Today’s Plan – September 9

InspiredBikeInspiredBike Introductions - meIntroductions - me Class Expectations and RoutinesClass Expectations and Routines

ResourcesResources WebWeb

Who are you?Who are you? Start Unit 1 – KinematicsStart Unit 1 – Kinematics Lab 1 – velocity and speedLab 1 – velocity and speed HOMEWORKHOMEWORK

What is Science?

3 things that shape our society:3 things that shape our society: ArtArt ReligionReligion ScienceScience

Science is the study of nature’s rulesScience is the study of nature’s rules And physics…And physics…

Physics The science that explains all

other sciences.

Physics

It explains the large…It explains the large… And the smallAnd the small

Examples of physics…

We start with Mechanics

““Classical” orClassical” or“Newtonian” physics“Newtonian” physics

Galileo & Newton are the Galileo & Newton are the heroesheroes

Mechanics

Objects pushing, Objects pushing, pulling, and bumping pulling, and bumping into each other.into each other.

““The study of how The study of how forces change the forces change the motion of an object”motion of an object”

Motion

Key to understanding Key to understanding mechanicsmechanics

A change in motion is A change in motion is an indication that a an indication that a force is being applied. force is being applied.

It is easy to recognize.It is easy to recognize.

When we describe motion it’s called KINEMATICS…

(not the explanation of the motion)

The “what” not the “why”.

What’s necessary to describe motion? Think about a moving object…Think about a moving object…

Like a race car… or the bikes… or…Like a race car… or the bikes… or…

To describe motion we need 5 things: 1. The object – What 1. The object – What

are we tracking? How are we tracking? How do we describe the do we describe the object?object?

2. Position – Where is 2. Position – Where is it?it?

3. Time – When is it 3. Time – When is it there? there?

4. Velocity – How fast 4. Velocity – How fast is it going?is it going?

5. Acceleration – Is 5. Acceleration – Is the motion changing?the motion changing?

We’ll leave acceleration for later…

Some finer points of Some finer points of speed and velocity.speed and velocity.

Explain to me…

Distance vs displacement?Distance vs displacement? Speed vs velocity? Speed vs velocity?

Instantaneous vs average

What is the difference?What is the difference? Think of an example where we would use Think of an example where we would use

each?each? Would we calculate them differently?Would we calculate them differently?

Average Speed =

Total distance / total timeTotal distance / total time

Average Velocity = Total displacement / total timeTotal displacement / total time

Displacement from start point to finish point in a straight line.

Velocity (& displacement) must always include a direction!!!

Simplifications and assumptions

1. 1. Point ObjectPoint Object An object is made of gazillions of An object is made of gazillions of

specific points, but specific points, but wewe look at the whole look at the whole object as a single point.object as a single point.

2. 2. Reference PointReference Point Measure distance relative to something Measure distance relative to something

(most of the time (most of the time wewe will measure in will measure in respect to Earth’s surface)respect to Earth’s surface)

Today’s Lab

READ THE LAB HANDOUT!READ THE LAB HANDOUT! Discuss how you are going to run the lab Discuss how you are going to run the lab

with your partners.with your partners. Each person hands in a lab sheet.Each person hands in a lab sheet. And…And…

September 11! Today’s Plan:

HomeworkHomework Lecture #2 – AccelerationLecture #2 – Acceleration Lab #2Lab #2

Homework and Lab

Homework – answers please…Homework – answers please… Lab – what questions do you have?Lab – what questions do you have?

Quick Review - Describe Motion…

ObjectObject PositionPosition TimeTime VelocityVelocity AccelerationAcceleration

Simplifications and assumptions

All measurements are relative to a All measurements are relative to a reference frame.reference frame.

Point objects Point objects We’re not concerned with odd We’re not concerned with odd

shapes or spinning objectsshapes or spinning objects

Displacement =

Measure Measure from start from start point to point to finish finish point in a point in a straight straight line.line.

Average speed =

Total distance / total timeTotal distance / total time

Average Velocity =

Total displacement / total timeTotal displacement / total time

Velocity always must include a direction!!!!

Acceleration

Instantaneous Velocity

The rate of motion in one direction at a The rate of motion in one direction at a given instant in time (car’s speedometer).given instant in time (car’s speedometer).

Hmmm…

An instant in time = 0 An instant in time = 0 secondsseconds

Distance traveled in an Distance traveled in an instant = 0 metersinstant = 0 meters

Velocity = Velocity = displacement / timedisplacement / time

0/0 = undefined??!!!0/0 = undefined??!!!

Solution…

Pick smaller and smaller interval:Pick smaller and smaller interval:Eye in the skyEye in the skyRubber tubes across the roadRubber tubes across the roadRadarRadar

Smaller “average” – approaches Smaller “average” – approaches instantaneousinstantaneous

Constant Velocity =

(uniform motion) motion in a straight (uniform motion) motion in a straight line at the same speed.line at the same speed.

Can You Accelerate?

1 m/s/s means…1 m/s/s means… An object speeds up one meter per An object speeds up one meter per

secondsecond EVERY SECONDEVERY SECOND

Acceleration occurs

When velocity When velocity changes changes

This means:This means: 1. Speed 1. Speed

changeschanges……

Or…Or…

Accelerated motion – part 2

2. 2. Direction changesDirection changes

Acceleration…

3. Both Change3. Both Change

(speed and direction)(speed and direction)

Speed Changes:

Speed up, increase, Speed up, increase, positive accelerationpositive acceleration

Slow down, decrease, decelerate (negative acceleration)

Direction Changes:

Turns right, leftTurns right, left CurvesCurves Turns aroundTurns around

Acceleration Equation

Acceleration = change in velocity / Acceleration = change in velocity / timetime

a = v/ta = v/t

Example

You start from rest and accelerate to 27 m/s You start from rest and accelerate to 27 m/s in 9 seconds…in 9 seconds…

Or…

Acceleration =Acceleration = (Final Velocity – Initial Velocity) / Time(Final Velocity – Initial Velocity) / Time

a = (va = (vff – v – vii) / time) / time

Example

Starting at 2 m/s and speed up to 6 m/s over Starting at 2 m/s and speed up to 6 m/s over an 8 second period of time…an 8 second period of time… What is the acceleration?What is the acceleration?

One more…

You accelerate at a rate of 2 m/sYou accelerate at a rate of 2 m/s22. Starting . Starting at 1 m/s, how fast are you going after 5 at 1 m/s, how fast are you going after 5 seconds?seconds?

Acceleration can be large due to:

1. Large change in velocity1. Large change in velocity

Acceleration can be large due to:

2. Change in velocity over a short period of time.2. Change in velocity over a short period of time.

                                                                                        

Homework

Read Chap. 2.4Read Chap. 2.4Finish labFinish labComplete handoutComplete handout

September 15: Today’s Plan:

1.1. Attendance Attendance

2.2. Grade Homework questionsGrade Homework questions

3.3. Lecture #3 – Acceleration, freefall and Lecture #3 – Acceleration, freefall and graphical representationgraphical representation

4.4. Domino Lab – more velocity…Domino Lab – more velocity…

5.5. Homework – NOTE – no “Race Car WS”Homework – NOTE – no “Race Car WS”

A little review

Three ways to change velocity?Three ways to change velocity? Change speedChange speed Change directionChange direction Change bothChange both

Two ways to make acceleration large. Make the velocity change a lot.Make the velocity change a lot.

aa = = vv/t/t

Make the time interval very small.

a = v/t

Quick Review…

Acceleration:Acceleration:

in velocity / time

If a car that is moving at 24.5 meters per second (about 55 mph) hits a tree and comes to a complete stop in 2 seconds – what is the car’s acceleration?

Acceleration

5:30 of this video clip: 5:30 of this video clip: “click on me”“click on me”

Position, velocity and acceleration Velocity = rate of change of positionVelocity = rate of change of position

Displacement / timeDisplacement / time v = d/tv = d/t

Acceleration = rate of change of velocityAcceleration = rate of change of velocity Velocity / timeVelocity / time a = v/ta = v/t

If acceleration is constantIf acceleration is constant Then the rate of change for velocity is constantThen the rate of change for velocity is constant

Let’s try something

TimeTime a (m/s/s)a (m/s/s) V (m/s)V (m/s) X (m)X (m)

00 33 00 00

11 33 33 ????

22 33 66 ????

33 33 ???? ????

Soooo?????

If acceleration is constant…If acceleration is constant… Velocity = a tVelocity = a t Displacement: d = ½ (Displacement: d = ½ (ΔΔv) tv) t

And d = ½ a tAnd d = ½ a t22

And d = ½ a tAnd d = ½ a t22

Let’s fill in the table…

And graph them!And graph them!

An example, please

You are accelerating at 2 m/s/sYou are accelerating at 2 m/s/s If you start from rest, how fast are you If you start from rest, how fast are you

going after 1 second?going after 1 second?• 2 seconds?2 seconds?

If you start from rest, how fast are you If you start from rest, how fast are you going after 7 seconds?going after 7 seconds?

How far have you traveled in those 7 How far have you traveled in those 7 seconds?seconds?

One more factoid…

When things fall to earth they accelerate at a When things fall to earth they accelerate at a constant rateconstant rate• 10 m/s/s10 m/s/s

This is HUGE!!This is HUGE!! From now on, as long as you have a meter stick… From now on, as long as you have a meter stick…

you can tell how much time has passed!!!you can tell how much time has passed!!! d = ½ (10 m/s/s) td = ½ (10 m/s/s) t22

d = 5 td = 5 t22 for falling thingsfor falling things

Another simplification

We have been ignoring…We have been ignoring… AIR RESISTANCEAIR RESISTANCE

What happens when we factor this in?What happens when we factor this in? For falling objectsFor falling objects

Today’s Lab

Purpose - More Purpose - More averageaverage velocity practice velocity practice Goal: Determine optimum spacing for max Goal: Determine optimum spacing for max

velocity!velocity! Toppling dominosToppling dominos

Vary distance between the dominosVary distance between the dominos Measure space in between the dominosMeasure space in between the dominos Measure total distance!Measure total distance! Measure time to fallMeasure time to fall

Sept 17th Today’s Plan:

1.1. AttendanceAttendance

2.2. Go Over HomeworkGo Over Homework

3.3. Turn in Domino labTurn in Domino lab

4.4. Free Falling LectureFree Falling Lecture

5.5. Reaction Time LabReaction Time Lab

Homework: Lab, book work and Freefall Homework: Lab, book work and Freefall questions (handout)questions (handout)

Remember the human accelerator? Acceleration = 1 m/sAcceleration = 1 m/s22

Velocity increases by 1 m/s per secondVelocity increases by 1 m/s per second Distance between second markers increases Distance between second markers increases

each time.each time.

Free fall = when a falling object is only affected by gravity (no air resistance).

All objects free fall at the same speed (10 m/s)

Elapsed time versus Instantaneous Speed Time 1 secTime 1 sec Inst. Speed = 10 m/sInst. Speed = 10 m/s 2 sec2 sec = 20 m/s = 20 m/s 3 sec3 sec = 30 m/s = 30 m/s 4 sec4 sec = 40 m/s = 40 m/s

Velocity (speed) of Falling Bodies: Velocity increases due to gravity as elapsed time increases (10 m/s for Velocity increases due to gravity as elapsed time increases (10 m/s for

each second).each second). ““little g”little g”

g = 10 m/s/sg = 10 m/s/s v = g tv = g t

How do we calculate the distance traveled by free-falling objects… After 1 second, After 1 second,

Instantaneous speed = 10 m/s Instantaneous speed = 10 m/s ((notnot average velocity) average velocity)

Speed? No, I want distance …

To get average speed take initial To get average speed take initial velocity and final velocity and velocity and final velocity and divide by 2.divide by 2.

VVf f ++ V Vii

22

Distance traveled of free-falling objects… After 1 second the average speed is After 1 second the average speed is

5 m/s. 5 m/s. Distance = average speed x timeDistance = average speed x time

d = vd = vavgavg t t

After 2 seconds, how far has the object traveled?

(20 + 0) (20 + 0) = 10 m/s = = 10 m/s = avg velocityavg velocity

2 2

distance = v t

Time = 2 seconds

After 3 seconds?

(30 + 0)(30 + 0)

22

d = v t

Ughhh – 3 equations…

1.1. vvff = gt = gt

2.2. VVavgavg = (v = (vff + v + vii)/2)/2

3.3. d = v td = v t

Or…Or…

Ahhh… easier equation:

distance traveled = (1/2)gtdistance traveled = (1/2)gt22

So how far will a freely falling object that is released from rest fall in 10 seconds?

In 3 seconds?

What happens to velocity when… The object is moving The object is moving upup to begin with? to begin with?

It’s velocity slows down by 10 m/s/sIt’s velocity slows down by 10 m/s/s

Until…Until… It stops and starts falling…It stops and starts falling…

And then its speed increases by 10 m/s/sAnd then its speed increases by 10 m/s/s

Initial upward speed of 20 m/s

T = 1 secondT = 1 second V = vV = vii - at - at V = 20 – 10 m/sV = 20 – 10 m/s

T = 2 secondsT = 2 seconds V = 20 – 20 m/sV = 20 – 20 m/s

T = 3 seconds ? T = 3 seconds ?

Lab!

Trying to verify constant accelerationTrying to verify constant acceleration Can we measure acceleration?Can we measure acceleration?

We’ll need to approximateWe’ll need to approximate Take care in the lab!Take care in the lab!

September 21 Plan:1.1. Review homework Review homework

2.2. Questions on lab?Questions on lab?

1.1. Graph expectationsGraph expectations

3.3. Accuracy vs. precisionAccuracy vs. precision

4.4. Lab #4 Lab #4

5.5. Homework – WorksheetHomework – Worksheet

11stst test on Friday!!!! test on Friday!!!!

Free-fall Notes…

Accelerates at constant Accelerates at constant raterate• g = 10 m/s/sg = 10 m/s/s

Change in v = atChange in v = at• d = ½ gtd = ½ gt22

Throwing an object straight up

When an object is at its highest When an object is at its highest point – it has a speed of “0”point – it has a speed of “0”

The change in speed (acceleration) each The change in speed (acceleration) each second is the same second is the same whether it is going up or down.whether it is going up or down.

Real Life… When you throw a ball straight up – When you throw a ball straight up –

the speed that it hits your hands the speed that it hits your hands when you catch it is the same as when you catch it is the same as when you threw it.when you threw it.

Accuracy versus Precision

Accuracy = how close to “correct”

Precision = smallest unit used

Don’t sacrifice accuracy (care in taking measurements)

Don’t sacrifice precision by dropping a bunch of digits (no more digits than smallest measurement).

Graphing expectations

TitleTitle Label axisLabel axis

What it is and What it is and what the units arewhat the units are

Best fit lineBest fit line

1. Distance/Time Plots Time is typically on horizontal axis (x-axis).Time is typically on horizontal axis (x-axis). Distance is on vertical axis (y-axis).Distance is on vertical axis (y-axis).

Time

Distance

2. Velocity/Time Plot

If the line is horizontal and straight – the If the line is horizontal and straight – the object is moving at a constant velocity.object is moving at a constant velocity.

Time

Velocity

3. Acceleration/Time Plot

We will limit ourselves to constant We will limit ourselves to constant accelerationacceleration

Time

Acceleration

Lab

Consider the accuracy and precision of your Consider the accuracy and precision of your datadata

Several steps – let’s set it up.Several steps – let’s set it up.

September 23 Review

HomeworkHomework More graphical analysisMore graphical analysis ReviewReview Lab 6Lab 6

Graphical Representation of Motion

Graphs can give a quick picture of what happens…

Graphing Rule #1

Independent variable – Independent variable – the variable that you changethe variable that you change goes on horizontal axis (x-axis).goes on horizontal axis (x-axis).

Dependent variable – Dependent variable – the variable that you measurethe variable that you measure goes on the vertical axis (y-axis).goes on the vertical axis (y-axis).

1. Distance/Time Plots Time is typically on horizontal axis (x-axis).Time is typically on horizontal axis (x-axis). Distance is on vertical axis (y-axis).Distance is on vertical axis (y-axis).

Time

Distance

1. Distance/Time Plots

If line is straight and horizontal – the If line is straight and horizontal – the object is at rest.object is at rest.

Time

Distance

1. Distance/Time Plot

If the line is at an angle, but is still If the line is at an angle, but is still straight – the object is moving at a straight – the object is moving at a constant velocity.constant velocity.

Time

Distance

1. Distance/Time Plot

If the line is curving up – the object is If the line is curving up – the object is speeding up (accelerating).speeding up (accelerating).

Time

Distance

1. Distance/Time Plot

If the line is “curving down” – the object is If the line is “curving down” – the object is slowing down (decelerating).slowing down (decelerating).

Time

Distance

1. Distance/Time Plot

If the line is a hill or a valley – the object is If the line is a hill or a valley – the object is changing direction.changing direction.

Time

Distance

2. Velocity/Time Plot

Time is on horizontal (x-axis) and Velocity Time is on horizontal (x-axis) and Velocity is on vertical (y-axis).is on vertical (y-axis).

Time

Velocity

2. Velocity/Time Plot

If the line is horizontal and straight – the If the line is horizontal and straight – the object is moving at a constant velocity.object is moving at a constant velocity.

Time

Velocity

2. Velocity/Time Plot

If the line is straight, but angled up – the If the line is straight, but angled up – the object is speeding up.object is speeding up.

Time

Velocity

2. Velocity/Time Plot

If the line is straight, but angled down – If the line is straight, but angled down – the object is slowing down.the object is slowing down.

Time

Velocity

2. Velocity/Time Plot

The steeper the line, the bigger the The steeper the line, the bigger the acceleration.acceleration.

Time

Velocity