To state the POSITION of an object, we must have the following:

To state the POSITION of an object, we must have the following:
Slide 1 How do we state the position of an object? To state the POSITION of an object, we must have the following: A Reference Point A Coordinate System Units of Measurement

Slide 2 What is a A REFERENCE POINT is a known location. Reference
This man might say, “the Ocean is in front of me.” He is using himself as the Reference point. . . . . . Or, it might be the board in the front of the classroom.

Slide 3 What is a Coordinate System?
A COORDINATE SYSTEM is a way you tell Which directions you will be moving from the reference point. If the “X” is your Reference point X So, our COORDINATE SYSTEM Is UP and DOWN AND RIGHT and LEFT Then the birthday girl is DOWN . . . .And to the RIGHT

Slide 4 The UNITS OF MEASUREMENT are the way
What are Units of Measurement? The UNITS OF MEASUREMENT are the way you tell how far you move from the reference Point along the coordinate system. So, for the Birthday girl, we might say . . . X She is 3 METERS Down, and . . . So, our UNITS OF MEASUREMENT are METERS 5 METERS to the right of the reference point

Slide 5 A “UNIT” is “one” of something
What are Units of Measurements? A “UNIT” is “one” of something A “MEASUREMENT” is a known amount of Something to which we can compare other Things. Examples: Units of Measurements? 5 yards means 5 times the unit of 1 yard 10 pounds means 10 times the unit of 1 pound In this class, we will abbreviate UNITS OF MEASUREMENT with the letters UoM.

Slide 6 There are two major measurement systems
What is the ENGLISH System of measurement? There are two major measurement systems The ENGLISH system: The ENGLISH system is used in daily life here in the US. It uses the UoM for distance that you are Familiar with, such as: Inch Foot Yard Mile

Slide 7 There are 2 major measurement systems
What is the Metric System of measurement? There are 2 major measurement systems The METRIC system: The METRIC system is used in most countries of the world. In addition, the METRIC system is used in Science and Engineering. It uses the UoM such as: Meter Centimeter (1/100 meters) Millimeter (1/1000 meters) Kilometers (1,000 meters)

Slide 8 The UoM for time are the same all over
What are theUoM for TIME? The UoM for time are the same all over The world, time uses the UoM such as: Seconds Minutes Hours Days Weeks Months Years

Slide 9 An ABBREVIATION is a shortened way to
What are some Common Abbreviations For UoM? An ABBREVIATION is a shortened way to Write a word. UoM are usually expressed in Their abbreviated form. Some of these are: Meters m Centimeters cm Kilometers km Seconds s Minutes min Hours h or hr

What is SPEED? SPEED is the distance you go in a certain unit of time. The formula for the average speed or velocity of an object is: d DISTANCE = AVERAGE SPEED = TIME t “d” is the abbreviation for “distance” “t” is the abbreviation for “time”

Slide 11 What are the UoM for SPEED?
The UoM for speed can be any measure of distance divided by any measure of time. For example: meters = m second s This is the most common UoM we will use for speed. Other examples are: Miles Yards cm Feet Hour Minute Day Year

Slide 12 Example: SPEED SPEED is the distance you go in a certain
unit of time. If Manuel runs 50 meters in 10 seconds, what is his average speed? Change in Distance: 50 meters Change in Time: seconds 50 meters Average Speed = = 5 m/s 10 seconds

Slide 13 Example: SPEED SPEED is the distance you go in a certain
unit of time. If Manuel walks 30m in 30s, then runs 50m in 10s, what is his average speed? Distance: 30m + 50m = 80m Time: s + 10s = 40s 80 meters Average Speed = = 2 m/s 40 seconds

SPEED, direction does not matter.
Slide 14 SPEED is the distance you go in a certain Amount of time What is the difference between SPEED and VELOCITY? SPEED does not care about direction. This runner is going 8 meters per second to The SOUTH. This runner is going 8 meters per second toThe NORTH. Are they going The same SPEED? YES, both are going 8 m/s. With SPEED, direction does not matter.

In different directions.
Slide 15 VELOCITY is the distance you go in a Certain amount of time AND IN A PARTICULAR DIRECTION What is the difference between SPEED and VELOCITY? VELOCITY does care about direction. This runner is going 8 meters per second to The SOUTH. This runner is going 8 meters per second toThe NORTH. Are they going The same VELOCITY? NO, both are going In different directions. With VELOCITY, Direction DOES Matter

Slide 16 What is AVERAGE VELOCITY?
Average Velocity = Change in Position = Δx Time t “Change in position”, Δx, is the straight line distance between where you started and where you ended

Slide 17 Example: The difference between SPEED and VELOCITY?
Luis walks from point A to point B to point C, and stops at point C (the path shown by the green arrows) in 50 seconds. The distances are shown on the diagram below. What is his total DISTANCE? What is his SPEED? What is his CHANGE IN POSITION? (This is the distance along the dashed yellow line) What is his average VELOCITY? Example: The difference between SPEED and VELOCITY? 100m + 100m = 200m 200m = 4 m/s 50s 150m 150m = 3 m/s 50s A B C 150m 100m

What is VELOCITY? VELOCITY is the distance you go in a certain unit of time AND IN A PARTICULAR DIRECTION. Velocity cares about direction The VELOCITY can be changed by: Making the object speed up or slow down. 2. Changing the direction of the object THIS IS KEY!!

Slide 19 What is the formula for VELOCITY?
The CST (state test) does not distinguish between speed and velocity, so v = d = Δx (change in position) t t For the rest of this course, we will treat speed and velocity as the same thing.

Slide 20 Compute the velocity of a car that travels 20 m in 10 s.
What is Breakdown Format? BREAKDOWN FORMAT is a 5 step process we will use to solve problems. Step 1: What is problem asking for Step 2: What does the problem give us Step 3: Choose a formula (and do algebra) Step 4: Substitute numbers and compute Step 5: Present final answer with UoM Example 1: Breakdown Format Compute the velocity of a car that travels 20 m in 10 s. v = ? (Step 1) v = d t (Step 3) d = 20 m (Step 2) t = 10 s v = 20 m 10 s (Step 4) v = 2 m s (Step 5)

Slide 21 5 10/5/09 INITIAL VELOCITY and FINAL VELOCITY
What is INITIAL and FINAL VELOCITY? INSTANTANEOUS VELOCITY is the velocity you are going at a particular instant. The abbreviation for instantaneous velocity is: vi Example: The speed on the speedometer of a car shows the speed that the car is going at that exact moment. We will deal with 2 special kinds of Instantaneous Velocities: INITIAL VELOCITY and FINAL VELOCITY Start Line Finish Line

6 10/5/09 What is INITIAL VELOCITY? INITIAL VELOCITY is the instantaneous velocity when you first start your measurement. This is also called BEGINNING VELOCITY or STARTING VELOCITY. We abbreviate INITIAL VELOCITY as v0 which is read, “the velocity when the time is 0 seconds.” The small “0” is called a subscript.

Slide 23 7 10/5/09 Example: INITIAL VELOCITY
INITIAL VELOCITY does not have to be zero. If Stick-girl is running at 5 m/s when we start our stopwatch, her INITIAL VELOCITY is 5 m/s Start Line

Slide 24 8 10/5/09 What is FINAL VELOCITY?
FINAL VELOCITY is the instantaneous velocity when you stop your measurement. We abbreviate FINAL VELOCITY as vf Example: FINAL VELOCITY If Stick-girl is running at 10 m/s when we STOP our stopwatch, her FINAL VELOCITY is 10 m/s Finish Line

Slide 25 2 10 10/5/09 What is the formula for AVERAGE VELOCITY?
Here is a new equation for AVERAGE VELOCITY v = v0 + vf 2 You add the INITIAL VELOCITY and the FINAL VELOCITY, then divide by 2

Slide 26 11 10/5/09 What is the formula for AVERAGE VELOCITY? ? v = ?
Tresor starts running with an initial velocity of 0 m/s and finishes with a final velocity or 10 m/s. What was his average velocity? ? v = ? v = v0 + vf 2 or v = d t v0 = 0 m/s vf = 10 m/s v = 0 m/s + 10 m/s 2 v = 5 m/s We have two formulas for v; Which one do we use? We use the one that contains the variables we were given in the problem. We know V0 and Vf. We do not know d or t. So, we use the first equation.

What is a VECTOR? A VECTOR is an ARROW used in math and science There are 2 parts to a VECTOR: DIRECTION: The variable stated by the VECTOR is going in the direction of the arrow. MAGNITUDE: Magnitude means “HOW BIG” or “HOW MUCH” You can ADD and SUBTRACT VECTORS just like regular numbers

If a car is moving to the right with a VELOCITY 10m/s, it could be represented by the following VECTOR: If another car is moving to the right at a VELOCITY of 20m/s, it could be represented by the following VECTOR: Both VECTORS show MAGNITUDE and DIRECTION. Notice that the 20m/s vector is twice as long as the 10 m/s vector. This is how you show that 20m/s is two times as much velocity as 10 m/s. Example: VECTOR 10 m/s 20 m/s

Slide 29 Vectors CAN be ADDED and SUBTRACTED from each other: 2 m/s
Can Vectors be ADDED and SUBTRACTED? Vectors CAN be ADDED and SUBTRACTED from each other: This bus is moving at 10 m/s. Stick-boy is walking towards the front of the bus at 2 m/s. Stick-boy is moving at the bus’s velocity added to his walking velocity. 10 m/s + 2 m/s = 12 m/s 2 m/s 10 m/s

Slide 30 Example: What is the NET VELOCITY? 2 m/s 10 m/s
If Stick-boy is walking towards the back of the bus at 2 m/s, what is his NET VELOCITY? 2 m/s 10 m/s 10 m/s - 2 m/s = 8 m/s When you add or subtract two numbers, the answer is called a NET result. In the examples above, 8 m/s and 12 m/s is called the NET VELOCITY, because it is the addition or Substraction of two velocities.

Slide 31 ACCELERATION IS ANY CHANGE IN VELOCITY per unit of time.
What is ACCELERATION? ACCELERATION IS ANY CHANGE IN VELOCITY per unit of time. The faster Velocity changes, the greater the acceleration. The VELOCITY can be changed by: Making the object speed up or slow down. 2. Changing the direction of the object

What is the formula for ACCELERATION? The units of measurement for ACCELERATION are ANY unit of DISTANCE divided by any Unit of TIME divided by any unit of TIME. The most common unit of measurement for ACCELERATION we use in class is: Meters per second per second, abbreviated, m s This is often written: m s 2

What does an Acceleration of 5 m/s/s mean? “For every second that goes by, the car’s velocity has increased by 5 meters per second.” 0 s 1 s 2 s 0 m/s 5 m/s 10 m/s The car begins At an initial Velocity of V0 = 0 m/s After 1 second, The velocity has Increased by 5 m/s To 5 m/s After 2 seconds, The velocity has Increased by 5 m/s To 10 m/s

Slide 34 a = Final Velocity - Starting Velocity Change in Total Time
What is ACCELERATION? The formula for AVERAGE ACCELERATION is: a = Final Velocity - Starting Velocity Change in Total Time We use the abbreviations: a = Vf - V0 = ΔV t t Vf = Final Velocity V0 = Starting Velocity t = Change in Total Time

Slide 35 When this rollercoaster is at the top
EXAMPLE: ACCELERATION When this rollercoaster is at the top It is going 0 meters per second. After 3 seconds it has sped up to 15 meters Per second. What is its average acceleration? a = ? vf – v0 a = vf = 15m/s t v0 = 0 m/s 15 m/s - 0 m/s a = 3 s t = 3 s a = 5 m/s/s

Slide 36 You can change VELOCITY by changing DIRECTION.
EXAMPLE: ACCELERATION You can change VELOCITY by changing DIRECTION. This race car is going In a circle at 80 m/s. Is its speed changing? No, it’s 80 m/s. Is its velocity changing? Yes, its direction is Changing. Is it accelerating? Yes, its velocity is Changing.

What is the formula for Instantaneous Velocity? “We can see a relationship between the acceleration, 5 m/s/s, the time, and the instantaneous velocity, vi. vi = at Instantaneous velocity = acceleration X time 0 s 1 s 2 s 0 m/s 5 m/s 10 m/s

Example: Instantaneous Velocity Laura begins from a position of rest (v0 = 0 m/s). If she accelerates at 4 m/s/s, how fast will she be going after 3s? This is read: “Laura’s instantaneous velocity at 3s is 12 m/s.” vi = ? vi = at a = 4 m/s/s vi = 4 m/s/s • 3 s t = 3s vi = 12 m/s

What does an Acceleration of 5 m/s/s mean? Example: Instantaneous Velocity What if Laura is already moving at 2 m/s when she accelerates at 4 m/s/s. How fast will she be going after 3s? Now, we must add the speed she is already moving to the final speed. This beginning speed is v0. This changes our formula to: vi = at + v0 vi = ? vi = v0 + at a = 4 m/s/s vi = 4 m/s/s • 3 s + 2 m/s t = 3s vi = 14 m/s v0 = 2 m/s

g =10 m/s/s (Exactly 9.8 m/s/s)
Slide 40 What is the ACCELERATION OF GRAVITY? GRAVITY will pull objects with DIFFERENT MASSES to Earth at the SAME ACCELERATION The ACCELERATION OF GRAVITY is: g =10 m/s/s (Exactly 9.8 m/s/s)

What is the ACCELERATION OF GRAVITY?
Slide 41 What is the ACCELERATION OF GRAVITY? If one object falls to the earth faster than another, it is because of AIR RESISTANCE (not gravity) Unless told otherwise, assume there Is NO AIR RESISTANCE when doing Gravity acceleration problems Bowling Ball Feather

How do we compute distance using acceleration?
Slide 42 How do we compute distance using acceleration? Distance can also be computed using acceleration, initial velocity, and time, as follows: d = ½ at2 + v0t A car with an initial velocity of 10m/s accelerates at 4m/s/s for 5s. What distance did it travel? d = ? d = ½ at2 + v0t a = 4m/s/s d = ½ (4m/s/s)(5s)2 + (10m/s)(5s) v0 = 10m/s t = 5s d = 100m Example

What is a FORCE? A FORCE is a push or a pull. A force does not need to Cause an object to move. The UoM for FORCE is called a NEWTON. The abbreviation for a NEWTON is N The abbreviation for FORCE is F 5 N 5 N

FORCE What is a FORCE? A FORCE is a push or a pull. A force does not need to Cause an object to move. Stick-Boy is pushing the box with 5 N of force . . . Does this mean that The box has to be moving? 5 N 5 N No. If there is a 5 N Force pushing back Against Stick-Boy, then The box will not move.

What are BALANCED FORCES? If the forces in opposing directions are equal, we say they are BALANCED. 5 N 5 N TRICKY If the forces on an object Are Balanced then the Object is: or 1. Not moving Moving at steady velocity

What are UNBALANCED FORCES? If the forces in both directions are NOT equal, we say they are UNBALANCED. 2 N 5 N If the forces on an object Are NOT Balanced then The Object is: Accelerating

Slide 47 10 N + 5 N = 15 N FORCES are VECTORS. FORCES can be ADDED.
Can FORCES be ADDED? FORCES are VECTORS. FORCES can be ADDED. If Stick-boy pushes with 10 N of force and Stick-girl pulls With 5 N of force in the same direction, then the total Force on the box is: 5 N = 15 N 10 N 10 N + 5 N = 15 N IN this example, 15 N is called the NET FORCE. A NET FORCE is What you get when you ADD or SUBTRACT 2 or more forces.

Slide 48 10 N - 6 N = 4 N in this direction FORCES can be SUBTRACTED.
Can FORCES be SUBTRACTED? FORCES can be SUBTRACTED. If Stick-boy pushes with 10 N of force and Stick-girl pushes with 6 N of force in the opposite direction, then the total Force on the box is: 10 N 6 N 10 N - 6 N = 4 N in this direction

Slide 49 These forces ARE Balanced A free-body diagram uses a simple
What is a FREE BODY diagram? These forces ARE Balanced 3 N 5 N A free-body diagram uses a simple Box to represent the NET FORCES on an Object.

Slide 50 Forces are BALANCED when all OPPOSING forces Are equal
What is a FREE BODY diagram? Forces are BALANCED when all OPPOSING forces Are equal Object is either: Standing Still, or Moving at a constant velocity 3 N 3 N 5 N Only the forces on OPPOSITE Sides of the box must be the Same for forces to be BALANCED

Slide 51 Forces are UNBALANCED when any OPPOSING forces Are NOT equal
What is a FREE BODY diagram? Object MUST be Accelerating 3 N Acceleration 5 N 2 N 3 N

Slide 52 MASS is the amount of matter (“stuff”) an object has in it
The amount of matter your body has in it does not change Whether you’re on Earth or in outer space, So . . .Your Mass NEVER changes anywhere in the Universe What is MASS? The Birthday Girl Has a MASS of 20 kg whether she Is on Earth or Floating in outer space

Slide 53 The basic UoM of MASS is the GRAM.
One large paperclip has a mass of 1 GRAM. Usually, we use a measure of 1000 grams called a KILOGRAM The abbreviations are: Mass m Gram g Kilogram kg Your Mass NEVER changes anywhere in the Universe What is the UoM of MASS?

Slide 54 Force equals mass times acceleration The formula is: F = ma
What is the formula for FORCE? Force equals mass times acceleration The formula is: F = ma Where F is force m is mass measured in kg (kilograms) a is accelerations measured in m/s/s

What is the UoM for Force?
Slide 55 What is the UoM for Force? What is a Newton? A Newton is the metric unit of measurement for FORCE 1 N = kg · m s Notice that this follows the Equation F= ma 2 Force = mass · acceleration So, a Newton is the amount of force that it takes to accelerate a 1 kg mass at 1 m/s/s

Example of FORCE? How much force is required to accelerate a 4 kg cart at 5m/s/s? F = ? F = ma m = 4 kg F = (4 kg)(5m/s/s) a = 5m/s/s F = 20N

Slide 57 GRAVITY is an attracting force between two or more objects
What is GRAVITY? GRAVITY is an attracting force between two or more objects GRAB-ity (I love you!) Remember to think of GRAVITY as “GRAB-ITY”, Because you and someone you like (2 people) want to GRAB each other

Slide 58 A force of GRAVITY exists between any two object with mass.
What is GRAVITY? A force of GRAVITY exists between any two object with mass. The force of gravity is referred to as a “gravitational attraction.” There is a gravitational attraction between you and your pencil! The reason you don’t feel it is because you and your pencil are small.

What determines the FORCE of GRAVITY?
Slide 59 The FORCE of GRAVITY depends on: What determines the FORCE of GRAVITY? The MASS of the objects (More mass means MORE gravity) and 2. The DISTANCE between them (More distance means LESS gravity)

WEIGHT WEIGHT IS A FORCE Slide 60
What is WEIGHT? The FORCE OF GRAVITY on an object is called its WEIGHT WEIGHT is measured in: 1. POUNDS (English Units) 2. NEWTONS (Metric System) WEIGHT IS A FORCE

Slide 61 Weight is the attractive force between an Object and Earth.
What is the formula for weight on Earth? Weight is the attractive force between an Object and Earth. To compute weight using the mass of an Object, use the formula: w = mg Where, w = weight m = mass in kilograms g = 10m/s/s

Slide 62 What is Flor’s weight on Earth if she has a mass of 45kg?
Example of weight? What is Flor’s weight on Earth if she has a mass of 45kg? w = ? w = mg m = 45kg w = (45kg)(10m/s/s) g = 10m/s/s w = 450N To convert between the metric measure of Force Newtons (N) and the English unit Pounds (lbs) use the formulas: lbs x 4.5 = N or N = lbs 4.5 So, Flor’s weight in pounds is: lbs = 450N = lbs

Slide 63 Ana pushes a 3 kg box with 17N of force.
How do you perform a NET FORCE calculation? Ana pushes a 3 kg box with 17N of force. A 5N Friction force opposes the motion. At what Rate does the box accelerate? First, we must find the net force: Fnet = F - FF Fnet = 17N – 5N Fnet = 12N Now, use Fnet to solve for a: a = ? Fnet = ma Fnet = ma m m Fnet = 12N a = 12N m = 3kg kg a = Fnet m a = 4m/s/s 3kg 17 N 5N

What effect does a pulley have on a force? If a force goes around a pulley (a wheel that guides a rope), the pulley does not change the value of the force. Stick-boy holds a 5kg box using a rope run over a pulley. How much force did he exert on the rope to hold the mass stationary? The downward weight (force) on the rope is: w = ? w = mg m = 5kg w = (5kg)(10m/s/s) g = 10m/s/s w = 50N Since the box is stationary, stick-boy’s pulling force must balance the weight of 50N, So Stick-boy is pulling with 50N of force. Example 5kg

Which way is this box moving? Net force = 500N Hercules is putting an unbalanced force of 500N on the block above. Can you tell which way the block is moving? No. The block does not need to be moving in the direction of the force. You must first know which way the block is Moving at the time Hercules applies the force.

Slide 66 Net force = 500N What you can tell is this:
Which way is this box moving? Net force = 500N What you can tell is this: If the block is standing still, it will speed up to the right If the block is moving to the right, it will speed up to the right If the block is moving to the left (against Hercules) it will be slowing down If the block is moving in any other direction, except toward or away from Hercules, it will be curving

Slide 67 What is Gravity? Gravity is the attractive force between
Two or more objects. What is Gravity? The formula for the FORCE of GRAVITY BETWEEN ANY TWO OBJECTS is: F = G m1m2 d2 What is the formula for Gravitational Attraction? G is called the Universal Gravitational Constant G = N m2 kg2 m1 and m2 are the masses d is the distance between the masses

Slide 68 BIG “G” and Little “g” G is called the Universal
Gravitational Constant G = N m2 kg2 BIG “G” and Little “g” Don’t confuse the UNIVERSAL GRAVITATIONAL CONSTANT, BIG “G”, Which equals: G = N m2 kg2 With the acceleration of an object due Gravity on EARTH, LITTLE “g”: g = 10 m/s/s

Slide 69 A 50 kg girl (about 110 pounds) and
Example: Formula for Gravitational Attraction? A 50 kg girl (about 110 pounds) and a 60 kg boy (about 130 pounds) stand 1 m apart. How many Newtons of Attractive force are there between them? F = ? F = G m1m2 d 2 m1 = 50 kg m2 = 60 kg F = ( ) (50)(60) (1)2 d = 1 m F = N This force is so small that it cannot be felt

What is the relationship Between Distance and Gravitational Force? To find how much gravity changes when two Objects move apart or move together, do this: Make a ratio of the old distance over the new Square it Example 1: Two objects double their distance from Each other, What happens to the force of gravity between them? Old New Step 1: Ratio Step 2: Square it Result: Old = = 1 New So, the gravitational attraction at 2m is ¼ as strong as at 1m. 1m 2m

What is the relationship Between Distance and Gravitational Force? Two objects move from 4m to 1m apart. What is the Effect on gravitational attraction? Old New Step 1: Ratio Step 2: Square Result: Old = = New When the objects are moved to ¼ of the previous distance, the force of gravity between them is 16 times stronger. 4m 1m Example 2:

Slide 72 1st Law of Motion An object at rest remains at rest and an
What are NEWTON’S LAWS? 1st Law of Motion An object at rest remains at rest and an object in motion remains in motion (constant velocity), unless acted upon by an outside force 2nd Law of Motion The acceleration of an object depends on its mass and the force applied to it. 3rd Law of Motion For every action (force) there is an equal and opposing reaction (force)

What is INERTIA? 1st Law of Motion An object at rest remains at rest and an object in motion remains in motion (constant velocity), unless acted upon by an outside force This is known as the Law of INERTIA INERTIA DEPENDS ONLY ON THE MASS OF AN OBJECT

What is INERTIA? When Stick-boy tries to push a car that is standing still, it is hard to get it going . . .

What is INERTIA? BUT, when stick-boy tries to stop a car that is already rolling, it is hard to stop

F = ma Slide 76 2nd Law of Motion
What is Newton’s 2nd Law? The acceleration of an object depends on its mass and the force applied to it. This equation is written in the form: F = ma read “Force equals mass times acceleration” ACCELERATION FORCE MASS 5 m/s/s

3rd Law of Motion What is Newton’s 3rd Law? For every action (force) there is an equal and opposing reaction (force) If the forces on an object are not equal, then the object will accelerate until the forces become equal again. When forces are equal (balanced) the object is in EQUILIBRIUM When the forces are not equal (unbalanced) then the object is in DISEQUALIBRIUM Objects in disequilibrium (unbalaced) Accelerate until forces are balanced again

What is FRICTION? FRICTION FORCE is a force that opposes motion by one object contacting another object Examples: When you push your desk across the floor, it resists moving because a friction force of the desk against the floor. It is hard for Stick-girl to pull the box because of the Friction force caused by the box touching the floor Stick-girl’s pulling force Friction Force acting against Stick-girl’s force

What is PROJECTILE MOTION? PROJECTILE MOTION is the motion of an object under the influence of gravity. Once a soccer ball is kicked into the air, the only force acting on it is gravity pulling it downward Objects under the influence of gravity form a shape called a PARABOLA g=10m/s2

Slide 80 Projectile motion has three parts:
What is PROJECTILE MOTION? Projectile motion has three parts: Upward vertical negative acceleration (slowing) Downward vertical positive acceleration (speeding up) Horizontal constant velocity The Soccer Ball slows As it rises The Soccer Ball Speeds up As it falls The Soccer Ball moves at a constant velocity in the horizontal (sideways) direction because the forces in this direction are balanced (= 0)

How can vectors be combined? We learned that vectors in the same or opposite directions can be netted. Vectors in other directions can be combined by placing the TIP of one vector to the TAIL of the other. The vectors being added are called COMPONENT VECTORS The vector that results from this is called the RESULTANT VECTOR The magnitude of the resultant can be determined by measuring it. Component Vectors Resultant Vector

How can vectors at right angles be combined? Most often, we will deal with vectors in the X and Y directions that you are used to from algebra and geometry class Usually, the component vectors are placed TAIL to TAIL so that the resultant can be seen clearly These two groups of vectors are the same Resultant Vector Component Vectors X Direction Y Direction Resultant Vector Component Vectors

What is PROJECTILE MOTION? A curve can be represented by the resultant vector of two perpendicular vectors. The horizontal vectors are the same length because the ball moves sideways at a constant velocity. Same Length

What is PROJECTILE MOTION? The vertical (up and down) vectors are long on the bottom because the ball is moving the fastest when it is first thrown upward and just before it hits the ground. The ball gets slower and the lines get shorter nearer to the top. The ball is moving slower Both going up and going down The ball is Moving faster Both going up And going down

What is PROJECTILE MOTION? The resultant of the vertical (up and down) vector and the horizontal (sideways) vector are shown in blue below The blue arrows are resultants of the red vectors. Notice how The blue vectors form the curved Shape of a parabola

Slide 86 So, the ball rose to a height of 20m
Projectile Motion: Example 1 A ball is punted and stays in the air for 4s. How high did the ball go? The ball is in the air for 4s, so it spends 2s going up and 2s coming down Since height is a distance, we can solve it this way: d = ? d = ½ at2 a = g = 10m/s/s d = ½ (10m/s2)(2s)2 t = 2s d = 20m So, the ball rose to a height of 20m (about the height of a six story building)

Projectile Motion: Example 2 A ball is punted and is moving at 30 m/s upward when it leaves the punters foot and travels 60m down field. How long did the ball stay in the air? We know the ball comes to a stop when it gets to its highest point, so the final velocity is 0 m/s t = ? a = - 10m/s/s v0 = 30 m/s vf = 0 m/s a = vf - v0 t t = (0 – 30)m/s -10m/s/s t = m/s - 10 m/s/s t = 3 s t • a = (vf – v0) • t t at = vf – v0 a a t = vf – v0 a Acceleration is negative because it is working against the motion of the ball The ball spends 3s going up and another 3s coming down, so the ball is in the air for 6s.

Slide 88 The ball rises to a height of 45m then falls
Projectile Motion: Example 3 A ball is punted and is moving at 30 m/s upward when it leaves the punters foot. The ball travels 60m down field. How high did the ball go? We know from the previous slide that t = 3s d = ? d = ½ at2 a = 10m/s/s d = ½ (10m/s/s)(3s)2 t = 3s d = 45m The ball rises to a height of 45m then falls Back to Earth 45m.

Slide 89 The ball traveled at 10 m/s in this direction
Projectile Motion: Example 4 A ball is punted and is moving at 30 m/s upward when it leave the punters foot. The ball travels 60m down field. What was the ball’s horizontal velocity (also known as ground speed)? We know that the ball traveled 60m down field in 6s, we don’t care about the upward or downward motion: v = ? v = d t d = 60m v = 60m t = 6s s v = 10 m/s The ball traveled at 10 m/s in this direction

What is Momentum? Momentum is the part of Newton’s 1st Law that deals with motion: An object that is already in motion wants to stay in motion.

Slide 91 The abbreviation for momentum is small “p”
What is the formula for Momentum? MOMENTUM is equal to an object’s MASS times VELOCITY The abbreviation for momentum is small “p” We write the formula for momentum as p = mvi Important: Some books write the formula as p = mv. You need to use instantaneous Velocity, vi, not average velocity, v.

Slide 92 Mass • velocity kg • m s The UoM for MOMENTUM is:
What is the UoM for Momentum? The UoM for MOMENTUM is: Mass • velocity kg • m s This is read “kilogram meters per Second”

Slide 93 Example: MOMENTUM
A 10 kg bowling ball rolls at a constant velocity of 2 m/s. What is its momentum? What is its force? a. p = ? p = mvi p = 10 kg • 2 m s m = 10 kg vi = 2 m/s p = 20 kg • m s b. There is NO FORCE because the ball is moving at a constant velocity, so a = 0 m/s/s

Slide 94 Compare these two equations and remember the difference
Compare MOMENTUM to FORCE Compare these two equations and remember the difference Force = ma kg • m/s/s (Newton) Momentum = mvi kg • m/s

When an asteroid is traveling through space at constant velocity, it has momentum but NO force (because there is no acceleration) Once the asteroid strikes a planet, the sudden negative acceleration (slowing down) creates force Compare MOMENTUM to FORCE

What is pulse? PULSE: A PULSE is a force times the amount of time it is applied Pulse = F • t The units of measurement for a PULSE are the same as for MOMENTUM: kg • m s PULSE is also called IMPULSE

What is the relationship between MOMENTUM and PULSE? The amount of PULSE needed to stop an object’s MOMENTUM is always CONSTANT Ft = mvi Or Ft = p

Impulse equal Momentum
Slide 98 Example 1: Impulse equal Momentum How much force would it take to stop a car with a momentum of 15,000 kg m/s in 10 seconds? F • t = mvi F • t = mv t t F = ? mvi = 15,000 kg m/s t = 10 s F = mv t F = 15,000 kg m/s 10 s F = 1,500 N

Impulse equal Momentum
Slide 99 Example 2: Impulse equal Momentum A soccer player shoots the ball at the goal with 15 kg m/s of momentum. Case 1: The goalie can punch the ball away, by using a lot of force for a short amount of time: p = F • t 15 kg m/s = N • s Case 2: The goalie can catch the ball by letting the ball hit his body softly. He does this by using A small amount of force spread out over a longer time: p = F • t 15 kg m/s = N • s

m1v1 + m2v2 = m1v1 + m2v2 Slide 100 What is
Conservation Of Momentum? Conservation of Momentum means that when two objects collide with each other, the total momentum of both objects after the collision is the same as the total momentum before the collision of the two objects Conservation of momentum is expressed as: Before collision After collision m1v1 + m2v2 = m1v1 + m2v2

Slide 101 4 m/s 3 m/s 2 m/s ?= 1 m/s Before After
A 4 kg bowling ball moving at 4 m/s to the right, collides with a 2 kg bowling ball moving to the left at 3 m/s. After the collision, the 4 kg ball is moving 2 m/s to the right. How fast is the 2 kg ball moving and in which direction? Example: Conservation Of Momentum? 4 m/s 3 m/s 2 m/s ?= 1 m/s 4 kg 2 kg 4 kg 2 kg Before After 16 kg m/s -6 kg m/s 8 kg m/s 2 kg m/s Conservation of Momentum 10 kg m/s 10 kg m/s

Slide 102 ? m/s = 2 m/s 5 m/s 0 m/s 8 kg 12 kg 8 kg 12 kg
An 8 kg train car moving at 5 m/s to the right, hooks onto a 12 kg train car that is standing still. After they hook together, are they moving? How fast? Which way? Example: Conservation Of Momentum? ? m/s = 2 m/s 5 m/s 0 m/s 8 kg 12 kg 8 kg 12 kg 40 kg m/s 0 kg m/s ? m/s • (8 + 12) kg = 40 kg m/s V = 2 m/s 40 kg m/s 40 kg m/s Conservation of Momentum

Slide 103 A collision is when one object strikes What is a
Another Object. What is a Collision? There are two types of collisions: Elastic and Inelastic An Elastic collision is one in which two Objects collide without sticking together Or changing shape. Think of two bowling Balls colliding What kinds of Collisions are there? An Inelastic collision is one in which two Objects collide and stick together or Change shape. Think of two train cars hooking together or two lumps of clay Sticking together.

W Slide 104 What is WORK? Remember, a FORCE does not need to make
Something move. When a FORCE does cause something to Move, it is called WORK, abbreviated W WORK is the amount of FORCE applied to An object times the DISTANCE it moves. So, W = F • d The Unit of Measurement for WORK is a: Joule (J)

Slide 105 Example: Work If you push a desk with 20 N of force
and it does not move, how much work Did you do? W = ? W = F • d F = 20 N d = 0 m W = 20 N • 0 m W = 0 J If you pushed a desk with 20 N of force And it moved 5 meters, how much Work did you do? W = ? W = F • d F = 20 N d = 5 m W = 20 N • 5 m W = 100 J

Slide 106 What is the Definition of Power?
POWER is the amount of work you do in A certain amount of time: What is the Definition of Power? The formula for POWER is: P = W t The UoM of Power is called a: WATT, abbreviated W

Slide 107 What is ENERGY? ENERGY is defined as the CAPACITY TO DO WORK
What are the UoM for ENERGY? ENERGY has the same UoM as WORK: This Unit of Measurement is called a: Joule

Slide 108 What kinds of There are two kinds of ENERGY: ENERGY are
KINETIC (KE) and POTENTIAL (PE) What is KINETIC ENERGY? KINETIC ENERGY is the energy of an Object in MOTION POTENTIAL ENERGY is the energy an Object has that can be converted into Kinetic energy but has not yet done so What is POTENTIAL ENERGY?

Slide 109 The formula for Gravitational PE PE = mgh where, m = mass
What is GRAVITATIONAL POTENTIAL ENERGY? GRAVITATIONAL POTENTIAL ENERGY is The force of an object due to gravity (remember, this is called WEIGHT) times The height the object is above the ground The formula for Gravitational PE PE = mgh where, m = mass g = gravitational acceleration h = height (Same Uom as distance)

Slide 110 Formula for Kinetic Energy? What is the
The formula for the Kinetic Energy of an Object is: KE = ½ mvi 2 What is the kinetic energy of a 20 kg shopping cart moving at 3 m/s? KE = ? KE = ½ mvi2 m = 20 kg KE = ½ (20 kg)(3 m/s)2 v = 3 m/s KE = 90 J

Slide 111 What is TOTAL ENERGY? TOTAL ENERGY is KE added to PE, or
Etotal = KE + PE Example of Total Energy If Potential Energy is 10 J and Kinetic Energy is 7 J, what is the total energy? 10 J + 7 J = 17 J

Slide 112 A 2 kg ball is held 3 m above the ground.
Example: GRAVITATIONAL POTENTIAL ENERGY? A 2 kg ball is held 3 m above the ground. What is the ball’s POTENTIAL ENERGY? PE = ? PE = mgh m = 2 kg h = 3 m PE = (2 kg)(10 m/s/s)(3 m) g = 10 m/s/s PE = 60 J What is the ball’s KINETIC ENERGY? KE = ½ mvi 2 KE = ? v = 0 m/s KE = ½ (2 kg)(0) 2 KE = 0 J

Slide 113 Example: What is TOTAL ENERGY?
What is the TOTAL ENERGY in the ball? Etotal = ? Etotal = KE + PE PE = 60 J Etotal = 0 J + 60 J KE = 0 J Etotal = 60 J What is Conservation Of Energy? THE LAW OF CONSERVATION OF ENERGY states: The TOTAL ENERGY of a falling object DOES NOT change KE + PE = CONSTANT (stays the same)

Slide 114 PE = mgh 120 J 0 J 120 J PE = (3)(10)(4) 4 m 120 J 3 m 90 J
Meters above The ground PE KE ETotal PE = mgh 120 J 0 J 120 J PE = (3)(10)(4) 4 m 120 J 3 m 90 J 30 J PE = (3)(10)(3) 120 J 2 m 60 J 60 J PE = (3)(10)(2) 1 m 30 J 90 J 120 J PE = (3)(10)(1) 120 J 0 m 0 J 120 J PE = (3)(10)(0) A 3 kg ball is held 4 m above the ground and then dropped. Fill in the blanks for the energy of the ball as it falls.

Slide 115 What is Circular Motion? An object is going
Centripetal force Tangential force What is Circular Motion? An object is going In a circle in this direction When an object moves in a circle, there are two components (“parts”) of Its force: Centripetal: A force holding the object in a circle points toward the center of the circle. Tangential: Force that is perpendicular to the centripetal force. A tangent is a line that touches a circle in exactly one place

Slide 116 What is Circular Motion?
Centripetal force What is Circular Motion? Tangential force When an object moves in a circle at a constant speed, its direction is changing all of the time, SO . . . Its velocity is changing all of the time (even though its speed stays constant) The changing velocity means that an object moving in a circle is ACCELERATING all of the time

Slide 117 What is Circular Motion?
The ball moving in a Circle moves forward Because of the Tangential force and Stays in a circle Centripetal force Slide 117 If the rope breaks at point A, then the Ball continues along The tangent where The rope broke Because only a Tangential force and NO centripetal force Is acting on the ball What is Circular Motion? A If you swing an object on a string around and then release it, this eliminates the centripetal force and leaves only the tangential force. This means that the object flys away in a STRAIGHT LINE along the tangent where it was released

Slide 118 3 kg vi r What is Angular Acceleration?
r is the radius of the circle vi is the tangential velocity r Acceleration is not only a change in speed, but also a change in direction Acceleration due to an change in direction is called ANGULAR ACCELERATION The formula for acceleration caused by a change in direction is: a = vi2 r

Slide 119 vi 3 kg r = 2m rope a = vi a =(4 m/s) a = 8 m/s/s r 2m
Example: Angular Acceleration r = 2m rope r is the radius of the circle vi is the tangential velocity Example: Wolfboy is swinging a 3kg block that Is moving in a circle on a 2m rope with a tangential velocity of 4 m/s? a = ? vi = 4m/s r = 2m 2 2 a = vi r a =(4 m/s) 2m a = 8 m/s/s

Slide 120 F = m • a vi 3 kg r What is Circular Motion?
r is the radius of the circle vi is the tangential velocity m is the mass of the object at the end of the rope What is Circular Motion? r Since F = ma, the force on the rope is given by: F = m • vi r F = m • a 2

Slide 121 3 kg Vi = 4 m/s 2 m rope r F = ? F = mvi2 m = 3 kg r
r is the radius of the circle vi is the tangential velocity What is Circular Motion? rope r Example: What is the force on the rope if Wolfboy swings a 3kg block in a circular path at 4 m/s at a radius of 2m? F = ? m = 3 kg vi = 4 m/s r = 2 m F = mvi2 r So, 24 N is the force on the rope, on the box, and on Wolfboy’s arms F = (3kg)(4 m/s)2 2m F = 24N

Slide 122 A CONVERSION FACTOR is a number
What are CONVERSION FACTORS? A CONVERSION FACTOR is a number with which you can multiply one UoM To get a different UoM. HERE ON EARTH, ONLY, you can Use the following CONVERSION FACTORS 1 kg (mass) • = Pounds (force) 1 kg (mass) • 10 = Newtons (force) 1 pound (force) • = Newtons (force)

Slide 123 A 2-stage or 3-stage problem has
Different accelerations at different points in the problem that are treated As separate problems. A 1000 kg cannon fires a 10 kg cannonball. The ball accelerates from a position of Rest to a velocity of 20 m/s in 2 s when it Exits the cannon (Positive Acceleration) The ball continues at 20 m/s until it hits the ground (Constant velocity) After it hits the ground, the ball takes 5s to come to a stop (Negative Acceleration) What are 2-stage And 3-stage problems? Example of a 3-stage problem: Stage 1 Example of a 3-stage problem: Stage 2 Example of a 3-stage problem: Stage 3

Stage 2: Constant Velocity
Slide 124 Stage 1: Positive Acceleration Stage 2: Constant Velocity Stage 3: Negative Acceleration Example of a 3-stage problem Stage 1 is a positive acceleration from 0 m/s to 20 m/s. Stage 2 is a constant velocity as the ball Flys through the air at 20 m/s. Stage 3 is the negative acceleration as the Ball hits the ground and comes to a stop.

Slide 125 a = ? a = (20 – 0)m/s 2 s v0 = 0 m/s
BOOM!!! Stage 1: Positive Acceleration a = ? a = (20 – 0)m/s 2 s v0 = 0 m/s vf = 20 m/s a = 10 m/s/s t = 2 s F = ? F = ma m = 10 kg F = (10 kg)(10 m/s/s) a = 10 m/s/s F = 100 N The cannon ball exerted 100 N of force on the Cannon (Newton’s 3rd Law) What was the Acceleration of The cannonball Out of the cannon How much force Did the cannon Exert on the Cannonball? How much force Did the Cannonball exert On the cannon?

Slide 126 p = ? p = mv v = 20 m/s p = (10 kg)(20 m/s) m = 10 kg
Stage 2: Constant Velocity p = ? p = mv v = 20 m/s p = (10 kg)(20 m/s) m = 10 kg p = 200 kg m/s KE= ? KE = ½ mv2 v = 20 m/s KE = ½ (10 kg)(20 m/s)2 KE = 2,000 J 0 N. Since there is no acceleration during this Time, there is no force. What was the Cannonball’s Momentum as It flew through The air? What was the Cannonball’s Kinetic Energy As it flew through The air? How much force Was on the Cannonball as it Flew?

Slide 127 Vf = 0 m/s V0 = 20 m/s F = ? F = mv t
Stage 3: Negative Acceleration Vf = 0 m/s V0 = 20 m/s F = ? F = mv t v = 20 m/s F = (10 kg)(20 m/s) m = 10 kg s t = 5 s F = 40 N Since the cannonball has 2000 J of KE that Must be removed to stop the ball, then 2,000 J of work must be done against the ball. d = ? W = F • d W = F • d W = 2000 J F F F = 40 N d = 2,000 J 40 N d = W d = 50 m F How much force was required to stop the cannonball? How much work Was required to Stop the ball? How far did the ball roll?

Slide 128 Two ice skaters have an initial velocity of
Example: Conservation of Momentum Two ice skaters have an initial velocity of 0 m/s when they push off of each other. What is the velocity of the 50 kg skater after the push if the 40 kg skater is moving 5 m/s? 0 m/s 0 m/s 5 m/s 4 m/s 40 kg 50 kg 40 kg 50 kg 0 kg m/s 0 kg m/s -200 kg m/s 200 kg m/s Conservation of Momentum 0 kg m/s 0 kg m/s

Example: What is a “Perfectly Elastic” Collision? A PERFECTLY ELASTIC Collision occurs when both kinetic energy and momentum are conserved. We will not work any problems of this type, but you should know this concept.

Slide 130 “THERMO” means HEAT “DYNAMICS” means MOTION
What is Thermodynamics? “THERMO” means HEAT “DYNAMICS” means MOTION THERMODYNAMICS studies HEAT, how heat moves, and how it produces WORK An Old Steam Locomotive Runs by Thermodynamics

Slide 131 HEAT TEMPERATURE tells us Average kinetic energy of the
Molecules in an object . What is Temperature? A hot object has more energy Than a cold object Internal energy is of no use in Doing useful work. We are Interested in energy that leaves An object due to a temperature Difference between the object And some other object. Energy leaving an object is HEAT And is measured in Joules (J) What is Heat?

On the CENTIGRADE scale
Slide 132 What scale is used In Science and in Other countries Around the world? In science, and in most of the Rest of the world,TEMPERATURE Is measured using the CENTIGRADE or CELSIUS system On the CENTIGRADE scale Water freezes at 0º C and Water boils at 100º C

What is the KELVIN system of temperature measurement? The KELVIN SYSTEM, of temperature measurement is one that defines 0 as the temperature at which an object has NO ENERGY. 0 on the Kelvin scale is called ABSOLUTE ZERO. It is impossible to have a temperature lower than 0 on the Kelvin scale The UoM of temperature in the Kelvin System is DEGREES CENTIGRADE or CELSIUS. Important: A degree on the Centigrade scale is exactly the same as a degree on the Kelvin scale. The scales differ only in what they define as “0”.

What is the KELVIN system of temperature measurement? The UoM of temperature in the Kelvin system is the same degree that is used in the Centigrade system. On the Kelvin System: Water Freezes at 273 Kelvin Water Boils at 373 Kelvin Notice that there are 100 degrees between freezing and boiling, just as on the Centigrade scale.

Slide 135 K = C + 273 Let’s Compare the Centigrade and
Kelvin scales at 3 different points How does the Centigrade scale Compare to the Kelvin scale? Kelvin Centigrade Boiling Water 373 K 100ºC Freezing Water 273 K 0ºC K = C + 273 0 K, or -273º C, is the lowest Temperature there is. It is called Absolute zero. 0 K -273ºC

What is the English, or Fahrenheit System, of temperature measurement? The ENGLISH, or FAHRENHEIT, SYSTEM of temperature measurement is the one we use here in the US. The UoM of temperature in the English System is DEGREES FAHRENHEIT. On the English System: Water freezes at 32° Fahrenheit Water Boils at 212° Fahrenheit

Slide 137 The 1st Law of Thermodynamics States:
What is the 1st Law of Thermodynamics? The 1st Law of Thermodynamics States: Whenever heat is added to a System, it transforms to an Equal amount of some other Form of energy Heat added to an engine (Q) = Increase in internal energy (U) + Work done by the system (W) Q = U + W

Slide 138 The Heat is added + Q 1st Law of Thermodynamics
Heat is removed - Q Internal Energy increases + U Internal Energy decreases - U Work is done by the system + W Work is done on the system - W

Slide 139 Example: 1st Law of Thermodynamics?
Lets say that heat is added to 30ºC (room temp) Water. The water absorbs heat until it reaches 100ºC when it begins to boil. Up until this point, All of the heat is absorbed as internal energy, no Work has been done. Once the water Simple begins to boil, Engine Its steam pressure Pushes the piston Upward, which is WORK. So, as the 1st Law states, all heat added, either Causes an increase in the energy of the water, Or causes the system to do work. Piston Water Heat added

Slide 140 What is the 2nd Law of Thermodynamics? Example: 2nd Law Of
The 2nd Law of Thermodynamics states: Heat will never naturally flow from a cold object to a hot object

Slide 141 How does the 2nd Law of Thermodynamics Apply to engines?
What is EFFICIENCY? The 2nd Law of Thermodynamics applies To an engine as follows: When work is done by a heat engine Running between two temperatures, QHOT and QCOLD, only some of the input Heat at QHOT can be converted to work, And the rest is expelled as heat at QCOLD. The amount of heat that is converted Into useful work as a percentage of The total heat that is put into the engine Is called the EFFICIENCY of the engine.

Slide 142 400 J 300 J 100 J What does a Simple heat Engine look like?
A simple engine consists of 3 parts: The hot reservoir, where the heat energy comes from. 2. The engine: Where the desired work is done. 3. The cold reservoir: Where waste heat that is not converted to work is dumped Piston 400 J 300 J 100 J Hot Reservoir Engine (Useful Work) Cold Reservoir

Slide 143 400 J 300 J 100J How do we Compute the Efficiency of an
Engine? Example: Engine Efficiency To compute the EFFICIENCY of an Engine, we use the absolute temperature Scale, the KELVIN scale, and the Following formula: Efficiency = QWork = Useful Work Done QH Heat Added Hot Reservoir Piston Cold Reservoir 400 J 300 J 100J Engine (Useful Work) Efficiency = = 25% 400

Slide 144 400 J 300 J How do we Compute the Efficiency of an Engine?
Example: Engine Efficiency Sometimes, you might be asked to compute the Amount of heat used for useful work by taking The amount of heat energy added and subtracting The amount wasted: Efficiency = QH – QC = Useful Work Done QH Heat Added Hot Reservoir Piston Cold Reservoir 400 J 300 J Efficiency = 400 – 300 = = 25%

Slide 145 What is Entropy? What is a subsystem? What is an example
Of a Subsystem? Entropy is the principle of science that says: Natural systems move from a state of greater order to a state of greater disorder A subsystem is a small system that Exists within a larger system. The Earth is a subsystem of the Universe.

Slide 146 If systems tend Toward disorder, How did the order
We see in our World come to be? While the disorder of the larger system Must increase, it is possible for there to Be greater order in a subsystem. So, the creation of the Earth and life on Earth is an increase in order. But in creating the Earth, the overall DISORDER OF THE UNIVERSE had to increase. Order on Earth increases Universe: The disorder of the universe Increases as it gives energy to the Earth to create life on Earth.

Slide 147 So, which is greater The increase in the Order of the
Subsystem, Earth, Or the increase in the disorder of The larger system, The universe? The increase in disorder of the universe is Greater than the increase in order of the Subsystem, Earth. So, when the increase in disorder of the universe Is added to the increase in order of the Earth, the Overall result is AN INCREASE IN DISORDER, or GREATER ENTROPY. Order on Earth increases Universe: The order of the universe Decreases as it gives energy to the Earth to create life on Earth.

What is the relationship between heat and temperature change in a substance The relationship between heat and temperature change is given by the equation: Q = mc(ΔT) Where, Q = heat (calories) m = mass of the substance (grams) c = specific heat ΔT = change in temperature (K or C) Specific Heat is a property of each substance. For water, specific heat is 1 What is a calorie Joules and calories are both measures of energy. The two units are related as follows: 1 Calorie = Joules

Slide 149 Example 1: Heat and Temperature
How many calories of heat will be needed to raise 1 kg (1000g) of water 15 C? Q = mcΔT Q = (1000g)(1.0)(15 C) = cal Q = calories or J How much will the temperature of 2 kg of water increase if 100,000 cal of heat is added? Solving for ΔT ΔT = Q = ,000 cal = 50 C mc (2000g)(1.0) So, the temperature of 2kg of water will Increase by 50 C if 100,000 cal of heat is added Example : Heat and Temperature

Slide 150 Example 1: Heat and Temperature
How many calories of heat will be needed to raise 1 kg (1000g) of iron 15 C? Q = mcΔT Q = (1000g)(0.45)(15 C) = 6750 cal Q = 6750 calories or J How much will the temperature of 2 kg of iron increase if 100,000 cal of heat is added? Solving for ΔT ΔT = Q = ,000 cal = 111 C mc (2000g)(.45) So, the temperature of 2kg of iron will Increase by 111 C if 100,000 cal of heat is added Example : Heat and Temperature

Slide 151 200K 500K Air Flow 500K What is THERMAL CONDUCTION?
Thermal Conduction is when heat passes through a thermal conductive material from a high temperature to a low temperature 500K 200K Conduction Convection is when moving molecules, such as air or water carry heat. What is CONVECTION? Air Flow 500K What is RADIATION? Radiation is when electromagnetic waves carry heat. This is how the sun’s heat reaches us through the vacuum of space.

Slide 152 D = m V What is DENSITY?
DENSITY is how much mass is “crowded” into an amount of space (volume) Density is the amount mass divided by the volume that object occupies The formula for DENSITY is: D = m V The Uom for density are g or kg cm L Read “grams per cubic centimeter” or “kilograms per liter”

What is BUOYANCY? Buoyancy is the ability of an object to float. Usually the substance in which it is floating is water. There are two definitions of BUOYANCY Archimedes Principle An object sinks until it displaces an amount of water equal to its own mass So, a 1kg object will sink until it displaces 1kg of water

What is BUOYANCY? The other definition of BUOYANCY states that an object that is LESS DENSE than water will FLOAT An object that is MORE DENSE than water will SINK These two definitions are really the same Water has a density of kg L Which is 1 kilogram per liter

What is BUOYANCY? The other definition of BUOYANCY states that an object that is LESS DENSE than water will FLOAT The block has the same density as water. This means that it floats so that it just touches the top of the water 1 kg This box is 1 kg of water that has a volume of 1 L This box is a 1 kg block that has a volume of 1 L

What is BUOYANCY? What if the block has a mass of 1 kg and a volume of 2 Liters? The density of the block is 1 kg = kg 2 L L The block has a density that is less than water The 1 kg block displaces 1 L of water, but what happens to the other liter of the block? It stays above the water, so it floats. 1 kg

Slide 157 This box is a 2 kg block that has a volume of
What is BUOYANCY? The other definition of BUOYANCY states that an object that is MORE DENSE than water will SINK Because the block displaces more than its own mass in water, it sinks 2 kg This box is a 2 kg block that has a volume of 1 L The white arrows push up with the force to support 1 kg of water

Slide 158 What Is Electrical force?
Electrical force is a force of nature The key point to remember about electricity is this: POSITIVE ATTRACTS NEGATIVE and NEGATIVE ATTRACTS POSITIVE POSITIVE REPELS (pushes away) POSITIVE And NEGATIVE REPELS NEGATIVE + + + - - -

Slide 159 Protons (positive magnets) Neutrons (no charge)
What is an ATOM? An ATOM is the smallest piece of an element there is. If you cut an atom of GOLD or IRON in half, you will no longer have GOLD or IRON. What are The parts of An ATOM? An ATOM consists of three components (parts): Protons (positive magnets) Neutrons (no charge) Electrons (negative magnets)

Slide 160 What does An atom Look like? Nucleus: Center of an atom = +
- Example: HELIUM Protons (+): Positively Charged magnets in the nucleus Electrons (-): Negatively charged Magnets that circle the nucleus Neutrons (=): Neutral (“No charge”) particles in the nucleus

Slide 161 What is an ELECTRIC FIELD? + -
An ELECTRIC FIELD is an invisible field that puts a Force on an electrical charge, such as a proton or Electron. The DIRECTION of an ELECTRIC FIELD is defined as The direction it makes a POSITIVE charge (such as A proton) move What is an ELECTRIC FIELD? + - The red plate, above has a positive charge and the blue Plate has a negative charge. A Proton (positive) would Be pushed from the positive to the negative plate. This Is the direction of the ELECTRIC FIELD.

Slide 162 In a METALLIC BOND, electrons are attracted to
The protons in the nucleus, but the electrons are not held closely to any particular atom, so they jump From one atom to the next What are METALLIC BONDS? - - - Example Of a METALLIC BOND Cu Cu Cu Cu Copper (abbreviation: Cu) easily pass electrons From one Cu atom to another We call this flow of electrons, ELECTRICITY -

Slide 163 Materials that DO NOT conduct electricity well are
The ability of electrons to move from atom to atom is called CONDUCTIVITY. Copper (Cu) and Other METALS that conduct electricity well are called CONDUCTORS. What is CONDUCTIVITY? - - Cu Cu Cu Materials that DO NOT conduct electricity well are Called INSULATORS. Materials such as plastic, Rubber, wood, or glass are examples of insulators. What is an INSULATOR? -

Slide 164 Non-metals Metals Metalloids Ge Te 1 H 1.01 2 He 4.00 3 Li
Hydrogen 1.01 2 He Helium 4.00 3 Li Lithium 6.94 4 Be Beryllium 9.01 17 Cl Chlorine 35.45 18 Ar Argon 39.95 B Boron 6 C Carbon 12.01 7 N Nitrogen 14.04 8 O Oxygen 16.00 9 F Fluorine 19.00 10 Ne Neon 20.18 12 Mg Magnesium 24.31 11 Na Sodium 22.99 13 Al Aluminum 26.98 Si Silicon 15 P Phosphorus 30.97 16 S Sulfur 32.07 Ge Germanium Po Polonium Arsenic Sb Antimony Te Tellerium The periodic table is divided into 3 major sections: Metals, Metalloids, and Non-Metals Non-metals Metals The Metalloids are BORON, SILICON, GERMANIUM, ARSENIC, ANTIMONY TELLERIUM, AND POLONIUM Everything to the LEFT is a METAL Everything to the RIGHT is a NON-METAL Metalloids Metalloids are used In computer SEMICONDUCTORS

Slide 165 What is an ELECTRIC FIELD? + -
An ELECTRIC FIELD between A POSITIVE AND A NEGATIVE point looks like this + -

What is an ELECTRIC CHARGE? The attraction and repulsion (pushing away) of Protons and Electrons is a result of their ELECTRIC CHARGE ELECTRIC CHARGE is measured in a Unit of Measurement called a COULOMB. The abbreviation for Coulomb is “C”

Slide 167 What is When Stick-boy holds a ELECTRIC
POTENTIAL? When Stick-boy holds a ball above the ground In the Earth’s gravitational Force field, it has a POTENTIAL ENERGY Measured in JOULES An electric charge in an Electric field also has a potential energy ELECTRIC (Voltage) X ELECTRICAL = POTENTIAL ENERGY POTENTIAL CHARGE The Unit of Measurement for Voltage is a VOLT 1 Volt x 1 Coulomb = 1 Joule A VOLT is abbreviated with the letter “V”

VOLTAGE is a measure of how much electrical “pressure” there is to push electrons What is VOLTAGE? If a garden hose has a nozzle, such as the one to the right, it is possible for there to be water pressure even if there is no flow. Similarly, it is possible for there to be “electrical pressure” or VOLTAGE, even if there is no flow of electricity.

Slide 169 What is What are The UoM for
If the water DOES have someplace to go, by opening the nozzle on the garden hose, it will Create a flow, or movement, of the water. What is CURRENT? Similarly, if electricity has a place to go, it creates a flow. The flow of electricity is called CURRENT. CURRENT is measured by how many COULOMBS Of charge pass a point each second. Current is abbreviated by the letter “i”. When one coulomb passes a point each second, it Is called an AMPERE. Amperes are abbreviated with the letter “A” What are The UoM for CURRENT?

One of the most common sources of voltage (electric potential) you are familiar with is a BATTERY. What is An VOLTAGE SOURCE? A battery creates an Electric Potential because it has a positive(+) side and a negative(-) side.

Slide 171 What is What is Positive Terminal (side) + - Metal wire,
“SCHEMATIC DIAGRAM”? A “SCHEMATIC DIAGRAM” is a kind of “stick figure diagram” of an electric circuit that we will use to solve electric circuit problems The SCHEMATIC DIAGRAM for a VOLTAGE SOURCE, such as a battery, is shown below What is the SCHEMATIC DIAGRAM For a Voltage Source? Positive Terminal (side) + - Metal wire, Such as copper Negative Terminal(side)

Slide 172 What is Needed for An electric Current to flow?
For an ELECTRIC CURRENT to flow, there must be: 1. High potential 2. Conducting Material 3. Low Potential What is Needed for An electric Current to flow? Conducting Material Low Potential High Potential

Slide 173 What is an ELECTRIC CIRCUIT? + -
An ELECTRIC CIRCUIT exists when a metal wire Is set up in a loop with a voltage source placed Somewhere in the loop. A VOLTAGE SOURCE, such as a battery contains both a source of electrons and a LOW POTENTIAL place, called a GROUND, for them To go to. + -

Slide 174 What is ELECTRICAL RESISTANCE?
RESISTANCE in an Electric Circuit reduces the amount of current that flows through the circuit and causes a drop in VOLTAGE across the resistance. There are two ways to cause resistance: By using a device called a RESISTOR, which is designed to produce resistance. By placing a LOAD in the circuit. A LOAD is any device which does useful work such as a light bulb or an electric fan.

Slide 175 Ω What is ELECTRICAL RESISTANCE?
The abbreviation for RESISTANCE is R The schematic symbol for a RESISTOR looks like this: The Unit of Measurement for RESISTANCE is an OHM. The symbol for an OHM is the Greek letter Omega: Ω

Slide 176 Electrical Coulomb The charge on Review of
Charge X electrons Voltage Volt Electrical “pressure” or potential Current Ampere How many coulombs pass a point each second Resistance Ohm Circuit element that uses power, slows current, and reduces voltage Review of Electrical Terms 18

Slide 177 + - Voltage Source Switch (open) Resistor or Load
What does a Basic Electrical Circuit look like A basic electrical circuit includes: A POWER SOURCE, such as a voltage source A device that uses power, such as a RESISTOR or a LOAD A switch that opens and closes the circuit + - Voltage Source Switch (open) Resistor or Load The Voltage Source provides pressure on the electrons at all times, BUT . . . Electrons only flow when the SWITCH IS CLOSED. This is called a CLOSED CIRCUIT. NO ELECTRIC CURRENT flows in an OPEN CIRCUIT.

The most important formula we will use with electricity
Slide 178 What is the Relationship Between current, voltage, And resistance? The relationship between voltage, current, and resistance is given by OHM’S LAW: Voltage = Current • Resistance OR V = iR ; Where Voltage is measured in VOLTS (V) Current is measured in AMPERES (A) Resistance is measured in OHMS (Ω) The most important formula we will use with electricity + -

Slide 179 + - Example 1: Ohm’s Law
How much Voltage is required to push 5 A of current across a 2 Ω resistor? V = ? V = iR i = 5 A R = 2 Ω V = (5 A)(2 Ω) V = 10 V i = 5 A + - V = ? R = 2 Ω

Slide 180 + - Ohm’s Law: Example 2
How much current flows when 20 V is placed across a 5 Ω resistor? V = iR R R i = ? V = iR V= 20 V R = 5 Ω i = 20 V 5 Ω i = V R i = 4 A i = ? + - V = 20 V R = 5 Ω

Slide 181 i (all of the current) R + R -
A SERIES CIRCUIT contains 2 or more resistors. Two resistors are in SERIES when ALL of the current that comes out of the first resistor goes through the second resistor AND all of the current going through the second resistor has passed through the first resistor. In the circuit below, all current that passes through Resistor 1 (R1) MUST pass through Resistor 2 (R2); There is nowhere else it can go. What is a Series Circuit? R 1 i (all of the current) + - R 2

Slide 182 + R - What is a PARALLEL CIRCUIT?
A PARALLEL CIRCUIT contains 2 or more resistors. Two resistors are in PARALLEL when they are not in series. + - R 2 1

Deana and Eduardo work at the San Ysidro border check point. Deana takes 3 minutes to check a car and let it pass. Eduardo takes 1 minute to do so. Let’s see how many cars should get into Deana’s line and how many should go into Eduardo’s line. Your job as the manager is to assign the cars to the line that will get them through the border the fastest. (If the times are equal, put them in Eduardo’s line). Deana: 3 minutes per Car 3 min 3 min 3 min Manager Eduardo: 1 minute per Car 1 min 1 min 1 min 1 min 1 min 1 min 1 min 1 min 1 min The point is that since it takes Deana 3 times longer to let a car pass, 3 times as many cars will go through Eduardo’s line.

Slide 184 + - How does Current decide Which path to Follow in a
PARALLEL CIRCUIT? In a PARALLEL Circuit, current wants to follow the path that offers less resistance, just as the Cars crossing the border. If R2 has 3 times the Resistance of R1, then 3 times as much current will flow through R1. 4 A + - R = 3 Ω 2 R = 1 Ω 1 3 A 1 A 3 A 4 A 1 A

Slide 185 + - ACROSS A RESISTOR: VOLTAGE CHANGES, How does
Voltage and Current change As we go Around the Circuit? ACROSS A RESISTOR: VOLTAGE CHANGES, CURRENT DOESN’T i = 5 A 10 V 10 V + 10 V R = 2 Ω V = 10 V - 0 V 0 V 0 V i = 5 A The 10 V power source and the 2 Ω resistor create a Constant current of 5 A THE ENTIRE WAY AROUND THE CIRCUIT. The Voltage is 10 V at every point along the red wire. Once The voltage crosses the resistor, it drops to 0 V at every Point along the green wire.

Slide 186 P = Vi How do we Compute POWER In an electric Circuit? 2
To find the POWER that a device in an electric circuit uses, we use the following equation: POWER equals VOLTAGE times CURRENT: P = Vi To calculate the POWER used by a particular circuit element, such as a lightbulb or a fan, we can also use the equation: P = i R Again, the UoM of POWER is WATTS 2

S N S N S N Slide 187 How are Magnets oriented?
In natural IRON, the atoms are pointed in random directions. When the IRON is placed under a magnetic field, the atoms line-up in a North-South orientation S N When a magnet is broken in two, the atoms in each new magnet have the same North-South orientation. S N S N

North pole is attracted to a South pole of another magnet. What does A Magnetic Field look like? S N S N In addition, a magnet’s North pole is attracted to its own South pole. This means that the magnetic field comes out of the North pole, wraps around the magnet, and comes back to the South pole. S N

Slide 189 How does Current create A magnetic field? Remember,
ALL ELECTRONS PRODUCE AN ELECTRIC FIELD WHEN ELECTRONS ARE IN MOTION, THEY ALSO PRODUCE A MAGNETIC FIELD Direction of Current Direction of Magnetic Field When current moves in a straight line, such as through a wire, the magnetic field circles the wire. If you point the thumb of your RIGHT HAND in the direction of the current, then the magnetic field will be in the direction of your other four fingers. This is called the RIGHT HAND RULE

Slide 190 How can a Magnet create An electric Current?
When a magnet is moved through a wire coil, it induces (causes) an electric current to flow in the wire (assuming the wire is a closed circuit). In the diagram below, I is the electric current and B is the direction of the magnet’s movement. How can a Magnet create An electric Current? A device that changes the motion of a magnet into electrical energy is called a GENERATOR

The amount of voltage and current in the wire coil depends on 2 factors: How many loops the coil has in it How fast the magnet is moved through the coil This is known as FARADAY’S LAW How can a Magnet create An electric Current?

Slide 192 Collector Base Emitter
A TRANSISTOR is an electric circuit device that AMPLIFIES the current or voltage, or acts as a SWITCH to turn on and off the current or voltage AMPLIFY means to make larger The schematic diagram representation for a TRANSISTOR is shown below What is a TRANSISTOR? Collector KEY POINT: TRANSISTORS AMPLIFY Base Emitter

Slide 193 Collector Emitter
A small current or voltage coming into the BASE Acts as a switch or amplifier of the current or Voltage from the COLLECTOR to the EMITTER How does a TRANSISTOR work? Collector Small Current Or Voltage Switch (Base) Large Current Or Voltage Controlled By the Switch Emitter

Slide 194 The little girl uses a small amount of energy to How does a
Open a valve that releases a large amount of Energy in the form of the water How does a TRANSISTOR work?

Slide 195 + - All you need to know is:
A capacitor is a circuit element that STORES ELECTRIC CHARGE. The capacitor in the circuit below builds up charge until No current flows through it. If the 20 V voltage source Is turned off, then the capacitor will release its charge And act like a temporary voltage source to the circuit. What is a Capacitor? Capacitor 20V + R 2 = 4Ω R = 2Ω - 1 0V All you need to know is: CAPACITORS STORE ELECTRIC CHARGE

Radio Circuit Exhibit: Do Not copy Example of a Ear piece
Resistors Op Amp Antenna Tuner to Change channels Transistor 1.5 V Battery On/off switch Ear piece Jack Capacitor This is the Circuit of a Basic radio. See how Many circuit Components You can recognize (this uses a Rectangle for Resistors)

When the two coils are wrapped around an iron core, it makes the magnetic field stronger and, therefore, changes the amount of voltage and current in the right side coil. This device is called a TRANSFORMER. A TRANSFORMER DOES NOT CREATE POWER; IT TRADES VOLTAGE FOR CURRENT What is a TRANSFORMER?

Characteristic Have a constant volume and a constant shape (example: ice) Has a constant volume but takes the shape of its container (example: water) Does not have a constant volume or a constant shape (example: steam) So much energy has been added that electrons are separated from the nucleus State Solids: Molecules Are held rigidly Liquids: Stay loosely together Gases: Move about freely Plasma: Atoms Are broken apart Diagram What are the 4 states of matter? H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O What is PLASMA? Extremely HOT! = + - = + - -

Slide 198 Which way Does ELECTRIC CURRENT flow? + -
Ben Franklin made several discoveries concerning electricity. Among them, he thought that it was the positive charges that were moving through a circuit (protons were not discovered until over 100 years later). He was wrong. It is the electrons (negative charges) that flow in the other direction. However, we still consider CURRENT FLOW to be from the positive terminal around the circuit to the negative terminal. WE DON’T CARE WHICH WAY ELECTRONS FLOW—WE CARE ABOUT CURRENT FLOW. Which way Does ELECTRIC CURRENT flow? + - I (Current flow) Electron flow

Slide 199 How do you Compute the
Force Between two Electric Charges? Slide 67 introduced the formula for the Force between two objects with mass There is a similar formula for the force Between two electric charges: : F = G m1m2 d2 F = k q1q2 Universal Gravitational Constant Coulomb’s Law Mass of two objects Charge on two objects

Slide 200 How does Distance Affect the Force Between Electric Charges?
The distance between two electric charges is cut in half. What is the Effect on electrical attraction? Old New Step 1: Ratio Step 2: Square Result: Old = = 4 New When the electric charges are moved to ½ of the previous distance, the electric field force between them is 4 times stronger. 2m 1m These problems are the Same as those on slides 70 and 71

Slide 201 What is Direct and Alternating Current? ~
The current we have talked about is called Direct Current (DC) Because it moves in one direction. Alternating Current (AC) moves in a back and Forth Motion. This is the best way to transmit Electricity over large distances because Electrons move a short distance back and forth rather than many miles through power lines. Fan has an AC to DC Converter ~ Current comes out of the wall as AC at 120 V and 60 Hz (back and forth movements per Second), but is converted to DC by Electric fans or washing machines. This is the symbol For an AC voltage source

How can Energy be Transferred Between two places? There are two ways ENERGY can be transported from one place to another. First, energy can be put into an object with mass. The object will then move between two points and then transfers its energy when it arrives at its destination When you throw a ball, the ball carries Energy and then transfers it to wherever It lands

Slide 203 WAVES ARE PURE ENERGY What is a wave?
WAVES are the main way nature transports energy from one place to another. Waves can move energy from one place to another without being carried by an object with mass. WAVES ARE PURE ENERGY Waves have NO mass or weight, but they might use objects with mass to be transported from one place to another.

Slide 204 What kinds Of waves are there?
There are 2 kinds of waves we will talk about in this class: What kinds Of waves are there? TRANSVERSE WAVES move up and down as they travel through space. Think ROLLERCOASTER LONGITUDINAL WAVES move back and forth as they travel through space. Think SPRING.

What is a MEDIUM? A medium is a substance with mass through which a wave moves. TRANSVERSE WAVES, such as light waves, can move without a medium. That’s why they can travel through the vacuum of space from the Sun to the Earth. Light waves move faster through a vacuum than they do through a medium such as air. LONGITUDINAL WAVES, such as sound waves, can ONLY move through a medium. Consequently, there is NO SOUND in outer space. Sound waves move faster through a more dense (thick) medium, such as water than through a less dense medium such as air.

What are MEDIUMS? A MEDIUM is a substance that a wave travels through, such as air or water. ELECTROMAGNETIC (Light) Waves DO NOT need a Medium (but they CAN travel through a medium) LONGITUDINAL Waves DO need a Medium The Birthday Girl is floating in outer space, where there is NO AIR, with a police car. She can see its lights because light waves DO NOT need a MEDIUM She CANNOT hear its siren because sound waves DO Need a medium

Slide 207 What is a Transverse Wave?
ELECTROMAGNETIC WAVES are a type of TRANSVERSE wave Electromagnetic waves move at the same WAVESPEED in a vacuum ( a vacuum is a place with nothing in it, not even air). This speed is called the SPEED OF LIGHT and is 300,000,000 m/s, which equals 186,000 miles per second

Slide 208 What are the Parts of a Transverse wave?
TRANSVERSE WAVES move in a repeating pattern. WAVELENGTH: A wavelength is the distance between the top of one wave crest (top) and the next wave crest AMPLITUDE: Amplitude is the distance from the midpoint of the wave and the crest (top) or trough (bottom) of the wave Wavelength Crest Amplitude Trough

Slide 209 How is the Speed of A transverse Wave measured?
When a transverse wave moves through space, A wavelength is called a CYCLE. The number of CYCLES that pass a point per second is called the FREQUENCY of the wave 1 cycle per second is called a HERTZ (abbreviated Hz) Point A Crest 2 Crest 1

Slide 210 Example of Frequency
At 0 seconds, crest 1 is at point A. At 1 second, crest 2 is at Point A. This is a FREQUENCY of 1 Hz Example of Frequency Point A 0 seconds Crest 2 Crest 1 Wave movement Crest 1 Crest 2 1 second

Slide 211 Example of Frequency 2 cycles 2 Hz ½ s 4 3 2 1
At 0 seconds, crest 0 is at point A. At 1 second, crest 2 is at Point A. How many cycles have passed point A? What is the frequency of the wave? What is the period of the wave? 2 cycles 2 Hz ½ s Point A Frequency = Cycles Second 0 seconds 4 3 2 1 Period = Frequency Wave movement 1 second 4 3 2 1

Slide 212 What is the PERIOD of a wave? 4 3 2 1 ¼ s ¼ s ¼ s ¼ s
The PERIOD of a wave is the amount of time it takes one cycle to pass Point A. If 4 cycles (wavelengths) pass by point A in 1 second, then it takes ¼ second for one cycle to pass. What is the PERIOD of a wave? 0 sec Point A 4 3 2 1 Wave movement 4 cycles per sec is 4 Hz 1 sec Mathematically, the Period is the reciprocal of the frequency. Period = frequency ¼ s ¼ s ¼ s ¼ s

Slide 213 Example of Frequency 4 3 2 1 4 3 2 1
At 0 seconds, crest 0 is at point A. At 1 second, crest 4 is at Point A. This is a FREQUENCY of 4 Hz. Point A 0 seconds 4 3 2 1 Wave movement 4 3 2 1 1 second

Slide 214 Example of Frequency 4 cycles 2 Hz ½ s 4 3 2 1 4 3 2 1
At 0 seconds, crest 0 is at point A. At 2 seconds, crest 4 is at Point A. How many cycles have passed point A? What is the frequency of the wave? What is the period of the wave? 4 cycles 2 Hz ½ s Point A Frequency = Cycles Second 0 seconds 4 3 2 1 Period = Frequency Wave movement 2 second 4 3 2 1

Slide 215 What are the abbreviations and UoM for waves?
These are the abbreviations and UoM used for waves: Variable Symbol UoM Frequency f Hz (Hertz) Period T s (seconds) Wavelength λ m (meters) (“Lambda”) Wavespeed v m/s

What is Wavespeed? Wavespeed = Wavelength • frequency or v = λ • f If you count the number of cycles (wavelengths) that pass point A in 1 second and then multiply this by the length of each wave (λ) you will get the speed (velocity) of the wave that has passed point A in 1 second. This is the WAVESPEED

Example of Wavespeed Wavespeed = Wavelength • frequency or v = λ • f A wave with a wavelength of 2 mm has a frequency of 5 Hz. What is its wavespeed? v = ? v = λ • f λ= 2mm f = 5 Hz v = 2 mm • 5 Hz v = 10 mm/s f = 5 cycles (wavelengths) per second λ = 2 mm Point A

Slide 218 What is Superposition Of waves? What are “IN PHASE” waves?
When two waves occupy the same space, they are said to be SUPERIMPOSED. This is called SUPERPOSITION. When two waves are Superimposed, the Amplitudes (heights) of The waves are added to each other. The maximum amplitudes of the two waves here are in the same place. These waves are said to be “IN PHASE”. What is Superposition Of waves? This is called “Constructive Interference” What are “IN PHASE” waves?

Slide 219 What is Superposition Of waves? What are “OUT OF PHASE”
Amplitude = +3 When two waves are “OUT OF PHASE,” they can cancel out and result in an amplitude that is less than the amplitudes of each of the waves This is called “Destructive Interference” Amplitude = -3 What are “OUT OF PHASE” waves? When the waves are added, The result is an amplitude = 0

Slide 220 What is an Electromagnetic Wave?
An ELECTROMAGNETIC WAVE is a type of TRANSVERSE WAVE caused by atoms producing a wave that is part electrical and part magnetic. Electromagnetic waves are the most common type of waves in the universe. All of the energy we receive from the sun is in the form of electromagnetic waves. Electromagnetic waves all travel at exactly the same speed, in a vacuum (a vacuum is a place where nothing exists, not even air) the SPEED OF LIGHT. This speed is 300,000,000 m/s or 3 X 10 m/s (this is 186,000 miles per second). The SPEED OF LIGHT is represented by the symbol c 8

Slide 221 Summary of the Different types Of waves Highest Frequency
TRANSVERSE WAVES move up and down LONGITUDINAL WAVES move back and forth ELECTROMAGNETIC WAVES are the most important kind of transverse wave SOUND WAVES and SPRINGS are the most common kind of longitudinal wave Types of Electromagnetic Waves Gamma Rays X-rays Ultraviolet Light Visible Light Infrared Wave Radio Waves Highest Frequency Lowest Frequency

The wavelength of an electromagnetic wave determines whether an object will react to it. For example, our eyes see wavelengths in the 400 to 700 nanometer range as visible light. How does the Wavelength of an electromagnetic Wave affect it? nm is “nanometer” and is One billionth of a meter This is called The Electromagnetic Spectrum

How does the Wavelength of an electromagnetic Wave affect it? The six major kinds of electromagnetic waves, from longest wavelength and lowest frequency to shortest wavelength and highest frequency are: Radio waves Used by radio/TV stations Infrared waves Put out by anything with heat Visible light We can see these with our eyes Ultraviolet light X-rays Used by doctors and dentists Gamma Rays Lowest frequency And longest wavelength Highest frequency And shortest wavelength

Slide 224 v = λ• f Wavespeed = Wavelength • Frequency What is the
Remember, all Electromagnetic waves travel at 300,000,000 m/s in a vacuum. This means that the WAVELENGTH and FREQUENCY of an electromagnetic wave are related by the equation 3 X 10 m/s = λ• f What is the Relationship Between the Wavelength and Frequency of an Electromagnetic wave? 8 What is the frequency of a radio wave where λ = 1 m? f = ? Solving c = λ • f, for f v = c = 3 X 10 m/s λ = 1 m f = c λ f = 3 X 10 m/s = 3 X 10 Hz 1 m Example of Electromagnetic Wavelength and frequency 8 8 8 8

Slide 225 Water What is REFRACTION?
Just as you can run faster in air than you can in water, a light wave moves faster through air than water. When a light wave going through air hits water, the side of the wave that hits the water first will slow down first. This causes the wave to bend in that direction. When light bends because of this kind of a change in medium, it’s called REFRACTION This side of the wave hits the water first, so the light refracts in that direction Direction of Light wave Water

What is DIFFRACTION? When light passes through an opening, it bends by a process called DIFFRACTION. The LONGER THE WAVELENGTH is compared to the width of the opening, the GREATER THE DIFFRACTION. Shorter wavelength = Less Diffraction Longer wavelength = Greater Diffraction

What is POLARIZATION? POLARIZATION means that only waves oriented in a certain direction can pass through a barrier. Glass can be POLARIZED so that only some of the light can pass through. Below, only the lightwave oriented up and down can pass through the glass. The sideways lightwave is blocked. THINK OF THE COUCH GOING THROUGH THE DOOR Up and Down Sideways

Slide 228 What are SOUND WAVES?
SOUND WAVES: As sound comes out of a speaker, it produces a LONGITUDINAL WAVE that causes the air molecules to press together then be released in alternating high pressure/low pressure areas. This is the same pattern as the spring. Slide 228 What are SOUND WAVES? Speaker Areas of HIGH air pressure Wave Direction Areas of LOW air pressure

What are SOUND WAVES? SOUND WAVES: Sound produces a LONGITUDINAL WAVE that causes the air molecules to move back and forth. This is the same pattern as the spring. “Longo” makes LONGITUDINAL waves by squeezing his accordian back an forth A spring moving back and forth also makes a LONGITUDINAL WAVE

Slide 230 Direction of Train
A moving train sounds its horn. The train is moving into the soundwave that goes out in front of the train. This “squeezes” the wave in front of the train. The train “runs away” from the soundwave going out the back of the train. This “stretches” this soundwave. A SHORTER wavelength produces a HIGHER pitch A LONGER wavelength produces a LOWER pitch What is the DOPPLER EFFECT? Direction of Train Longer Wavelength = Lower Pitch Short Wavelength = Higher Pitch

Slide 231 Loud Quiet Loud Quiet Quiet Loud Medium Loud What are BEATS?
BEATS: When two sounds of different frequencies are heard together, the sound alternates between loud and quiet. Sound waves can be added to one another and can subtract from one another just as transverse waves do. Loud Quiet Loud Quiet Quiet Destructive Interference Loud Medium Constructive Interference Loud

Slide 232 Frequency of beats is computed as follows:
How is the Frequency of BEATS computed? Frequency of beats is computed as follows: fbeat = | f2 – f1 | The absolute value symbols | | mean that the answer is always positive. What is the beat frequency of a 340 Hz and 360 Hz wave? f beat = | 340 – 360 | = 20 Hz What is the beat frequency of a 400 Hz wave and a 250 Hz wave? f beat = | 400 – 250 | = 150 Hz Beats: Example

How are Electric and Magnetic Fields Related? In an electromagnetic wave the electric part of the wave travels at a right angle to the magnetic portion of a wave

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