rapid Learning Series
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Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.Keith Duda, M.Ed.
Peddi Prasad, Ph.D.Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.
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AP Physics Rapid Learning Series - 06
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Learning Objectives
Understand Newton’s three laws of motion
By completing this tutorial, you will:
three laws of motion.
Solve equilibrium problems.
Explain the role of forces like friction and air resistance.
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resistance.
Apply these laws to dynamics problems.
Concept MapPhysics
Studies
Previous content
New content
Motion
F
Caused by
Constant V l it
Slowed byFriction
May be either
Static or Kinetic
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ForcesVelocity
Adding many yields
Net Force
described by
Static Equilibrium Vectors
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Newton’s Laws
These three basic laws, formulated by Isaac Newton describe the forces acting
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Isaac Newton, describe the forces acting on objects.
Newton’s First Law
Every object continues in its state of rest, or uniform motion in a straight line,
unless it is acted upon by an outside force.
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BAM!
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Inertia
This tendency to continue in a given state,
Newton’s 1st law is often called The Law of InertiaInertia.
The more mass an object has, the more inertia it has.
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Large amount of inertia!
Small amount of inertia!
Mass vs. Weight
Mass: The amount of matter in an object. Unit: kg, g (kg is the SI unit)
fWeight: The force upon an object due to gravity.Unit: Newtons
Don’t confuse
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Don t confusemass & weight! They might be similar, but they are not the same.
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Mass Question
If you travel deep into space, does your mass change?
Your location doesn’t change th t f tt t
No!
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the amount of matter present in your body. Even if you are floating in space, you still possess the same number of atoms and molecules.
Weight Question
If you travel deep into space, does your weight change?
Yes!
In space, there may be less gravitational pull
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less gravitational pull on you. Thus your weight, a force, will be less.
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Force UnitsSome are familiar with the English unit for force the
However, the typical metric unit for force i th N tforce, the
pound, lb.is the Newton, N.
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1 N = 1 kg m/s2.On earth, 1 kg of mass would weigh 9.8 N.
Newton’s Second Law
Fnet = ma
The acceleration of an object is directly proportional to the net force and inversely
net force, N
mass, kg acceleration, m/s2
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proportional to the net force, and inversely proportional to the mass.
It may also be seen as Fnet = ΣF. This indicates that the net force is the sum of all the forces acting on an object.
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The Net ForceThe net force is simply the resultant of all the forces acting on an object.
C
B
C
D
E
FEDCBA =++++
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It can be considered the leftover, or sum of all forces.
AnetFEDCBA =++++
Paycheck AnalogyYou may work 10 hours at $10 per hour, but your pay at the end of the period is definitely not $100.
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After all taxes and deductions are accounted for, what you actually get is your net pay. This is similar to the net force.
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Second Law ObservationsA larger mass is more difficult to accelerate than a smaller one! This is common sense!
Also, a larger force accelerates a mass more than a smaller one!
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more than a smaller one!
Second Law Example
If a 10 kg block rests on a frictionless surface, how much will it accelerate if a 50 N force is applied to it?applied to it?
10 kg50 Na = ?
Fnet = ma
a = F t/ m
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a Fnet/ m
a = 50 N /10 kg
a = 5 m/s2
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Newton’s Third Law
For every force, there is an equal and opposite force.
For every action, there is an equal and opposite reaction.
Reaction Action
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ForceForce
Newton’s Third Law Example
The exhaust gases from a rocket are forcefully pushed downward out the rear of the nozzle.
An equal and opposite force is exerted upwards on the rocket itself.
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The Normal Force
The chair supports, or pushes up on you. This reaction force is called the normal force.is called the normal force.
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Your weight due to gravity pulls you down.
The Normal Force Direction
This normal force is always perpendicular to the surface.
If the surface is horizontal (flat), it is equal in magnitude to the weight of the object.
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FN
W
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Normal Force on an Incline
If there is an incline, the normal force is still perpendicular to the surface, but it isn’t equal in magnitude to the weight.magnitude to the weight.
FN
W
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W
Equilibrium
Sometimes the forces acting on an object balance out perfectly
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balance out perfectly.
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Equilibrium Definition
When all the forces on an object balance out, or cancel out, the object has a net force of 0.
2N
2
2 N 2 N Fnet = 0 N
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This condition is known as equilibrium.
N
Static Equilibrium
When an object is in equilibrium, and not moving, this is called static equilibrium.
Person hanging motionless
Tension in rope
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Weight Fnet = 0 N
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Static Equilibrium Example
Imagine a 50 N sign hanging from a cable and a lightweight rod as shown below. What (tension)/(force) is necessary in the cable to hold the sign? Neglect the weight of the rod.
Newton’s Diner 60o
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Open
Force DiagramIt is often very useful to show a diagram that describes all the forces acting in the problem.
60o
Vert
ical
co
mpo
nent
of
cab
le
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Open
Sign weight
Horizontal component of cable
Wall pushing back on rod
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Equilibrium ConditionsFor the sign to remain hanging, all the forces on it just balance.
The vertical
60o
Th h i t l
The vertical components must balance.
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OpenThe horizontal components must balance.
Fnet = 0N
Calculating Tension - 1To calculate the tension, look at the right triangle formed. We will solve for the hypotenuse which represents the cable tension.
O
60o
The vertical component of the tension must be 50 N because that is the
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Open because that is the weight of the sign.
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Calculating Tension - 2
hypadjcosθ =Hypotenuse
= tension in
60o cosθadj hyp =
cos6050N hyp =
50N
cable
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cos60
100N.5
50N hyp ==adjacent = 50 N equal to weight
of sign
Dynamic Equilibrium
An object can be moving and still be in equilibrium.
It could be moving at a constant velocity. There would be no net force or acceleration on it. This is called dynamic equilibrium.
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Applied Force Resistance ForceFnet = 0
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Friction
Since it tries to slow all motion, one of the most important forces to study is
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the most important forces to study is friction.
Direction of Friction
As previously mentioned, friction is a force that always opposes motion.
friction
Air drag and air resistance are examples of friction
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between an object and the air.
friction
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Types of Friction
There are two types of friction:
static (stationary) and kinetic (moving).
F = ma
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Static friction keeps him from sliding off the chair.
Kinetic friction slows him as he slides.
Simple Friction ExampleImagine a man is pushing a 20 kg sled along a floor at a constant velocity by applying a force of 40 N.
What is the weight of the sled?
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Fnet = ma weight = (20 kg)(9.8 m/s2) = 196N
Here we consider the pull from gravity, not the horizontal
motion due to the man’s push.
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Frictional Force on Sled
What is the force from friction on the sled?
Since it has a constant velocity, Fnet = 0. Friction must also be 40N
frictionapplied force = 40 N
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Fnet = 0 N, dynamic equilibrium
Coefficient of Friction
There is a way to mathematically describe the amount of friction between any two given surfaces.surfaces.
N
f
FFμ =
Force from friction, N
Coefficient of friction,
Greek letter
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μ (mu) is a unit-less ratio.
Normal force, N
mu
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Static and Kinetic Friction
Because the amount of friction depends on whether the object is moving or still, there are two possible µ values:two possible µ values:
μs= static coefficient of friction
μk = kinetic coefficient of friction
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The one you use depends on the situation!
Kinetic Friction Example
Previously, a man pushed a 20 kg sled at a constant velocity with a force of 40N. What is the coefficient of kinetic friction, µk in thisis the coefficient of kinetic friction, µk in this case?
N
fk F
Fμ =
)m/s(20kg)(9.840Nμ 2k =
The normal force is
equal in size
Since it moves at a constant velocity, the
frictional force t l th
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196N40Nμk =
.20μk =
)( g)(
No units for µ
equal in size to the weight
must equal the pushing force.
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Dynamics Problems
The study of the forces acting on an object is called dynamics These forces
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object is called dynamics. These forces produce motion!
Inclined Plane Example
Calculate the acceleration of this block sliding down a frictionless incline.
3 kg The weight of the object still points directly down:
F = ma
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30 o
Fnet = ma
W = (3kg) (9.8 m/s2)
W=29.4 N down
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Component Vectors on Inclined Plane
Notice how this weight vector could be broken into two components.
These two component vectors, when added tip to tail give the
3 kg
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tail, give the weight as a resultant:
W=29.4N
30 o
Perpendicular Force Component
3 kg F i th t3 kg
W=29.4N
F⊥ is the component of weight that is perpendicular to the inclined surface.
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30 o
This component is responsible for pushing the object into the surface. The reaction force to this one is the normal force, FN.
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Parallel Force Component
3 kg F⎟⎟ is the 3 kg
W=29.4N
⎟⎟component of the weight that pushes parallel to the surface.
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30 o
This component is responsible for pushing the object along the incline.
F║
Right Triangles
3 kg
W=29.4N
30 o
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F⎟⎟ , and F⊥ can be found relatively easily using simple trigonometry. The triangle they form is a right triangle. The weight is the hypotenuse.
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Similar Triangles
3 kg
W=29.4N
30 o
30o
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30 o
The angle at the top of the triangle is the same as the angle of the incline. The two form similar triangles. This concept can be used for any inclined plane.
Calculation of Parallel Force
3 kg WF
sinθ =
30o
29.4N 14 7NF
29.4NF
sin300 =
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14.7NF =
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Calculation of Acceleration
Finally, since we now have the force that is pushing the object down the incline, we can
se F mause Fnet= ma.
F║=Fnet=ma
14.7N=3kg(a)
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a=14.7N/3kg=4.9m/s2
Friction opposesFriction opposes
Newton’s 1st Law: Inertia is the property that
Newton’s 1st Law: Inertia is the property that
In either static or dynamic
ilib i
In either static or dynamic
ilib i
Learning Summary
Newton’s 3rd Law: Newton’s 3rd Law:
opposes motionμ = Ff / FN
opposes motionμ = Ff / FN
p p ymatter has to
resist changes in its motion.
p p ymatter has to
resist changes in its motion.
equilibrium, the net force
equals 0.
equilibrium, the net force
equals 0.
Newton’s 2nd Law: Newton’s 2nd Law:
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For every force there is an equal
and opposite reaction force.
For every force there is an equal
and opposite reaction force.
Fnet=maConsider all the forces acting on
an object.
Fnet=maConsider all the forces acting on
an object.
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