Transcript Motion - ILM.COM.PK

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?
Vf  Vi V
a

tf  ti
t
 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/s
Δv = ?
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 / 10s
a = 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)
0
1
2
3
4
5
*
t
Instantaneous Speed (m/s)
0
10
20
30
40
50
*
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)
0
1
2
3
4
5
*
t
Distance of fall (m)
0
5
20
45
80
125
*
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=5s
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=mxa
F = 270kg x 4 m/s2
F = 1080 kgm / s2 or N
What is a Newton?



F=mxa
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=mxg
(g = gravity)
If a person has a mass of 50 kg what is
their weight?
W=mxg
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/109
N/more_stuff/Applets/ProjectileMotion/jar
applet.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 straightline 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 velocity
p=mxv
kg 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=mxv
p = 4kg x 6 m/s
p = 24 kgm/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=Fxd
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