Motion How fast is fast?

 Frame of reference – a system used Motion  Motion – change in position relative to a reference point.  Frame of reference – a system used to identify the precise location of an object

Distance Vs. Displacement  Distance: How far an object has moved.  SI unit = meter  “Total steps taken”  Total Displacement: The distance and direction of an object’s change in position from the starting point  Displacement includes direction  “How far are we from where we started?”

Distance Vs. Displacement

SIDENOTE: Direction?!?!? by both magnitude AND direction  Vector – quantity that is described by both magnitude AND direction  Ex: 10m/s south, 8m upward, 9.8m/s2 to the ground

SIDENOTE: Vector  Distance is a Scalar (Just a number)  Displacement is a Vector (A Number and A Direction)  The image to the right shows vector addition (multiple vectors). We will deal with this in a bit.  The arrow length indicates the magnitude of velocity  Vector Video!!!

Speed and Velocity is moving changes it’s position  Speed – how fast an object moving  Does NOT include a direction is  Velocity – rate at which an object changes it’s position  Basically, it is how long it takes an object to get from point A to point B  Includes both magnitude AND direction

Speed vs. Velocity Units for:  Speed – distance / time  Simply the magnitude of Velocity  S = d/t  Velocity – displacement / time Speed WITH a direction  V = d/t   SI  Units for: Distance+Displacement Time = seconds (s) = meters (m) Speed+Velocity = meters/second (m/s)

Scalar vs Vector  Scalar (Just a number)  Distance  Speed  Vector (A Number and A Direction)  Displacement  Velocity

Two Kinds of Speed We will almost ALWAYS calculate average speed total divided distance traveled by the total time  Ex: speed on trip to Orlando from Chas  Instantaneous Speed: speed at a specific instant  Ex: speedometer

Practice which travels from New York City hours? to Los Angeles (4800  What is the speed of a commercial jet which travels from New York City hours? to Los Angeles (4800 km) in 6  What would the velocity be?  800 km/hr WEST

More Practice travels 355 seconds? speed meters of a bike that in  What is the travels 355 seconds? speed meters of a bike that in 103.7  What would the velocity be?  3.42 m/s DOWNHILL

train travels 100 km/hr for 2 hours. What distance has it traveled? S And Even More Practice! A train travels 100 km/hr for 2 hours. What distance has it traveled? S = d/t = d / 100km/hr 2hrs 200km = d

SIDENOTE: Velocity  A vector is a quantity with a direction  Notice speed has no + or –  Velocity however, can be + or – magnitudes. That indicates a direction n  A vector is a quantity with a direction  Positive velocity is right and up  Negative velocity is left and dow

Unit 6.1: Motion Assessment 1 will cover information from slides 1- 15

Position vs Time Graphs Pictures say 1000 words…

Position vs Time Graphs graph.  Motion can be studied using a position vs. time graph.  POSITION (or DISPLACEMENT) on the vertical axis  TIME on the horizontal axis.  The SLOPE of the line indicates the VELOCITY

Calculating Slope finding the change in position (y2 – y1) over the  Slope (which is the velocity), can be calculated by finding the change in position (y2 – y1) over the change in time (x2 – x1) RUN OR RISE over

Calculating Slope  So let’s try it:

Calculating Slope 1) Choose 2 points to start y2 = x2 = and end at. 2) Calculate the change between the Difference in Position (y) = Difference in Time (x) = Calculate Slope = Position / Time (y2 – y1) / (x2 – x1) points. 3) AND REMEMBER, SLOPE = VELOCITY

Different Slopes mean… a POSITIVE velocity greater the velocity the  POSITIVE slope indicates  Positive velocity means it is a POSITIVE velocity moving forward greater the velocity  The greater the slope, the  The less the slope, the smaller the velocity Which has a greater velocity? A – It has a greater slope and is steeper.

Different Slopes mean… a ZERO velocity Which has a greater velocity?  ZERO slope indicates a ZERO velocity horizontal  Zero slope means that the line is Which has a greater velocity? They are both the same. Neither is moving.

Different Slopes mean… Which has a greater negative velocity?  NEGATIVE slope indicates a NEGATIVE velocity  Negative velocity means negative direction. that the object is traveling in the Which has a greater negative velocity? B – It has a greater slope, therefore a greater neg velocity

Put it all together… So what is happening at each of these positions? B) C) D) Moving forward Stopped Moving in negative direction Could you calculate the velocity for each portion? YES! Rise over Run

Unit 6.2: Position v. Time Graphs Assessment 2 will cover information from slides 16-25

MOMENTUM  Momentum – the motion of mass  If an object is moving, it has momentum ▪ An object with lots of momentum will be hard to stop. ▪ An object with little momentum will be easier to stop.

MOMENTUM  Law of Conservation of Momentum  Examples:  Momentum is never created or destroyed, it can only be transferred from one object to the next.  The total amount of momentum in a system will be conserved. ▪ The TOTAL MOMENTUM in a system cannot increase or decrease.  This applies any time 2 (or more) objects collide.  Examples:  When a pool ball is hit into a stationary pool ball, causing that to move with the same momentum 2nd ball  When a golf club hits a golf ball off of a tee, the momentum of the golf club will be transferred to the ball.  Two football players hitting each other on a football field.

MOMENTUM Momentum of Object1 P1 M1 * V1 = Momentum P2 M2 * V2  Momentum is CONSERVED. Never created or destroyed. So in our simple examples…  The equation: Momentum of Object1 P1 M1 * V1 = Momentum P2 M2 * V2 of Object2 M1 V1 = mass of 1st object M2 = mass of 2nd object velocity of 1st object V2 = velocity of 2nd

MOMENTUM with a mass of 12kg, what will be the velocity that the  A 3kg ball is traveling at 8m/s. If it hits an empty bottle, with a mass of 12kg, what will be the velocity that the bottle travels assuming the ball stops momentum is transferred? on impact and all M1 * V1 = M2 * V2 So if we knew that… 3kg * 8m/s 24kg*m/s = 12kg * V2 = V2 = 2m/s

ACCELERATION

Review that: measure of distance over time direction  Remember  Speed is a measure of distance over time  How long it takes you to get from one place to another  Velocity was speed in a direction

Scalar vs Vector  Vector (A Number and A Direction)  Scalar (Just a number)  Distance  Speed  Magnitude of Acceleration  Vector (A Number and A Direction)  Displacement  Velocity  Acceleration

What is acceleration?  Change  Change in velocity can be caused by:  Acceleration is the rate of change of velocity.  A change in velocity can be caused by:  Change  Speed in speed up or slow down  Change in direction

3 ways to cause acceleration Direction at green light  Increasing speed  Example: Car speeds up at green light  Decreasing speed screeeeech  Example: Car slows down at stop light  Changing  Example: Direction Car takes turn (can be at constant speed)

Zero Acceleration be changing to be zero, the velocity cannot  For acceleration be changing to be zero, the velocity cannot  ONLY when you in one direction are traveling at a constant speed  So, would it still be zero if you were traveling at a constant speed in a circle?

The Math a = change in velocity change in time acceleration Vf –Vi divided by the a = change in velocity change in time  A = Vf –Vi t  Units = m/s2  m/s2 ALWAYS means acceleration

FORMULAS:  A = Vf – Vi t  T = Vf – Vi A  Vf = (A x t) + Vi

The numbers never lie… means velocity is increasing gradually rapidly  A SMALL acceleration means velocity is increasing gradually  A LARGE acceleration rapidly means velocity is increasing  A POSITIVE acceleration means an object is speading up  A NEGATIVE acceleration means an object is slowing down  This is called deceleration

Example your velocity goes from 10 m/s to 40 m/s in 5 secs.  You are driving from school home and your velocity goes from 10 m/s in 5 secs. m/s to 40  What is your acceleration?

Example a football is thrown from rest with an acceleration of  If a football is thrown from rest with an acceleration of 8.5 m/s2, and had an 25m/s, how long was final velocity of the football accelerating?

 In a vacuum, things fall towards Gravity and Acceleration  Gravity is the force that pulls everything toward the center of the Earth  Acceleration due to Gravity = 9.8m/s2  In a vacuum, things fall towards 9.8m/s2 every second  A vacuum is a space entirely void of matter the earth at  When not in a vacuum, air resistance will slow down a falling object. Hammer vs Feather on the Moon (1 min) http://www.youtube.com/watch?v=5C5_dOEyAfk

Gravity and Slinky!  Just cuz it looks cool …

Falling From Space over 24 MILES up exactly 1 http://www.youtube.com/watch?v=dOoHArAzdug  In a vacuum, things fall towards the 9.8 m/s2 every second earth at  Jumps from over 24 MILES up  At exactly exactly exactly 1 2 5 second, traveling at 9.8m/s seconds, traveling at 19.6m/s seconds, traveling at 49m/s

Gravity and Acceleration objects to stop accelerating and reach a  In real life, sometimes wind resistance causes objects to stop accelerating and reach a maximum velocity  This is what causes “Terminal Velocity”  Terminal Velocity for a falling Human is ~56 m/s (~120mi/hr)

Law of Universal Gravitation object. But the pulls aren’t all equal.  Technically, gravity pulls everything towards everything else  Every object exerts a gravitational pull on every other object. But the pulls aren’t all equal. They depend on a few things  The gravitational force between depends on 2 things:  The MASS of the both objects two objects  As the masses increase, the gravitational force INCREASES  The DISTANCE between the two objects  As the distance increases, the gravitational force DECREASES.

Universal Gravitation: Math  r = distance between 2 objects  M1 = mass  M2 = mass of object 1 of object 2  r = distance between 2 objects  G = universal gravitational constant = 6.6726x10-11 N-m2/kg2 While standing on the Earth’s surface, you are 6378100m from the center. What is the gravitational force between earth (m=5.97219x1024 kg) and you (m=75kg)?

Universal Gravitation: Math Compare that to 2 students that each have a mass of 75kg and are only 1m apart. G = universal gravitational constant = 6.6726x10-11 N-m2/kg2  F = G (M1 * M2) r2 Compare that to gravitational force between and the earth? F = 9.8017 N you (at 150lbs)

Unit 6.3: Momentum, Acceleration and Gravity Assessment 3 will cover information from slides 26-49

ACCELERATION GRAPHS Pictures are worth even MORE than words now!

Knowing this, what do you think RECALL… Motion can be graphed Acceleration is merely a speed over time change in Knowing this, what do you think the two axis of our acceleration graphs are going to be?

ACCELERATION GRAPHS  SLOPE = Acceleration  The vertical axis (y) will be velocity (m/s)  The horizontal axis (x) will be time (s)  SLOPE = Acceleration

GRAPHING  How can you tell? these is a velocity graph, AND ACCELERATION Which of these is a velocity graph, and which is an acceleration graph?  How can you tell?

velocity changes over time VS TIME GRAPHS Velocity v. Time graph shows velocity changes over time how ANY slope at all shows an acceleration

POSITIVE acceleration DIFFERENT SLOPES… A POSITIVE slope means there is POSITIVE acceleration  Positive acceleration means speeding up Which of these lines has a greater acceleration? B – It has a greater slope

acceleration of 0m/s2 DIFFERENT SLOPES… A slope of ZERO shows an acceleration of 0m/s2  This just means there is a constant speed  Slope of zero = horizontal line Which of these lines has a greater acceleration? Neither – Both are zero has a greater velocity? A – It has velocity of 130m/s

NEGATIVE acceleration DIFFERENT SLOPES… A NEGATIVE slope means there is NEGATIVE acceleration  Negative acceleration means slowing down  Slowing down = DECELERATING Which of these lines has a greater deceleration? A – It has a greater slope

Positive acceleration SLOPES: RECAP Line slopes up Velocity is increasing Positive acceleration Line slopes down Velocity is decreasing Negative acceleration Straight Horizontal line Constant velocity No acceleration

CALCULATING ACCELERATION is the formula for acceleration?  What is the formula for acceleration? velocity at 1 velocity at 4 acceleration s? between 1 and 4 seconds? A = (Vf-Vi) t = (2m/s – 8m/s) 3 s - = - 6 m/s = -2 m/s2 - 3s

PUTTING IT ALL TOGETHER Tell me what is happening for each line A  A – Decelerating B – Constant velocity (0 m/s) AND no acceleration. This is STOPPED. C – Acceleration D – Constant velocity (15 m/s) AND no acceleration. is NOT STOPPED This

Unit 6.4: Velocity v. Time Graphs Assessment 4 will cover information from slides 50-61