introduction (day 0)

Introduction (Day 0)

1-D Kinematic Motion

Day One

• Find your seat• Introduction

– Syllabus– Textbooks– Homework and Lab Expectations– Room tour– Computer Etiquette and Sign-Out

• Complete the warm-up• Math Assessment• Chapter 2 Vocabulary Acceleration

How can I be successful in physics?

After Introduction

• Pickup and sign out your computer

• Log into www.plutonium-239.com

• Select the Warm-Up link

• Complete today’s warm-up and submit it

• Logout and return the computer to the cart


What would happen if I drop this?Physics I Mechanics

Mr. Roe when he was 10


Summary

• Ticket out the Door– Write down 3 things that will help you be

successful in physics.

• Homework– Chapter 2 Vocabulary Acceleration


Day 1


UEQ: How can the motion of an object be described in a measurable and

quantitative way?

†After Attendance(†EQ Sheet, Concept Map, & WebAssign)

• Place HW on my desk• †Pickup an Essential Question WS and a Translational

Motion Concept Map• Pickup and sign out your computer• Log into www.plutonium-239.com• Select the Warm-Up link• Complete today’s warm-up and submit it• †Select the webassign link from plutonium-239.com • Username: (first initial)(last name) ex. sroe• Institution: cedarcliff.pa• Password: ccphysics• Logout and return the computer to the cart

How can the position of an object be measured and quantified?

Feed Back for Google Docs

• Was anything confusing on google docs?

• Noteworthy Student Responses

Kinematics: Position

EQ: How can the position of an object be measured and quantified?

Start: Turn and tell partner where your house is, discuss where Pittsburgh is?

Units of 1-D Kinematic Motion•Reference Frames and Displacement

•Average Velocity

•Instantaneous Velocity

•Acceleration

•Motion at Constant Acceleration

•Solving Problems

•Falling Objects

•Graphical Analysis of Linear Motion

How can the motion of an object be described in a measurable and quantitative way?

Reference Frames and DisplacementAny measurement of position, distance, or speed must be made with respect to a reference frame.

For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher.


Reference Frames and Displacement

We make a distinction between distance and displacement.

Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.

Distance traveled (dashed line) is measured along the actual path.


Reference Frames and Displacement

The displacement is written:

Left:

Displacement is positive.

Right:

Displacement is negative.


Does a odometer measure distance traveled or displacement?

• Insert Picture of Jeff (aka. Cameron) here.

Ferris Bueller’s Day off Ferrari (with 301 mi) through window.


Pasco EZMotion Graph MatchHow can the position of an object be measured and quantified?

Pasco Position Match Lab(if we can get it to work:)

• Work in groups of no more than 4 people.• Return all supplies to the counter/cart.


Summary

• Ticket out the Door– Why is having a frame of reference important?– Provide an example problem and solution for position.

• HW: – Position-Match Graph Lab (Questions and Conclusions)


Day 2


After Attendance

• Place HW on my desk• Pickup and sign out your computer• Log into www.plutonium-239.com• Select the Warm-Up link• Complete today’s warm-up and submit it• Logout and return the computer to the cart

How can the velocity of an object be measured and quantified?

Kinematics: Velocity

EQ: How can the velocity of an object be measured and quantified?

Start: Compare themotion of a turtleand a train. Howdo you know it ismoving fast or slow?

The Turtle vs. The TrainCan the turtle make it to the water before a

train passes by (or hits it)?

QuickTime™ and a decompressor

are needed to see this picture.




Average Velocity

Speed: how far an object travels in a given time interval

Velocity includes directional information:

(2-1)


Instantaneous Velocity

The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short.

These graphs show (a) constant velocity and (b) varying velocity.

(2-3)


Pasco Position-Match Lab(if we can get it to work:)



WebAssign/Lab Time

• Work on WebAssign Problems 2.7 - 2.12 or Position-Match Lab

• Final Copy Criteria– State the problem (Ex. Find displacement)– Draw a picture/diagram– Provide a list or table of all given data (Ex. t = 2 s)– Solve the problem symbolically (Ex. v=x/t x = vt)– Plug in numbers and units to obtain answer.

(Ex. x = (5 m/s)(2 s)= 10 m)

• Notes about WebAssign: – Positive vs. negative answers (Try a negative sign)– Look at the final unit (hours or minutes or seconds)


Summary

• Ticket out the Door– Who was the best at matching the graph in your

group?– Provide an example problem and solution for

velocity.

• HW: – Position-Match Graph Lab (Questions and

Conclusions)– WebAssign Problems 2.1 - 2.6


Day 3


After Attendance


How can the acceleration of an object be measured and quantified?

Kinematics: Acceleration

EQ: How can the acceleration of an object be measured and quantified?

Start: How quicklycan a Porsche 911Turbo go from0 - 60? What abouta Voxel Victor?

Voxel Victor

• What is its acceleration?



2200 hp 0-60 in 1s!!!


AccelerationAcceleration is the rate of change of velocity.


AccelerationAcceleration is a vector (magnitude and direction), although in one-dimensional motion we only need the sign.

The previous image shows positive acceleration; here is negative acceleration:


How long will it take the car to stop?

7.5 sHow fast will it be going after 10 s?

0 m/s; unless the driver put it in reverse.

AccelerationThere is a difference between negative acceleration and deceleration:

Negative acceleration is acceleration in the negative direction as defined by the coordinate system.

Deceleration occurs when the acceleration is opposite in direction to the velocity.


Frame of Reference

Velocity Direction Acceleration Direction

Result: Speed Up or Slow Down?

Left (+) Left (+) Speed Up

Left (+) Right (-) Slow Down

Right (-) Right (-) Speed Up

Right (-) Left (+) Slow Down


Frame of Reference

Velocity Direction Acceleration Direction

Result: Speed Up or Slow Down?

UP (+) UP (+) Speed Up

UP (+) DOWN (-) Slow Down

DOWN (-) DOWN (-) Speed Up

DOWN (-) UP (+) Slow Down


AccelerationIs the car undergoing positive or negative acceleration?


a =10 m s

1s= 10 m s2

Is the car accelerating or decelerating?

If the following scenario takes place in 1 second, what is the car’s acceleration?

positive acceleration (velocity is in the negative direction!)

decelerating

AccelerationHow can the acceleration of an object be measured and quantified?

Using the previous reference frame is the car undergoing positive or negative acceleration?

−25.0 m s

Is the car accelerating or decelerating?

What is the car’s velocity after 1 second if it is accelerating at -10m/s2?

Negative acceleration

Accelerating

Acceleration

The instantaneous acceleration is the average acceleration, in the limit as the time interval becomes infinitesimally short.

(2-5)


Calculus Applications of Motion

Velocity is the time derivative of position:


v =dxdt

Acceleration is the time derivative of velocity: a =

dvdt

The “jerk” function is the time derivative of acceleration: j =

dadt

The change in jerk (known as the “marriage” or the “nagging spouse” function) is the time derivative of jerk:

m =djdt

Finally, the change in the change in jerk (*only known as the “death” function) is the second time derivative of jerk:

d =d2 jdt2

*Please note: Death is the only thing that can really change a jerk.

For those who have or have had calculus:

AccelerationHow long will it take the car to stop?


a =vt

=??− ??

Δt=v2 − v1

Δt=v2 − v1

??− ??=v2 − v1

t2 − t1=v2 − v1

t2 − t1=v2 − v1

t2 − t1=

−v1

t2→ t2 =

−v1

a

t2 =−15 m s−2 m s2 = 7.5 s

Find t2

Pasco Acceleration on an Inclined Track



WebAssign/Lab Time

• Work on WebAssign Problems 2.7 - 2.12 or Acceleration on an Inclined Track


(Ex. x = (5 m/s)(2 s)= 10 m)



Summary

3-2-1• Will an object speed up or slow down if . . .

– (1) it has a positive velocity and a negative acceleration?– (2) it has a negative velocity and a negative acceleration?– (3) it has a negative velocity and a positive acceleration?

• Write down 2 thing you know about motion.• Write down 1 question you have about motion

• HW: – Acceleration on an Inclined Track Lab (Questions and



Day 3 1/2: Work Day


Day 4


After Attendance


How are position, velocity, acceleration, and time related?

Kinematics: The Equations

EQ: How are position, velocity, acceleration, and time related?

Start: How far doesa Porsche 911Turbo travel as itaccelerates from0 - 60? Does itmatter if it accelerates slower?

Mechanics

• Mechanics: the study of the motion of objects– Kinematics - describes how objects move– Dynamics – deals with force and explains why

objects move


Translational Motion

• Translational Motion: Objects that move without rotating– One Dimensional: Objects move in a straight line

• Forwards or Backwards (x-direction)

• Up or Down (y-direction); [Note: Gravitational acceleration applies]

– Two-Dimensional: Objects move in an arced path (ie. Like a basketball)


The average velocity of an object during a time interval t is

The acceleration, assumed constant, is

Motion at Constant AccelerationHow are position, velocity, acceleration, and time related?

Motion at Constant Acceleration

In addition, as the velocity is increasing at a constant rate, we know that

Combining these last three equations, we find:

(2-8)

(2-9)


Motion at Constant Acceleration

We can also combine these equations so as to eliminate t:

We now have all the equations we need to solve constant-acceleration problems.

(2-10)

(2-11a)

(2-11b)

(2-11c)

(2-11d)


–* (2-11e)

Kalculamatic Equation

By starting with the equation:

(2-11a)


v=v0 +atWe can take the integral with respect to time to get:

vdtt0

t

∫ = v0 +at( )dtt0

t

∫dx

dtdt

t0

t

∫ = v0 dtt0

t

∫ + at( )dtt0

t

∫

x−x0 =v0t+ 12 at2 (2-11b)

Of course, we could take the time derivative of 2-11b to derive 2-11a!

Problem Solving Strategies

1.Read the whole problem and make sure you understand it. Then read it again.

2.Decide on the objects under study.

3.Write down the known (given) quantities, and then the unknown one(s) that you need to find.

4.Draw a diagram and choose coordinate axes.

5.What physics applies here? Plan an approach to a solution using the known and unknown quantities.


Problem Solving Strategies6.Which equations relate the known and unknown

quantities? Are they valid in this situation? Solve algebraically for the unknown quantities and check that your result is sensible (correct dimensions).

7.Calculate the solution by substituting known values (and units) and round it to the appropriate number of significant figures.

8.Look at the result – is it reasonable? Does it agree with a rough estimate?

9.Check the units again. Do you have them?


Pasco Acceleration on an Inclined Track



WebAssign/Lab Time

• Work on WebAssign Problems 2.13 - 2.17 or Acceleration on an Inclined Track


(Ex. x = (5 m/s)(2 s)= 10 m)



Summary

• Ticket out the Door– If a Porsche 911 Turbo accelerates at a rate of 6.7 m/s2 from

rest to 26.7 m/s, how far did it travel?– If a Porsche 911 Turbo now accelerates at a rate of 3.35 m/s2

from rest to 26.7 m/s, how far did it travel?– Does changing the rate of acceleration change the distance

that it travels to reach the same speed? If so, how does it affect the distance traveled?

• HW: – Acceleration on an Inclined Track (Questions and



Day 5


After Attendance



Kinematics: The Equations


Start: How can youcalculate the heightof a bridge withoutmeasuring the distance(or reading the sign)?

Rock Drop

How high is the bridge?




Falling Objects

Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity.

This is one of the most common examples of motion with constant acceleration.


Falling Objects

In the absence of air resistance, all objects fall with the same acceleration, although this may be hard to tell by testing in an environment where there is air resistance.


Doin’ the Wolfman

Falling Objects

In the absence of air resistance, all objects fall with the same acceleration, although this may be hard to tell by testing in an environment where there is air resistance.




Falling Objects

The acceleration due to gravity, g, at the Earth’s surface is approximately 9.80 m/s2.


Pasco Acceleration Due to Gravity



WebAssign/Lab Time

• Work on WebAssign Problems 2.18 - 2.22 or Acceleration Due to Gravity


(Ex. x = (5 m/s)(2 s)= 10 m)



Summary

• Ticket out the Door– If a rock is dropped off of a bridge and hits the water 6.24 s

seconds later, how high is the bridge?

• HW: – Acceleration Due to Gravity Lab (Questions and

Conclusions)– WebAssign 2.18 - 2.22


Day 8: The Graphs


After Attendance



Kinematics: The Graphs


Start: What does thegraph of velocity vs. time look like if a Porsche 911 Turbo undergoes constantaccelerates from 0 - 60? What about theposition vs. time graph?

Graphical Analysis of Linear Motion

This is a graph of x vs. t for an object moving with constant velocity. The velocity is the slope of the x-t curve.


slope=riserun

=position

time=m

s=velocity

On the left we have a graph of velocity vs. time for an object with varying velocity; on the right we have the resulting x vs. t curve. The instantaneous velocity is tangent to the curve at each point.



The displacement, x, is the area beneath the v vs. t curve. (Integrals)



So, what is the area under the “curve”?Atriangle = 1/2 b h

Atriangle = 1/2 (15 s) (15 m/s) = 112.5 m

Arectangle = b h

Arectangle = (5 s) (15 m/s) = 75 m

Atriangle = 1/2 b h

Atriangle = 1/2 (5 s) (10 m/s) = 25 m

Arectangle = b h

Arectangle = (10 s) (5 m/s) = 50 m

Atotal = 262.5 m; What does it mean?

So what does it MEAN?!?!?


2-8 Graphical Analysis of Linear Motion

The area beneath the v vs. t curveAreatriangle = 1

2 bh= 12 s( ) m

s( ) =m =displacement

Arearectangle =bh= 12 s( ) m

s( ) =m =displacement

Atotal = 262.5 m

Is the DISPLACEMENT, x!!.Does it match?

xtotal = 262.5 mPretty close;)



AGAINis the . . .

So what does it MEAN?!?!?

The AREA beneath the v vs. t curve

DISPLACEMENT, x!!.Pretty Cool?

On the left we have a graph of velocity vs. time for an object with varying velocity; It is interesting to note that the acceleration is the slope of the v-t curve.



xtotal = 262.5 m

slope=riserun

=velocity

time=m / s

s=m

s2=acceleration

Positive acceleration

No acceleration

Negative acceleration

No acceleration

Summary of Motion Graphs

Graph SlopeArea Under the

“Curve”

x-t N/A

v-t

a-t

velocity

acceleration

jerk

displacement

velocity


WebAssign/Lab Time



(Ex. x = (5 m/s)(2 s)= 10 m)



Summary

• Ticket out the DoorUsing constant acceleration (a = 10 m/s2)

– sketch a graph of velocity vs. time (tf = 5 s).

– sketch a graph of position vs. time (tf = 5 s).

• HW: – Acceleration Due to Gravity Lab (Questions and



Day 9: Summary/Work Day


After Attendance


How can position/velocity/acceleration be measured and quantified?How are position, velocity, acceleration, and time related?

†WebAssign Final Copy• Final - Definition

– 2: being the last in a series, process, or progress– 3: of or relating to the ultimate purpose or result of a process


(Ex. x = (5 m/s)(2 s)= 10 m)


†Kinematic Essential Questions

• How can the position of an object be measured and quantified?

• How can the velocity of an object be measured and quantified?

• How can the acceleration of an object be measured and quantified?

• How are position, velocity, acceleration, and time related?

†Answer these before the test.


Summary of 1-D Kinematics• Kinematics is the description of how objects move with respect to a defined reference frame.

• Displacement is the change in position of an object.

• Average speed is the distance traveled divided by the time it took; average velocity is the displacement divided by the time.

• Instantaneous velocity is the limit as the time becomes infinitesimally short.


Summary of 1-D Kinematics

• Average acceleration is the change in velocity divided by the time.

• Instantaneous acceleration is the limit as the time interval becomes infinitesimally small.

• The equations of motion for constant acceleration are given in the text; there are four, each one of which requires a different set of quantities.

• Objects falling (or having been projected) near the surface of the Earth experience a gravitational acceleration of 9.80 m/s2.


†EQ/WebAssign/Lab Time• †Answer the Essential Questions



(Ex. x = (5 m/s)(2 s)= 10 m)



Summary• Ticket out the Door

Write down two questions and their answer for the test tomorrow and turn it in.

– One conceptual problem– One mathematical problem

• HW: – Answer the Essential Questions– Acceleration Due to Gravity Lab (Questions and

Conclusions)– WebAssign Problems 2.1 - 2.22– Web Assign Final Copy


Day 10: Work Day


Day 11: Test


†After Attendance• Place HW on my desk (in Reverse Alphabetical Order):

WebAssign Final CopyEssential QuestionsLaboratory Assignment(s)

• Pickup the following:Chapter 3 Vocabulary AccelerationScantron Sheet

• Fill in the following on the scantron sheet front:Name: Write your name on it!!Subject: PIMTest: 1-D KinDate: S10Period: Block 2


quantitative way?

†1-D Kinematics Test• Do not write on Part I (the scantron questions)

• Put your name on Part II and complete it

• Verify any corrections below that have made before submitting your test.

• Complete the Chapter 3 Vocabulary Acceleration

Test Corrections

• Question


quantitative way?

Summary

• Ticket out the DoorTurn in the 1-D Kinematics Test

• HW: – Chapter 3 Vocabulary Acceleration


quantitative way?

introduction (day 0)

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