MECHANICS

Motion

Chapter 1 Notes

What is a RATE?

A rate tells how fast something happens.

Some rates that we will use to describe motion are:• Speed

• Velocity

• Acceleration

What is Motion???

A change in position.

What is speed?

Rate of Change in Position. “Rate of Motion” Types of Speed

• Instantaneous

• Constant

• Average

Speed Formula

speed = the change in distance

the change in time

v = ∆ d

∆ t

∆ is the Greek letter DELTA. In science this means CHANGE.

Speed Units

m/s km/s m/h km/h

When you read the first unit, you say meters “PER” second.

Do not write mps

Instantaneous Speed

The rate of motion at a given instant.

A speedometer in a car shows the instantaneous speed of the car.

Average Speed

On a trip from Chicago to Texas could you stay the same speed?

You could get an average of all the speeds during the trip.

How do we calculate average speed?

The total distance of the trip divided by the total time of travel.

Constant Speed

A speed that does not change over a period of time.

Cruise Control in a car.

Any questions about the Section Review Questions?

Page 14

Speed is Relative!

What does it mean when we say that a car moves at a rate of 80 km/h?

What do we mean that it is relative to?

Unless the problem says something else, the motion that we discuss is ALWAYS relative to Earth.

Everything is in constant motion

Do you agree?

Galileo

Why did he have such difficulty spreading his findings?

Velocity

Notes 1.2

What is Velocity?

Describes the motion and the direction.

Even if speed remains the same, if the direction changes then the velocity has changed.

Any questions about the Section Review Questions?

Page 16

VELOCITY VECTORS

VECTOR: An arrow drawn to scale that represents the magnitude and direction of a given velocity.

10m/s left 5m/s rt

RESULTANT: The single vector that results when two vectors are combined.

10m/s left

5m/s rt 5m/s left

Turn to the question on Page 17:

A motor boat is moving 10 km/h relative to the water. If the boat travels in a river that flows at 10km/h, what is the velocity relative to the shore when it heads directly up stream?

When it heads directly downstream?

Now, let’s Check Your Understanding!

Calculating Average Speed / Velocity

d= distance v= speed / velocity t= time

Follow the steps to solve an equation.

Problem: You walk 5 meters in 3 seconds. What is your velocity? Step 1: Write what you know.

d = 5 meters

t = 3 seconds

v = ? Step 2: Write the formula you will use. v = d / t Step 3: Put the numbers in for the variables that you know.

v = 5 meters

3 seconds Step 4: Do the math.

v = 1.6667meters/seconds = 1.7m/s

Your velocity is 1.7 meters per second.

Equations for Speed and Velocity

v = d / t d = v t t = d / v

Sample Speed / Velocity Problems

A car travels a distance of 16 m in 1.8 seconds. What is it’s speed?

d = 16 m t = 1.8 s v = ? v = d/t

v = 16m / 1.8s

v = 8.89 m/s

Sample Speed / Velocity Problems Sound travels at a speed of 330 m/s. If a lightning bolt

strikes the ground 1 km away from you, how long will it take for the sound to reach you?

v = 330m/s d = 1km t = ? t = d/v

t = 1km / 330m/s

t = 1000m / 330m/s

t = 3.03 s

Your Turn!

Complete the worksheet.

Acceleration

Section 1.3

What is Acceleration?

The rate of change of velocity. Car commercial 0 to 60 mph in 10

seconds. Speeding up The amount of change of velocity in a

time interval.

How do you measure a change?

The water was at 50m and it rose to 100m. What is the change?

We started at 9:00am and the class was over at 11:00am. What is the change?

The dog grew from 8 lbs to 15 lbs. What is the change?

We had 20 gallons, and now we have 5. What is the change?

How to Calculate Acceleration?

tV

ttVV

aif

if

means “change in”

How do you calculate Δv?

The change in velocity = the final velocity – the initial velocity.

Δv = vf – vi

You are stopped at a red light. When it turns green, you speed up to 45m/s. What is your change in velocity?

vi = 0m/s

vf = 45m/sΔv = ?

Δv = vf-vi = 45m/s- 0m/s = 45m/s

Acceleration Units

velocity unit/ time unit

km/h/s m/s/s or m/s2

What are some other ways to say that the car is accelerating?

Any questions about the Section Review Questions?

Page 20

What is negative acceleration?

Also known as DECELERATION. The negative rate of change of

velocity. Slowing down. The amount of negative change of

velocity in a time interval.

How does it feel?

When you accelerate?

When you decelerate?

Look at Fig 1.10 on pg 21

Which ball will hit the ground first? Which ball accelerates the most? Which ball will have the fastest speed at

the end?

What did Galileo find from the ramp experiment?

Steeper inclines = greater acceleration All materials fall with the same

acceleration. (when you can neglect air resistance)

How will we use the acceleration formula to solve problems?

a = v / t v = a X t t = v / a

Let’s Practice with some Problems

A car’s velocity changes from 0 m/s to 30 m/s in 10 seconds. Calculate the car’s average acceleration.

v = 30m/s t = 10s a = ? a = v / t

a = 30 m/s / 10sa = 3 m/s/s or 3 m/s2

Practice Problems

A swimmer speeds up from 1.1 m/s to 1.3 m/s during the last 20 s of the workout. What is the acceleration during this interval?

v = 1.3 m/s – 1.1 m/s = 0.2m/s t = 20s a = ? a = v / t

a = 0.2 m/s / 20s

a = 0.01 m/s/s or m/s2

Let’s Review Speed!

http://www.unitedstreaming.com/

Graphing Motion Review

FREE FALL

A falling object that has only the force of gravity working on it.

What pattern do you notice?Table 1.2 (pg. 22)

Time of free fall (s) Instantaneous Speed (m/s)

0 0

1 10

2 20

3 30

4 40

5 50

* *

t 10 t

What is the acceleration of any free falling object?

The table shows that the velocity increases 10 meters per second for each second that it falls.

So a = 10 m/s/s or 10 m/s2

g

g = ACCELERATION DUE TO GRAVITY g = - 9.8 m/s/s If you are calculating, use -9.8m/s/s Why do we use negative numbers when we

describe an object falling?

Let’s review the acceleration formulas!

The formulas you will use:

a = Δv / Δt Δv = a X Δt Δt = Δv / a

REMEMBER: • Δv = final v – initial v

• Δt = final t – initial t

A NEW FORMULA

distance = ½ (acceleration X time X time) d = ½ (at2)

Your book says d = ½ (gt2) when talking about falling objects…why?

Does our formula work?

Time of free fall (s) Distance of fall (m)

0 0

1 5

2 20

3 45

4 80

5 125

* *

t ½ 10 t 2

Feather & Hammer drop

Which would hit the ground first? Why?

Let’s Practice!

We will start with page 20. Read the directions. Let’s try the example!

What is the velocity of a rubber ball dropped from a building roof after 5 seconds?

vf = ? vi = 0 m/s t = 5 s a = -9.8 m/s2

Δv = a X Δt Δv = -9.8 m/s2 X 5 s Δv = -49 m/s Δv = vf –vi

-49m/s = vf – 0 m/s vf = -49 m/s or 49 m/s down

HOMEWORK

Worksheets 20 & 21 Complete ALL problems. Show your set up and ALL of your work.

Let’s review falling objects & Check out Galileo’s experiments!

http://www.unitedstreaming.com/

Newton’s Laws

Which law is shown here? How do you know?

DINNER PARTY EXAMPLE…

Forces

Notes 3.4

What is a Force?

A push or pull on an object.

Some forces are seen, for example a box being pushed across the table.

Some forces are not seen, for example the floor pushing up on your feet.

Balanced Forces

A balanced force is a force on an object that is equal in size and opposite in direction.

Tug of war is a good example. Each person is pulling on the other with

an equal and balanced force.

Unbalanced Forces

Sometimes forces are not equal or opposite.

Example: Pushing a car. An unbalanced force is a net force. A net force acting on an object will

change the velocity and/or direction.

Why do objects stand still if no force is applied?

Inertia! The tendency of objects to

resist a change in motion. If it is moving – it will keep

moving. If it is still – it will not move. UNLESS….. A net force acts

on it!

Inertia

Examples:• A book on your desk will sit there and not

move, unless you apply a force to the book to move it. If your arm pushed the book, that would be a force.

• If you drive in a car and hit a wall without the force of a seat belt to stop you, your body will continue to move even though the car has stopped. This is why people go through the windshield.

Which object has more inertia?

Heavier objects are harder to stop moving and start moving.

The larger the mass, the greater the inertia.

Example: A semi truck is harder to stop than a toy truck.

Newton’s First Law of Motion(Law of Inertia)

“An object moving at a constant velocity will keep moving at that velocity unless a net force acts on it. If an object is at rest it will stay at rest unless a net force acts on it.”

An object in motion will stay in motion (rest at rest)

Hmmm- Isn’t that Inertia?

Why don’t object stay moving forever????

If the Law of Inertia is true, than any moving object should move forever!

In outer space this is true because there is no friction.

What is Friction?

The force that pushes in the opposite direction of motion between two surfaces that are touching each other.

For Example: A car will eventually slow down because of the friction between the car tires and the road.

Gravity

Notes 3.5

What is Gravity?

The force in the universe between all objects.

Every object in the universe exerts a force on other objects.

Gravitational Force

The amount of force that gravity exerts is called gravitational force.

How much gravitational force there is depends on the mass and distance between objects

Gravitational Forces Example

Earth is larger than the moon, therefore the moon is stuck in the gravitational pull of the earth.

Gravity and Weight

The measure of the force of gravity on an object is weight.

Weight is different from mass!!!

Mass vs. Weight

Definition Measuring Tool

Unit Location

Mass The amount of matter in an object

Balance g, kg Not changed by location

Weight Amount of gravitational force acting on an object

Scale Newton

(N)

Changed by location

Mass vs. Weight

Mass is not a force. It is a quantity. Weight is the force of gravity on an

object. A mass of 1 kg weighs 9.8 N.

Newton’s Second Law

Notes 4.1

Newton’s Second Law of Motion

This Law is best explained as an equation.

Force = mass x acceleration The net force acting on an object causes

that object to accelerate in the direction of the force.

Newton’s Second Law of Motion Example:

How much force is needed to accelerate a 70 kg rider and her 200 kg motorcycle at 4 m/s2?

F = m x a

F = 270kg x 4 m/s2

F = 1080 kgm / s2 or N

What is a Newton?

F = m x a F = kg x m/s2

F = kg m

s2

1 kg m = 1 Newton

s2

How do I calculate weight?

Because any force can be calculated using the equation F = m x a, weight of an object (a force) can be calculated using a similar equation W = m x a.

Because weight is the force of gravity on an object the rate of acceleration is the pull of gravity. (remember? 9.8 m/s2)

Weight Example

W = m x g (g = gravity) If a person has a mass of 50 kg what is

their weight? W = m x g

W = 50 kg x 9.8 m/s2

W = 490 N

Acceleration Caused by the Force of Gravity

Gravity is a force that pulls objects towards the center of an object. (Earth)

Near the Earth’s surface, gravity causes all falling objects to accelerate at 9.8 m/s2.

Acceleration due to gravity is the same for all objects.

The bowling ball and the feather…

If acceleration due to gravity is the same for all objects, regardless of mass, then all objects should fall at the same rate.

Does a leaf fall as fast as an acorn?

Air Resistance

Two objects will only fall at the same rate if no other force is present.• For example: in outer space

On Earth we have Air Resistance. The force that air exerts on a moving

object. This force acts in the opposite direction

of the objects motion.

Air Resistance Example

If you drop two pieces of paper, one whole and the other crumpled up into a ball- which would hit the ground first?

The crumpled ball because there is less air resistance.

Air resistance pushes up as gravity pulls down.

Air Resistance

The amount of air resistance on an object depends on the speed, size, shape and density of the object.

Projectile Motion

Notes 4.2

What is a Projectile?

Anything that is thrown or shot through the air.

Projectiles have velocities in two directions.• Horizontal Motion: Motion parallel to the

Earth’s surface.

• Vertical Motion: The force of gravity pulling down on the object.

Projectile Motion

A projectile’s horizontal and vertical motion are completely independent of each other.

Gravity will effect a projectile and a falling object in the same way.

Therefore, if an object is dropped and thrown at the same time they will hit the ground at the same time. It does not matter that the projectile travels a farther distance.

Projectile Motion Example

http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html

Circular Motion

Notes 4.2

Motion along a curve

Acceleration is a rate of change in velocity caused by a change in speed or direction!

If you are riding a bicycle in a straight path you will not accelerate. But, if you travel around a curve the speed will accelerate because the direction is changing.

Centripetal Acceleration

The change in velocity is towards the center of the curve.

Acceleration toward the center of a curved or circular path is Centripetal Acceleration.

The word Centripetal means “towards the center”.

Centripetal Force

In order for the bicycle to be accelerating, some unbalanced force must be acting on it in a direction toward the center of the curve.

This force is called Centripetal Force. Centripetal force acts toward the

center of a curved path.

Example of Centripetal Force

When a car goes around a sharp curve the centripetal force is the friction between the tires and the road.

Although, if the road is icy, the tires may lose their grip. The amount of centripetal force will not be enough to overcome the car’s inertia.

So the car would continue to move in a straight line.

                                                                           

As a car makes a turn, the force of

friction acting upon the turned wheels of the car provide the

centripetal force required for circular

motion.

As a bucket of water is tied to a string and spun in a circle, the

force of tension acting upon the

bucket provides the centripetal force

required for circular motion.

As the moon orbits the Earth, the force of

gravity acting upon the moon provides

the centripetal force required for circular

motion.

Action and Reaction

Notes 4.4

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.

Newton’s Third Law

For every action, there is an equal and opposite reaction.

For example: If you jump out of a boat the boat exerts a force on your feet pushing your forward, although your feet exert an equal and opposite force on the boat sending it backwards.

Unbalanced action - reaction pairs

Sometimes action and reaction forces are not balanced.

For example, if a toy truck rolls towards you, you can stop it with your hand. The action of the truck is not equal to the force of your hand.

Momentum

While you can stop a toy truck with your hand, you would not be able to do the same for a pickup truck.

It takes more force to stop a pickup truck than a toy truck. This is because of Momentum.

Momentum

Momentum is the strength of motion due to the mass and velocity of the object.

The Momentum of an object can be calculated.

Momentum = mass x velocityp = m x vkg x m/s

Momentum Practice Problem

A 4 kg bowling ball rolling at 6 m/s hits a bowling pin. What is the momentum of the bowling ball?

p = m x v

p = 4kg x 6 m/s

p = 24 kgm/s

Conservation of Momentum

The momentum of an object does not change unless the mass or velocity of the object changes.

However- momentum can be transferred from one object to another.

The total amount of momentum does not change unless an outside force acts on the object(s).

The Energy of Motion

Notes 5.1

What is Energy

Is the ability to cause change Many different forms of energy

• Chemical

• Electrical

• Thermal

• Nuclear

Kinetic Energy

The energy in the form of motion The amount of Kinetic Energy depends

on the mass and velocity of the moving object.

More mass = more KE More Velocity = more KE

Potential Energy

The stored energy of position.• A flower pot on a window ledge has the

potential to fall.

Potential energy depends on position. • A flower pot on the fifth floor has the ability to

cause greater change than a flower pot on the first floor.

Relationship between PE and KE

Mechanical Energy is the total amount of Kinetic and Potential Energy in a system.

Pendulum Example

Conservation of Energy

Energy can not be created or destroyed, it can only change form.

How do we transfer energy?

Work is the ability to transfer energy through motion.

The amount of work done can be calculated.

W = F x d

Work Practice Problem

Machines

Notes 7.1

What is a Machine?

A machine is any device that makes work easier.

Some machines are powered by engines or motors, others are simple and only require one movement.

Machines

An ideal machine would have the work output equal to the input.

Machines help to overcome obstacles like gravity and friction.

Simple Machines

There are six types of simple machines• Levers

• Pulleys

• Wheel and Axle

• Inclined Plane

• Screw

• Wedge

Compound Machine

A combination of two or more simple machines

A bicycle