Newton’s First Law€“ a measure of the gravitational force acting on the object a. One Kilogram...

Newton’s First Law

of Motion-Inertia

I. Aristotle on Motion

A. Aristotle (4th century BC– first to suggest

force causes motion.

1. Divided motion into two types

a. Natural Motion– said to

be either straight up or down.

Objects would seek their

natural resting place (boulder

fall to ground, smoke rise)

b. Violent Motion -was “imposed” motion. Result of

forces that pushed or pulled. (this motion had an

external force) 2. Objects in natural resting

places could not move by

themselves. (had to be pushed

or pulled)

B. Before 16th century though Earth must be in its

natural resting place (a force large enough to move it

was unthinkable)

http://upload.wikimedia.org/wikipedia/commons/d/d4/Cellarius_ptolemaic_system_c2.jpg

II. Copernicus and the Moving Earth

A. Nicolaus Copernicus (1473-1543)- said

Earth and other planets move around sun.

1. Worked on his idea in secret to

escape persecution

2. Wrote book De Revolutionaibus about his work

(reached him on the day of his death)

III. Galileo on Motion

A. Foremost scientist of the late-Renaissance

Italy

1. supported Copernicus–

heliocentric theory (planets rotate

around sun)

2. Resulted in house arrest for his

thinking

B. Said force was not necessary to keep an object

moving

1. Force– is any push or pull

Contact vs. Long Range Force

Contact Force- acts on an object by

touching it.

Long-range Force- is

exerted without contact (e.g.

magnetic forces, gravity

Which kind of force is

acting here?

2. Friction– name given to the force that acts

between materials that touch as they move past

each other

Galileo on Motion

• Galileo stated that if friction were entirely

absent, a ball moving horizontally would

move forever.

• No push or pull would be required to

keep it moving once it is set in motion.

Galileo tested his idea by rolling balls along

plane surfaces tilted at different angles.

• A ball rolling down an inclined plane

speeds up.

• A ball rolling up an inclined plane—in a

direction opposed by gravity—slows

down.

• A ball rolling on a smooth horizontal

plane has almost constant velocity.

Galileo on Motion

• Downward, the ball moves with Earth’s

gravity.


gravity.

• Upward, the ball moves against gravity.


gravity.

• Upward, the ball moves against gravity.

• On a level plane, it does not move with or

against gravity.

•Galileo stated that if friction were entirely

absent, a ball moving horizontally would

move forever.

•No push or pull would be required to keep it

moving once it is set in motion.

Galileo on Motion

• The ball rolling down the incline rolls up the

opposite incline and reaches its initial height.



• The ball rolls a greater distance to reach its

initial height.



• The ball rolls a greater distance to reach its

initial height.

• If there is no friction, the ball will never stop.

3. Galileo argued that only when friction is present–

as it usually is– a force needed to keep an object

moving.

4. He stated– every material object resists

change to its state of motion– called ineretia

5. Led the way for Isaac Newton

IV. Newton’s Law of Inertia

A. Isaac Newton (1642-1727)- born same

year that Galileo died

B. Developed famous laws of motion (replaced

Aristotelian ideas that dominated for previous

2000 years)

1. Newton’s First Law of Motion– usually referred

to as the law of inertia

Every object continues in a state of rest, or of

motion in a straight line at constant speed,

unless it is compelled to change that state by

forces exerted upon it.

a. Restatement of Galileo’s ideas

b. Simply put– things tend to keep doing what

they're already doing

V. Mass-A Measure of Inertia

A. Mass is Not Volume– entirely different

concepts

1. Volume-a measure of space (units

like cubic meters, liters, etc.)

2. Mass -measured in kilograms

Which has a larger mass, the pillow or the

battery? A larger volume?

B. Mass is Not Weight

1. Often confused with weight

2. Mass– measurement of amount of material

in an object and depends on number of and

kind of atoms that compose it

3. Weight– a measure of the gravitational

force acting on the object

a. One Kilogram Weighs 9.8

Newtons

1). Newton (N)-SI unit of mass

Which would be harder

to shake? A stone in its

weightless state in

space or in its weighted

state on Earth?

Mass—A Measure of Inertia

2). Weight = Mass x acceleration of gravity

mgWeight

mgFg

1. Two thousand years ago, people thought that Earth did not

move. One major reason for thinking this was that

a. no force was large enough to move the Earth.

b. Earth’s motion would be unnatural.

c. Earth was near the center of the universe.

d. Earth moved in a perfect circle.

Assessment Questions

1. Two thousand years ago, people thought that Earth did not

move. One major reason for thinking this was that

a. no force was large enough to move the Earth.

b. Earth’s motion would be unnatural.

c. Earth was near the center of the universe.

d. Earth moved in a perfect circle.

Answer: A


2. According to Aristotle and his followers over centuries, Earth was at

the center of the universe. The first European to effectively challenge

that notion was

a. Copernicus.

b. Galileo.

c. Newton.

d. Einstein.


2. According to Aristotle and his followers over centuries, Earth was at

the center of the universe. The first European to effectively challenge

that notion was

a. Copernicus.

b. Galileo.

c. Newton.

d. Einstein.

Answer: A


3. Galileo’s conclusions about motion helped advance science because

they were based on

a. experiments rather than philosophical discussions.

b. philosophical discussions rather than experiments.

c. nonmathematical thinking.

d. Aristotle’s theories of motion.


3. Galileo’s conclusions about motion helped advance science because

they were based on

a. experiments rather than philosophical discussions.

b. philosophical discussions rather than experiments.

c. nonmathematical thinking.

d. Aristotle’s theories of motion.

Answer: A


4. If gravity between the sun and Earth suddenly vanished, Earth would

continue moving in a(n)

a. curved path.

b. straight-line path.

c. outward spiral path.

d. inward spiral path.


4. If gravity between the sun and Earth suddenly vanished, Earth would

continue moving in a(n)

a. curved path.

b. straight-line path.

c. outward spiral path.

d. inward spiral path.

Answer: B


5. To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter

a. will weigh 10 N everywhere.

b. has ten times less volume than 10 kg of matter.

c. has ten times more inertia than 10 kg of matter.

d. is attracted to Earth with 10 N of force.


5. To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter

a. will weigh 10 N everywhere.

b. has ten times less volume than 10 kg of matter.

c. has ten times more inertia than 10 kg of matter.

d. is attracted to Earth with 10 N of force.

Answer: D


6. The Earth moves about 30 km/s relative to the sun. But when you

jump upward in front of a wall, the wall doesn’t slam into you at 30

km/s. A good explanation for why it doesn’t is that

a. the sun’s influence on you is negligible.

b. the air in the room is also moving.

c. both you and the wall are moving at the same speed, before,

during, and after your jump.

d. the inertia of you and the wall is negligible compared with that of

the sun.


6. The Earth moves about 30 km/s relative to the sun. But when you

jump upward in front of a wall, the wall doesn’t slam into you at 30

km/s. A good explanation for why it doesn’t is that

a. the sun’s influence on you is negligible.

b. the air in the room is also moving.

c. both you and the wall are moving at the same speed, before,

during, and after your jump.

d. the inertia of you and the wall is negligible compared with that of

the sun.

Answer: C


Unit 1

Chapter 5: Newton’s Second

Law of Motion-Force and

Acceleration

An object accelerates when

a net force acts on it.

I. Force Causes Acceleration

A. Force causes acceleration

1. Acceleration depends on net force

2. Objects acceleration is directly

proportional to the net force acting on it.

acceleration α net force

(the symbol α stands for “is directly proportional to.”)

II. Mass Resists Acceleration

A. Acceleration depends on mass

1. acceleration produced is inversely

proportional to the mass.

2. Inversely– means that the two values

change in opposite directions

massonaccelerati

1

III. Newton’s Second Law

A. Newton’s Second Law states:

The acceleration produced by a net force on an

object is directly proportional to the magnitude of

the net force, is in the same direction as the net

force, and is inversely proportional to the mass of

the object

In equation form:

acceleration α mass

net force

1.Using units of newtons (N) for force, kilograms

for mass (kg), and meters per second squared

(m/s2) for acceleration, we get the new equation

2. If we let a = acceleration, F = force, and m =

mass:

acceleration = mass

net force

m

Fa

think!

If a car can accelerate at 2 m/s2, what acceleration can it

attain if it is towing another car of equal mass?

Newton’s Second Law

think!

If a car can accelerate at 2 m/s2, what acceleration can it

attain if it is towing another car of equal mass?

Answer: The same force on twice the mass produces half

the acceleration, or 1 m/s2.


do the math!

A car has a mass of 1000 kg. What is the acceleration

produced by a force of 2000 N?


do the math!

A car has a mass of 1000 kg. What is the acceleration

produced by a force of 2000 N?

5.3 Newton’s Second Law

do the math!

If the force is 4000 N, what is the acceleration?

5.3 Newton’s Second Law

do the math!

If the force is 4000 N, what is the acceleration?

Doubling the force on the same mass simply doubles the

acceleration.


do the math!

How much force, or thrust, must a 30,000-kg

jet plane develop to achieve an acceleration of

1.5 m/s2?


do the math!

How much force, or thrust, must a 30,000-

kg jet plane develop to achieve an

acceleration of 1.5 m/s2?

Arrange Newton’s second law to read:

force = mass × acceleration

F = ma

= (30,000 kg)(1.5 m/s2)

= 45,000 kg•m/s2

= 45,000 N


IV. Friction

A. Friction is a force

1. Acts on materials that are in contact

with each other

2. friction acts in opposite direction to

oppose motion

3. friction mainly due to irregularities in the

two surfaces.

B. Friction not restricted to solids sliding over one

another

1. Occurs in liquids and gases

a. both called fluids

b. Friction of liquids appreciable even at

low speeds.

2.Air resistance (friction acting on something

moving through air) is common form of fluid friction

3. When friction is present, an object may move

with a constant velocity even when outside force is

applied to it.

a. In such case, friction force balances applied

force

b. Can diagram using a free-body diagram

think!

Two forces act on a book resting on a

table: its weight and the support force

from the table. Does a force of friction

act as well?

Friction

think!

Two forces act on a book resting on a table:

its weight and the support force from the

table. Does a force of friction act as well?

Answer: No, not unless the book tends to

slide or does slide across the table. Friction

forces occur only when an object tends to

slide or is sliding.

Friction

V. Applying force– Pressure

A. Pressure– amount of force per unit area

B. In equation form:

(Pressure is measured in Newton’s per square

meter, or pascals)

A

FP

pressure = area of application

force

think!

In attempting to do the bed-of-nails

demonstration, would it be wise to begin

with a few nails and work upward to

more nails?

Applying Force-Pressure

think!

In attempting to do the bed-of-nails demonstration, would it

be wise to begin with a few nails and work upward to more

nails?

Answer: No, no, no! There would be one

less physics teacher if the

demonstration were performed with

fewer nails. The resulting greater

pressure would cause harm.

Applying Force-Pressure

VI. Free Fall Explained

A. Galileo showed falling objects accelerate

equally, regardless of their masses

1. strictly true if air resistance is negligible

2. approximately true when air resistance

is very small

B. Aristotle believed that an

object weighing tens times

as much would fall ten times

faster (disproved by Galileo

and others

Galileo’s famous

demonstration at Leaning

Tower of Pisa)

C. Use equation for weight (force of gravity):

or

Rearrange and get

(when mass is also

considered, the acceleration

of any object is the same)

mgFg maFg

m

Fa

g

VII. Falling and Air Resistance

A. Air resistance decreases the net forces

acting on a falling object

1. When air resistance equals downward

force on falling object (force of gravity–

also called weight) then net force is zero

and no further acceleration occurs.

2. terminal speed– when acceleration terminates

3. When consider direction (which is down for falling

objects) we call this maximum speed terminal

velocity

Fg

Fdrag

B. Air resistance is often negligible at low speeds, but

very noticeable at high speeds

think!

Which experiences a greater air

resistance force, a falling piece of paper

or a falling elephant?

Falling and Air Resistance

think!

Which experiences a greater air resistance force, a falling

piece of paper or a falling elephant?

Answer: The elephant! It has a greater frontal

area and falls faster than a piece of paper—

both of which mean the elephant pushes

more air molecules out of the way. The effect

of the air resistance force on each, however,

is another story!


think!

If a heavy person and a light person

open their parachutes together at the

same altitude and each wears the same

size parachute, who will reach the

ground first?


think!

If a heavy person and a light person open their parachutes

together at the same altitude and each wears the same size

parachute, who will reach the ground first?

Answer: The heavy person will reach

the ground first. Like a feather, the light

person reaches terminal speed sooner,

while the heavy person continues to

accelerate until a greater terminal speed

is reached.


1. An object will accelerate when

a. SF = 0.

b. it is unbalanced.

c. it is pushed or pulled with a net

force.

d. its mass increases.


1. An object will accelerate when a. SF = 0.

b. it is unbalanced.

c. it is pushed or pulled with a net force. d. its mass increases.

Answer: C


2. When a net force acts on an object, its

acceleration depends on the object’s

a. initial speed.

b. mass.

c. volume.

d. weight.


2. When a net force acts on an object, its

acceleration depends on the object’s a. initial speed.

b. mass. c. volume.

d. weight.

Answer: B


3. A cart is pushed and undergoes a certain

acceleration. Consider how the acceleration

would compare if it were pushed with twice

the net force while its mass increased by

four. Then its acceleration would be

a. one quarter.

b. half.

c. twice.

d. the same.


3. A cart is pushed and undergoes a certain

acceleration. Consider how the acceleration

would compare if it were pushed with twice

the net force while its mass increased by

four. Then its acceleration would be a. one quarter.

b. half. c. twice.

d. the same.

Answer: B


4. Friction is a force like any other force and

affects motion. Friction occurs in

a. solids sliding over one another.

b. fluids.

c. air.

d. all of these


4. Friction is a force like any other force and

affects motion. Friction occurs in a. solids sliding over one another.

b. fluids.

c. air.

d. all of these

Answer: D


5. When you stand on one foot instead of

two, the pressure you exert on the ground

is

a. half.

b. the same.

c. twice.

d. quadruple.


5. When you stand on one foot instead of

two, the pressure you exert on the ground

is a. half.

b. the same.

c. twice.

d. quadruple.

Answer: C


6. The reason a 20-kg rock falls no faster than

a 10-kg rock in free fall is that

a. air resistance is negligible.

b. the force of gravity on both is the same.

c. their speeds are the same.

d. the force/mass ratio is the same.


6. The reason a 20-kg rock falls no faster than

a 10-kg rock in free fall is that

a. air resistance is negligible.

b. the force of gravity on both is the same.

c. their speeds are the same.

d. the force/mass ratio is the same.

Answer: D


7. Kevin and Suzanne go sky diving. Kevin is

heavier than Suzanne, but both use the

same size parachute. Kevin has a greater

terminal speed compared with Suzanne

because

a. he has to fall faster for air resistance to

match his weight.

b. gravity acts on him more.

c. he has greater air resistance.

d. he has weaker terminal velocity.


7. Kevin and Suzanne go sky diving. Kevin is

heavier than Suzanne, but both use the

same size parachute. Kevin has a greater

terminal speed compared with Suzanne

because

a. he has to fall faster for air resistance to

match his weight. b. gravity acts on him more.

c. he has greater air resistance.

d. he has weaker terminal velocity.

Answer: A


Chapter 5: Newton’s 2nd Law

So, do you think you’ve got it?

Newton's Second Law

• The acceleration of an object is equal

to the force you apply divided by the

mass of the object.

Newton's Second Law

• If you apply

more force

to an

object, it

accelerates

at a higher

rate.

Newton's Second Law

• If an object

has more

mass it

accelerates

at a lower

rate

because

mass has

inertia.

Newton's Second Law

a = F

m

Force (newtons, N)

Mass (kg)

Acceleration (m/sec2)

Newton's Second Law

Three forms of the second law:

Calculate acceleration

• A cart rolls down a

ramp.

• The cart has a mass of

500 grams (0.5 kg).

• Using a spring scale,

you measure a net

force of 2 newtons

pulling the car down.

• Calculate the

acceleration of the

cart.

Calculate acceleration

• Three people are pulling on a wagon applying forces

of 100 N,150 N, and 200 N.

• The wagon has a mass of 25 kilograms.

• Determine the acceleration and the direction the

wagon moves.

Calculate force

• An airplane needs to

accelerate at 5 m/sec2 to

reach take-off speed before

reaching the end of the

runway.

• The mass of the airplane is

5,000 kilograms.

• How much force is needed

from the engine?

Calculate force

• A tennis ball contacts the racquet

for much less than one second.

• High-speed photographs show that

the speed of the ball changes from -

30 to +30 m/sec in 0.006 seconds.

• If the mass of the ball is 0.2 kg, how

much force is applied by the

racquet?

Equilibrium

• The condition of zero acceleration is

called equilibrium.

• In equilibrium, all forces cancel out

leaving zero net force.

• Objects that are standing still are in

equilibrium because their acceleration is

zero.

• Objects that are moving at constant

speed and direction are also in

equilibrium.

• A static problem usually means there is

no motion.

Equilibrium Rule

For any object or system of

objects in equilibrium the sum

of the forces acting equals zero

ΣF = 0

Tension force acts upwards

Weight acts downwards

Calculate force

• A woman is holding

two dogs on a leash.

• If each dog pulls with

a force of 80 newtons,

how much force does

the woman have to

exert to keep the dogs

from moving?

The Second Law:

Force, Mass, and Acceleration

Key Question:

• What is the relationship between force,

mass, and acceleration?

How about an easy one…

A single force of 40 N acts upon a 5-kg

block. What is the magnitude of the

acceleration of the block?

(Don’t forget the units!)

F = ma, so a = F/m

= (40 N)/(5 kg) = 8 (kg m/s2)/kg = 8 m/s2

Consider this…

After returning home from the beach, Samantha

hangs her wet 0.20-kg bathing suit in the

center of the 6.0-m-long clothesline to dry.

This causes the clothesline to sag 4.0 cm. What

is the tension in the clothesline?

Solution First, convert cm to m. 4.0 cm = 0.040 m

Because the bathing suit is hung in the center of the clothesline, the tension in each side of the line is the same. You must find the downward force on the clothesline, which is simply the weight of the bathing suit.

Given: m = 0.20 kg Unknown: w = ?

g = 10.0 m/s/s Original equation: w=mg

Solve: w = mg = (0.20kg)(10.0m/s/s) = 2.0 N

Consider this…

Butch, the 72.0-kg star quarterback of

Belmont High School’s football team,

collides with Joe, a stationary left tackle,

and is brought to a stop with an

acceleration of -20.0 m/s/s. (a) what

force does Joe exert on Butch? (b) what

force does Butch exert of Joe?

Solution (a) The force depends upon the rate at which Butch’s

mass is brought to rest.

Given: m = 72.0 kg Unknown: F = ?

g = -20.0 m/s/s Original equation: F =ma

Solve: F = ma = (72.0 kg)(-20.0 m/s/s) = -1440 N

The – sign in the answer implies that the direction of

the force is opposite that of Butch’s original

direction of motion.

(b) Newton’s 3rd law states that for every action there

is an equal and opposite reaction. Therefore, if Joe

exerts a force of -1440 N on Butch, Butch will exert

the same 1440 N force back on Joe, but in the

opposite direction.

Try this one…

A 30.0-g arrow is shot by William Tell

through an 8.00-cm thick apple sitting on

top of his son’s head. If the arrow enters

the apple at 30.0 m/s and emerges at 25.0

m/s in the same direction, with what force

has the apple resisted the apple?

Solution: First, convert g to kg and cm to m.

30.0 g = 0.0300 kg 8.00 cm = 0.0800 m

Next, find the acceleration of the arrow before finding the force.

Given: Vo = 30.0 m/s Unknown: a = ?

Vf = 25.0 m/s Original equation:

Solve: (25.0 m/s/s) – (30.0 m/s/s) = 625 m^/s^ - 900 m^/s^

2(0.0800 m) 0.160 m

= -1720 m/s^

The – sign before the answer implies that the apple was causing the arrow to slow down.

Now solve for the force exerted by the apple.

Given: m = 0.0300 kg Unknown: F = ?

a = -1720 m/s^ Original formula: F = ma

Solve: F = ma = (0.0300 kg) (-1720 m/s^)

= -51.6 N

This is the force that the apple exerts on the arrow. It

is negative direction is opposite of the arrow’s

direction of motion.

Chapter 6: Newton’s Third Law or Motion

Action and Reaction

I. Forces and Interactions (6.1)

A. Force is part of a mutual action– an

interaction

1. Acts between one thing and another

2. Each exert a force on the other object

B. Always a pair of forces– led Newton to his third

law (law of action and reaction)

II. Newton’s Third Law (6.2)

A. Third law states:

Whenever one object exerts a force on a second

object, the second object exerts an equal and

opposite force on the first object

1. One force called action force and the other is

called the reaction force

a. It doesn’t matter which we call action or

reaction force

b. They are “partners” in single interaction

c. Neither force exist without the other

d. They are equal in strength and opposite in

direction

(“To every action there is always an equal opposing

reaction”)

B. Without the action force there cannot be

reaction force

1. Thus no resulting forward motion

2. Forces include contact and long-range

forces

III. Identifying Action and Reaction (6.3)

A. Identifying action and reaction pair

1. Can be difficult to identify sometimes

a. Start by identifying the interaction (e.g. Object A

interacts with object B)

1). Action: Object A exerts a force on

object B

2). Reaction: Object B exerts a force on

object A

IV. Action and Reaction on Different Masses (6.4)

A. Interaction between falling boulder and the

Earth

1. Forces are equal in strength and

opposite in direction

a. Boulder falls to Earth

b. Earth falls to boulder

2. Forces between Earth and boulder are equal, but

masses not

a. Newton’s second law states that

acceleration is not only proportional to net

force, but also inversely proportional to

mass.

b. Earth’s large mass– infinitesimally small

acceleration

B. Cannon example

1. Interaction between cannon and

cannon ball is exactly equal in magnitude

and opposite in direction

2. Must consider Newton’s Second law

m

Fa

a. Cannonball

b. Cannon

F

m = a

F

m = a

F

m = a

F = a

m

Fcannonball = Fcannon

V. Defining Systems (6.5)

A. If action and reaction forces are internal to

a system, they cancel each other and

produce no acceleration of the system

B. Action and reaction

forces do not cancel each

other when either is

external to the system

being considered.

VI. The Horse-Cart Problem (6.6)

A. Can look at from three points of view

1. Cart system (net force exerted on cart divided by

mass of cart = acceleration

2. Horse system (horse moves forward by interaction

with the ground– horse pushes backwards on the

ground and the ground pushes forward on the

horse

3. Horse-cart system (when consider only internal

forces , forces that act and react within the

system, they cancel. There must be interaction

with ground to produce acceleration)

Acceleration of horse-cart system due

to net force of F - f

B. Stalled car example– you cannot move car

forward by sitting in car and pushing on the

dashboard. Must interact with the ground-

make ground push car.

VII. Action Equals Reaction (6.7)– for every

interaction between things, there is always a pair

of oppositely directed forces that are equal in

strength.

Newton’s First Law€“ a measure of the gravitational force acting on the object a. One Kilogram...

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