Newton's Laws

AP Physics Rapid Learning Series - 06

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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.



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



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!



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.



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.



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.



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.



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



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



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.



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



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



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.



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



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



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.



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



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.



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



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.



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.



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 =



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.



Congratulations

You have successfully completed the core tutorial

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