Stem notes topics 1 and 2

QQ

To me there has never been a higher source of earthly

honor or distinction than that connected with advances in science.

Isaac Newton

Mr. Motuk (Room 124)

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Frames of Reference You don't always need to see something

move to know that motion has taken place A reference point is needed to determine the

position of an object Ever felt like you were slowly moving

backwards when a semi truck passed you on the highway?

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Frames of Reference You have mistakenly made the truck your

frame of reference, measuring your motion relative to the truck

Both vehicles move forward relative to the stationary tree (the ground is the proper frame of reference)

Proper Frame of Reference 33

Motion- a change in position, measured by distance and time

The SI unit of length or distance is the meter (m) Shorter distances are measured in centimeters (cm) Longer distances are measured in kilometers (km)

The following quantities are used to describe motion: Speed Velocity Acceleration

Describing One-Dimensional Motion

The fastest “thing” travels at ~670,000,000 mph…

What is it?Light44

Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark Distance- quantity that tells you how far something

has moved The runner travels 50 m in the original direction

(east) plus 30 m in the opposite direction (west), so the total distance she ran is 80 m

Change in Position

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Sometimes you may want to know not only your distance but also your direction from a reference point, such as from the starting point Displacement- the distance AND direction of an

object’s position relative to a starting point Adding displacement: 50 m east, turn around and

run 30 m west = 20 m east total displacement

Change in Position

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Speed Speed- the distance traveled

by a moving object over a period of time

Kilometers/sec, miles/hour, meters/min

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Speed Formula

Example: A rifle bullet travels 1200 meters in 4 seconds.

What is the speed of the bullet?

S = D / TStep # 2 Step # 1 Step # 3

S = 1200m/4 sec.

S = 300 m/sec.

D = S X T

T = D/S

S = D/T

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Constant Speed A moving object that doesn’t change its

speed travels at constant speed Constant speed- equal distances are

covered in an equal amount of time (i.e. 25 miles/hour)

This results in a linear position vs. time graph

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Changing Speed Usually speed is not

constant Usually the speed

will change for any number of reasons (wind, stop lights, etc.)

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Instantaneous speed

Instantaneous speed- speed at any instant which the word “speed” alone is representing“My speed is 60 miles/h” is referring to your speed at that particular moment, but likely to change

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and speeds up again to 60 km/hand speeds up again to 60 km/h

Average Speed

Its average speed over the whole journey:

overall distance travelled total time of travel

slows down to 0 km/h, slows down to 0 km/h,

A car travels at 50 km/h,A car travels at 50 km/h,

=

Instantaneous speeds

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Graphing Motion On a distance (or position)-

time graph, the distance,or position, is plotted on the vertical axis and the time on the horizontal axis Each axis must have a

scale that covers the range of number to be plotted

The slope on a distance-time graph is equal to speed

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Check for Understanding

What is the difference between distance and displacement?

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__________ is the distance an object travels per unit of time.

A. acceleration

B. displacement

C. speed

D. velocity

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Check for UnderstandingName two observations you can make about

the cars speed from looking at the graph.

Calculate the speeds of both cars from the graph by choosing two points on each line.

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Calculate the average speed of the car below:

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Velocity

Velocity- a speed in a given direction It’s possible for two objects to have the

same speed, but different velocities

velocity

Has directio

n!direction

magnitude(speed)

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Earth’s speed at the equator: 1670 km/hEarth’s velocity at the equator: 1670 km/h to the

East1919

Velocity Velocity depends on direction as well as

speed, so the velocity of an object can change even if the speed of the object remains constant

The speed of this car might be constant, but its velocity is not because the direction of motion is always changing

2020

Velocity and Momentum

A moving object has a property called momentum that is related to how much force is needed to change its motion

Momentum (p) takes into consideration not only an object’s velocity AND mass

Mass- the amount of matter (atoms) in an object (kg)

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Velocity and Momentum Momentum is given the symbol p and

can be calculated with the following equation

p = mass (kg) X velocity (m/s)

The unit for momentum is kg · m/s. Notice that momentum has a direction because velocity has a direction.

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Velocity and Momentum When two objects have the same velocity, the one

with the larger mass has the larger momentum The 1,000-kg car traveling at 20 m/s east has a

momentum of 20,000 kg•m/s east. p = m X v = 1000kg X 20 m/s What about the truck?

Law of conservation of momentum- the total momentum of a system stays the same before and after an interaction

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Speed or Velocity? A race car traveling 155 miles per hour

turning left on a circular racetrack A sprinter running 3 meters/sec A tornado heading west at 15 km/hour

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Speed or Velocity? A race car traveling 155 miles per hour

V turning left on a circular racetrack A sprinter running 3 meters/sec S A tornado heading west at 15 km/hour

V

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A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum?

A. 1,500 kg•m/s

B. 150,000 kg•m/s

C. 1,400 kg•m/s

D. 1,600 kg•m/s2626


A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum?

B. 150,000 kg•m/s

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Change in Velocity Velocity rarely stays constant Acceleration is the rate of change of velocity

When the velocity of an object changes, the object is accelerating

A change in velocity can be either a change in how fast something is moving, or a change in the direction it is moving

Acceleration occurs when an object changes its speed, its direction, or both

Acceleration- the rate at which velocity changes in time (speed OR direction components)

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Change in Velocity

In a car we can change our velocity 3 ways: Speed up Slow down Change direction

All of these would be considered acceleration

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Change in Velocity

We say that this car is acceleratingbecause its velocity is increasing

We say that this car is acceleratingbecause its direction is changing as it

turns, which means its velocity is changingeven though its speed stays

constant

We say that this car is accelerating because its velocity is decreasing.

Decreasing velocity is still acceleration, although it is a negative

acceleration

30 km/h 60 km/h

60 km/h

60 km/h

60 km/h 30 km/h 0 km/h

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Change in Velocity Changing speed changes velocity

and is therefore considered acceleration Positive acceleration speeding up Negative acceleration slowing down

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Negative Negative accelerationacceleration

Positive Positive acceleratioacceleratio

nn

Velocity vs. Time GraphsThe slope of the line on a speed-time graph

equals the object’s acceleration

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Change in Velocity Is the velocity for each car constant or

changing? Which car has the highest velocity?

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Example: A cars velocity changes from 0.0m/s south to 50.0m/s south in 10.0 seconds. Calculate the cars acceleration.

Step # 2 Step # 1 Step # 3

A = 5.0 m/s/s or m/s2

T

A = Vfinal–Vinitial

OR

A = Vfinal – Vinitial

T

A = 50.0m/s – 0.0m/s

10.0s

Acceleration Formula

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Check for UnderstandingA car traveling at 60 mph accelerates to

90 mph in 3 seconds. What is thecar’s acceleration?

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Acceleration = Velocity(final) - Velocity(initial)

time

Check for UnderstandingA car traveling at 60 mph accelerates to

90 mph in 3 seconds. What is thecar’s acceleration?

=90 mph - 60 mph

3 seconds

=30 mph

3 seconds

=10 mph/second3636

PositivePositiveacceleratiaccelerati

onon

AccelerationVelocity vs. Time Graph

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Check for Understanding A car traveling at 60 mph slams on the breaks

to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks.

What is thecar’s acceleration?

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Acceleration = Velocity(final) - Velocity(initial)

time

Check for Understanding A car traveling at 60 mph slams on the breaks

to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks.

What is thecar’s acceleration?

=0 mph - 60 mph

6 seconds

=-60 mph

6 seconds

= -10 mph/second3939

Negative Negative accelerationacceleration

AccelerationVelocity vs.Time Graph

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Acceleration in 2D The speed of the horses

in this carousel is constant, but they are accelerating because their direction is changing

This would be considered centripetal accelerationacceleration of an object toward the center of a curved or circular path

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Horizontal & Vertical Motion

Are Independent

Gravity makes both bullets fall at the same rate

The bullet from the gun keeps going forward while it falls.

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Projectiles keeps moving forward with the same speed.

What if the Projectile is Thrown Upward?

Gravity

slows projectiles down

while going up

and speeds them up

while going down.

.

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Check for UnderstandingCheck for Understanding

Which is NOT a form of acceleration?

A. maintaining a constant speed and direction

B. speeding upC. slowing downD. turning

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Which is NOT a form of acceleration?

A. maintaining a constant speed and direction

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The question is… why?

Why does everything in the universe move?

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The answer…

Big, huge, massive forces!

And little ones too.

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Forces

A force is a pull (an attraction)

Or, a push (a repulsion)

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Forces

All forces have two properties: Direction Size

A newton (N) is the unit that describes the sizeof a force and is equal to 1kg X m/s2

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Changing Motion A force can cause the motion of an object to

change If you have played pool, you know that you can

force a ball at rest to roll into a pocket by striking it with another ball

The force of the moving ball causes the ball at rest to move in the direction of the force

Force does not always change motion, though

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When all the forces acting on an object are considered together, you determine the net force on the object

An object with a net force of anything other than 0 N on it will change its state of motion

Net Force

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Forces in the Same Direction

When forces are applied in the same direction, they are added to determine the size of the net force

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When two forces act in opposite directions, you subtract the smaller force from the larger force to determine the net force

The net force will be in the same direction as the larger force

Forces in Different Directions

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Balanced forces cancel each other out!They are forces that are equal in size and opposite in direction

Balanced Forces

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Types of Forces

1. Friction2. Gravity3. Electromagnetic4. Nuclear 5. Etc.

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1. Friction Friction- the force that opposes

the sliding motion of two surfaces that are touching each other i.e. skateboard stops rolling It always slows a moving object

down The amount of friction between two

surfaces depends on two factorsthe kinds of surfaces and the force pressing the surfaces together.

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1. Friction

Force on person by box

Force on floor by boxForce on box by floor

Force on box by person

Corrugations and imperfections in the surfaces grind when things slide.

How can we reduce friction?5858

Cause of Friction

•The larger the force pushing the two surfaces together is, the stronger these microwelds will be, because more of the surface bumps will come into contact

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Types of Friction Static-prevents two surfaces from sliding

past each other at all (move a box of books) Sliding- opposes sliding motion (box of

books that is sliding stops moving) Rolling- acts over the area where the wheel

and surface meet like traction (skateboard with box of books on it stops moving)

Fluid (Viscous)- opposes the motion of objects traveling through a fluid (air or water)

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2. Gravity Galileo-1600’s studied how things fell Gravity is an attractive force

between any two objects that depends on the masses of the objects and the distance between them

Isaac Newton formulated the law of universal gravitation, which he published in 1687

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Law of Universal Gravitation

This law can be written as the following equation

F is the force of gravity, G is a constant called the universal gravitational constant, and d is the distance between the two masses, m1 and m2

The greater the mass of two objects, the greater the gravitational force (F) between them

The greater the distance between two objects, the less the gravitation force between them

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Gravitational Force

No matter how far apart two objects are, the gravitational force between them never completely goes to zero Because of this gravity is called a long-range

force The strength of the gravitational field is 9.8

N/kg near Earth’s surface and gets smaller as you move away from Earth

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Weight Because the weight of an object on Earth is equal to

the force of Earth’s gravity on the object, weight can be calculated from this equation:

Where Fg is the force of gravity on an object…..in other words, its weight…and g is 9.8 N/kg near Earth’s surface (9.8N/kg = 9.8 m/s2)

or (m/s2)

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Mass

Weight and mass are not the same Weight is a force and mass is a measure

of the amount of matter an object contains

Weight and mass are related. Weight increases as mass increases

or (m/s2)

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The amount of matter (atoms) in an object

A measure of gravity’s pull on an object

Measure with a balance

Measure with a Newton scale

Never changesChanges due to

gravity

Both are measure-ments

of matter

Mass vs. Weight

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• What is the weight of a 10-kg block?

9.8 N/kg

Fg

m10 kg

Fg = mg = (10 kg)(9.8 N/kg)

Fg = 98 NFg = 98 N

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Newton’s Laws of Motion

Newton lived from 1642–1727 #1 An object in motion stays in motion

and an object at rest stays at rest unless acted upon by an unbalanced force

#2 Force equals mass times acceleration (F = ma)

#3 For every action there is an equal and opposite reaction

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Newton’s First Law

An object in motion

stays in motion and an object at rest stays at rest unless acted upon by an unbalanced force

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Newton’s First Law

What does this mean? AAn object will keep doing what it’s doing

UNLESS acted on by an unbalanced force like friction If it is moving at a constant velocity it will

continue If it is at rest, it stays at rest

In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain speed and direction would keep going in that same direction and same speed forever

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Newton’s First Law Called the Law of Inertia- the tendency of

an object to resist changes in its state of motion Recall that mass is the amount of matter

(atoms) in an object Newton’s First Law states that all objects have

inertia The more mass an object has, the more inertia

it has (and the harder it is to change its motion)

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Then why don’t moving objects keep moving forever?

Things don’t keep moving forever because there’s almost always an unbalanced force

acting upon it

A book sliding across a table slows down and stops because of the force of friction

If you throw a ball upwards it will eventually slow down and fall because of the force of gravity 7272

Newton’s Second Law

Force equals mass times acceleration

F = ma

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Newton’s Second Law What Does F = ma Mean?

The force of an object comes from its mass and its acceleration so that the acceleration of an object is in the same direction as the net force on the object

A massive glacier that’s changing speed very slowly (low acceleration) can still have great force due to its mass

Something very small (low mass)like a bullet that’s changing speed very quickly (high acceleration) can still have a great force

7474

Force = Mass X Acceleration

Force is directly proportional to mass and acceleration First ball: has a certain mass, m,

moving at a certain acceleration, a, and therefore a certain force, f.

Second ball: has double the mass of the first ball, 2m, and the same acceleration, a, therefore has twice the force of the first ball, 2f

Third ball: has mass m moving at twice the first ball’s acceleration, 2a, would have a force of 2f.

a

a

a

m

m

m

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Newton’s Third Law

For every action there is an equal and opposite reaction

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Newton’s Third Law What Does this Mean?

When one object exerts a force on a second object, the second one exerts a force on the first that is equal in strength and opposite in direction

Gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force

There are balanced forces acting on you– gravity pulling down and your seat pushing up- so you are not moving

gravity

your seat7777

Newton’s Third Law

The action force is exerted by the _____ on the _____.

The reaction force is exerted by the _____ on the _____.

barbar

handhandss

barbar

handhandss

Action

Reaction

For every action force, there must be an equal and opposite reaction force

Forces occur in pairs

For every action force, there must be an equal and opposite reaction force

Forces occur in pairs

Newton’s Laws on teachersdomain7878


One newton is a force which imparts an acceleration of 1 m/s2 to a mass of 1 kg.

F (N) = m (kg) a (m/s2)F (N) = m (kg) a (m/s2)

What resultant force will give a 3 kg mass an acceleration of 4 m/s2?

F = 12 NF = 12 N

F = m aF = ?

a = 4 m/s2

3 kg F = 3 kg X 4 m/s2

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Inertia is__________. A. the tendency of an object to

resist any change in its motion B. the tendency of an object to

have a positive acceleration C. The tendency of an object to

have a net force of zero. D. The tendency of an object to

change in speed or direction.

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Inertia is__________. A. the tendency of an object to

resist any change in its motion

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Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object. A. acceleration B. momentum C. speed D. velocity

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Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object. A. acceleration

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Newton’s Law Applied to Life

Newton’s 3 laws can be used to explain everyday events, such as falling, and collision

These laws have been applied to aid in technology, safety, and countless other ways

Newton’s Laws on Science360

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Newton’s First Law with Seat Belts

Don’t let this be you

Due to inertia, objects (including you) resist changes in their motion. When you and the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 km/hour

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Newton’s First Law with Air Bags

Air bags also reduce injuries in car crashes by providing a cushion that reduces the force on the car's occupants

When impact occurs, a chemical reaction occurs in the air bag that produces nitrogen gas

The air bag expands rapidly and then deflates just as quickly as the nitrogen gas escapes out of tiny holes in the bag

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Newton’s First Law and Centripetal Force

According to Newton, as a car tries to make a

turn, the car would continue in a straight line unless there was a force acting on the car to turn it

This force of friction acting upon the turned wheels provides centripetal force required for circular motion

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Without a centripetal force, an object in

motion continues along a straight-line path

With a centripetal force, an object in motion will

be accelerated and change its direction

Centripetal Force

Inertia

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As a bucket of water is spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion

The force of gravity acting upon the moon provides the centripetal force required for orbit

Nascar and Centripetal Force

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Newton’s Second Law and Gravitational

Acceleration If gravity is the only force being exerted on an object’s mass then the net force is Fg

****Combining the above gravitational law with Newton’s second law, F=ma, the force due to gravity only would cause an object to accelerate at 9.8 m/s/s (m/s2)

Papers falling demo 9090

Acceleration Due to Gravity

Gravity causes objects to accelerate at the SAME rate, 9.8 m/s/s (~10 m/s/s)

WITHOUT air resistance, a friction-like force, all objects would fall at the same speed

Galileo on the moon Doesn’t depend on mass After 1 second falling at ~10

m/s After 2 seconds ~20 m/s 3 seconds ~30 m/s 9191

Terminal Velocity Air resistance (fluid

friction) will increase as object falls faster causing an upward force on the object Eventually gravity will

balance with air resistance

Reaches terminal velocity - highest speed reached by a falling object

Terminal velocity

No air resistance Air resistance which is greater on the feather

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Summary of Formulas Speed = distance traveled (m)

time (s) Velocity = displacement (distance with direction) (m)

time (s) Momentum (p) = velocity (m/s) X mass (kg)

Acceleration = change in velocity (m/s) or m/s2

time (s) Force of gravity (weight in N) = mass (kg) X gravitational

strength 9.8 (N/kg) Force = mass X acceleration (9.8 m/s2 if due to

gravity)9494

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Date post:	17-Jan-2015
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Stem notes topics 1 and 2

Education