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Newton's Laws of Motion

- By Sandrine Colson-Inam, Ph.D

- References
- Conceptual Physics, Paul G. Hewitt, 10th edition,

Addison Wesley publisher - http//www.glenbrook.k12.il.us/gbssci/Phys/Class/v

ectors/u3l2a.html

Outline

- Intro
- Newton's First Law of Motion
- Forces and Free-Body Diagrams, Net Force
- Newton's Second Law of Motion
- Newton's Third Law of Motion
- Friction

INTRODUCTION

- Newton's Laws of Motion are the most fundamental

laws that explain the physical world around us.

Newton's First Law of Motion

- An object at rest tends to stay at rest and an

object in motion tends to stay in motion with the

same speed and in the same direction unless acted

upon by an unbalanced force.

Inertia and Mass

- Inertia the resistance an object has to a change

in its state of motion. - The tendency of an object to resist changes in

its state of motion varies with mass. Mass is

that quantity which is solely dependent upon the

inertia of an object. - Inertia tendency of an object to resist changes

in its velocity. - Inertia tendency of an object to resist

accelerations.

Check your understanding

- 1. Imagine a place in the cosmos far from all

gravitational and frictional influences. Suppose

that you visit that place (just suppose) and

throw a rock. The rock will - a. gradually stop.
- b. continue in motion in the same direction at

constant speed. - 2. Ben Tooclose is being chased through the woods

by a bull moose which he was attempting to

photograph. The enormous mass of the bull moose

is extremely intimidating. Yet, if Ben makes a

zigzag pattern through the woods, he will be able

to use the large mass of the moose to his own

advantage. Explain this in terms of inertia and

Newton's first law of motion. - 3. The group of physics teachers are taking some

time off for a little putt-putt golf. The 15th

hole at the Hole-In-One Putt-Putt Golf Course has

a large metal rim which putters must use to guide

their ball towards the hole. Mr. S guides a golf

ball around the metal rim When the ball leaves

the rim, which path (1, 2, or 3) will the golf

ball follow?

Answers

- 1. According to Newton's first law, the rock will

continue in motion in the same direction at

constant speed. - 2. The large mass of the bull moose means that

the bull moose has a large inertia. Thus, Ben can

more easily change his own state of motion (make

quick changes in direction) while the moose has

extreme difficulty changing its state of motion.

Physics for better living! - 3. The answer is 2. Once leaving the rim, the

ball will follow an "inertial path" (i.e., a

straight line). At the instant shown in the

diagram, the ball is moving to the right once

leaving the rim, there is no more unbalanced

forces to change its state of motion. Paths 1 and

3 both show the ball continually changing its

direction once leaving the rim.

About 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. - A force is a vector quantity.
- Forces only exist as a result of an interaction.
- Force is a quantity which is measured using the

standard metric unit known as the Newton (N). - For simplicity sake, all forces (interactions)

between objects can be placed into two broad

categories - contact forces, and
- forces resulting from action-at-a-distance

Contact Forces

- Those types of forces which result when the two

interacting objects are perceived to be

physically contacting each other. Examples of

contact forces include frictional forces,

tensional forces, normal forces, air resistance

forces, and applied forces. - Contact Forces
- Frictional Force
- Tension Force
- Normal Force
- Air Resistance Force
- Applied Force
- Spring Force

Actions at Distance

- Those types of forces which 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 of action-at-a-distance forces include

gravitational forces. Electric forces are

action-at-a-distance forces. magnetic forces are

action-at-a-distance forces.

Balanced Forces

- The book is said to be at equilibrium.

Unbalanced Forces

- In this case, an unbalanced force acts upon the

book to change its state of motion.

Check your understanding

- Several of Luke's friends were watching the

motion of the falling cat. Being "physics types",

they began discussing the motion and made the

following comments. Indicate whether each of the

comments are correct or incorrect? Support your

answers. - a. Once the cat hits the water, the forces are

balanced and the cat will stop. - b. Upon hitting the water, the cat will

accelerate upwards because the water applies an

upward force. - c. Upon hitting the water, the cat will bounce

upwards due to the upwards force.

Answers

- a. False.
- Once the cat hits the water, the forces are

balanced (50 N down and 50 N up). However, an

object in motion (such as the cat) will continue

in motion at the same speed and in the same

direction. When the cat strikes the water, it

stops accelerating yet it does not stop moving. - b. False.
- Once the cat hit the water, the forces are

balanced (50 N down and 50 N up). The upward

force of the water on the cat is balanced by the

downward pull of gravity. The cat will continue

in motion at constant speed. - c. False.
- Once the cat hits the water, the forces are

balanced (50 N down and 50 N up). The cat would

only bounce upwards if the water applied an

upward force greater than 50 N. As stated in the

problem, the water applies only 50 N of upward

force. Furthermore, the upward force would first

contribute to slowing the cat down (an upward

acceleration) before it could begin to actually

move it upward.

Types of Forces 1/2

Types of Forces 2/2

Confusion of Mass and Weight

- Many students of physics confuse weight with

mass. - The force of gravity acting upon an object is

sometimes referred to as the weight of the

object. - The mass of an object refers to the amount of

matter that is contained by the object. - The weight of an object is the force of gravity

acting upon that object. Mass is related to how

much stuff is there and weight is related to the

pull of the Earth (or any other planet) upon that

stuff.

Weight

- Weight is the magnitude of the force of gravity

acting on an object. - Weight Fgrav
- Fgrav mass x gravity

Normal Force

- Normal Force is a force exerted by one object on

another in a direction perpendicular to the

surface of contact. - The normal force is always perpendicular to the

surface but is not always opposite the force of

gravity.

Normal Force at an angle

- On an angle, the normal force is calculated using

Fn mgcos?. - The ? is the angle of the ramp.

FRICTION

- Friction opposes the applied force.
- The force of friction is proportional to the

normal force. - It is easier to push a chair across the floor at

a constant speed than to push a heavy desk across

the floor at the same speed. - Because the desk is heavier than the chair, the

desk experiences a greater normal force and

therefore greater friction. - Two types of friction Static and Kinetic

STATIC FRICTION

- The resistive force that keeps objects from

moving is called the force of static friction. - Static Friction Fs
- As long as the object doesnt move, the static

friction is always equal to the opposite in

direction to the applied force. - Fs -Fapplied
- When the applied force is as great as it can be

without moving the object, the force of static

friction reaches its maximum value, called Fsmax

KINETIC FRICTION

- Once an object exceeds Fsmax, it begins to move.
- The resistive force that opposes the relative

motion of two contacting surfaces that are moving

is called the force of kinetic friction (Fk)?

Coefficients of Friction

- Friction depends on the surfaces in contact.
- The quantity that expresses the dependence on

frictional forces on the particular surfaces in

contact is called the coefficient of friction. - Coefficient of friction is represented by the

symbol µ and pronounces mu.

Coefficient of kinetic friction

- µk Fk/Fn
- Divide the Force of kinetic friction by the

normal force

Coefficient of static friction

- µs Fsmax / Fn
- Divide the maximum value of static friction by

the normal force

Finding Friction

- If the value of µ is known and the normal force

is known, then the magnitude of the force of

friction can be calculated. - Ff µFn
- The kinetic friction is always less than or equal

to the maximum static friction. - Think about pushing a car that is sitting still

or pushing a car that is already moving. - The coefficient of kinetic friction is always

less than or equal to the coefficient of static

friction.

Materials µs µk

Air Resistance

- Whenever an object moves through a fluid medium,

like air or water, the fluid provides a

resistance to the motion. - When an object falls through the air, its

velocity increases until the air resistance

balances the downward force of gravity. - The object falls with a constant speed, called

terminal speed.

Check Your Understanding

- A 24 Kg crate initially at rest on a horizontal

floor requires a 75 N horizontal force to set it

into motion. Find the coefficient of static

friction. - Knowns?
- m 24 kg, Fsmax 75 N
- Unknown?
- Coefficient of static friction ?
- Equations?
- µs Fsmax / Fn and Fn mg

ANSWER

- Fn 24(9.8) 235.2 N µs 75/235.2 .32

More Practice

- A student moves a box down the hall with a rope

by pulling with a force of 185 N at an angle of

25 degrees to the horizontal. The box has a mass

of 35 kg and a coefficient of kinetic friction

of .27. What is the acceleration? - On Board
- Draw it first and find the resultant force.
- Write knowns, unknowns, equations, and work it.

ANSWER

- 2.7 m/s2 in the positive x direction

Drawing Free-Body Diagrams

- 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.

Check your understanding

- A book is at rest on a table top. Diagram the

forces acting on the book. - A girl is suspended motionless from the ceiling

by two ropes. Diagram the forces acting on the

combination of girl and bar. - An egg is free-falling from a nest in a tree.

Neglect air resistance. Diagram the forces acting

on the egg as it is falling. - A flying squirrel is gliding (no wing flaps) from

a tree to the ground at constant velocity.

Consider air resistance. Diagram the forces

acting on the squirrel. - A rightward force is applied to a book in order

to move it across a desk with a rightward

acceleration. Consider frictional forces. Neglect

air resistance. Diagram the forces acting on the

book.

Answers

3

1

2

5

4

Determining the Net Force (or Unbalanced Force)?

- The unbalanced force refers to that force which

does not become completely balanced (or canceled)

by the other individual forces. If either all the

vertical forces (up and down) do not cancel each

other and/or all horizontal forces do not cancel

each other, then an unbalanced force exists. - The existence of an unbalanced force for a given

situation can be quickly realized by looking at

the free-body diagram for that situation. - Free-body diagrams for three situations are shown

below. Note that the actual magnitude of the

individual forces are indicated on the diagram.

What is the net force?

Answer

Summary for Net Force/Newton's 1st Law

- The net external force is the vector sum of all

the forces acting on an object. - A simple problem occurs when all forces act

directly along the x and y axis. You would just

add and subtract and use Pythagorean theorem. - However, most of the time, we must use vector

component method. - Newtons 1st law states one condition must be

true for equilibrium the net external force

acting on a body in equilibrium must be equal to

zero.

Newtons 2nd Law of Motion

- Force is proportional to mass and acceleration.
- Force Mass x Acceleration (Fma)?
- a (Vf Vi)/ (tf ti)?

Newtons 3rd Law of Motion

- Forces always exist in pairs.
- Every action has an equal and opposite reaction.

Check your understanding

- The net external force on the propeller of a 3.2

kg model airplane is 7 N forward. What is the

acceleration of the plane? - Knowns?
- m 3.2 kg, F 7 N
- Unknown?
- a ?
- Equation?
- Fma
- Answer?
- 7 3.2a, a 2.2 m/s2 Forward (vector need

direction)?

THE END!