Chapter 2 Notes - Physics3310 - homephysics3310.wikispaces.com/file/view/Chapter+2+Notes.pdf/...Physics 3310 Chapter 2 Notes Mr. Kim 7 Speed and Velocity •Chapter 2. Describing Motion:

Physics 3310 Chapter 2 Notes

Mr. Kim 1

Chapter 2 NotesBy: Mr. Kim

Physics 3310-xx

• Definitions:

• Kinematics – Study of Motion• Kinetic Energy - Energy associated with motion•

• Motion in physics is broken down into 3 categories• 1.) Translational Motion - motion such that an object

moves from one position to another along a straight line.• 2.) Rotational Motion - motion such that an object moves

from one position to another along a circular path.• 3.) Vibrational Motion - motion such that an object moves

back and forth in some type of periodicity.

Kinematics in 1-D.

•Chapter 2. Describing Motion:


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Example: Diatomic Molecule Moving Through Space.•Chapter 2. Describing Motion:

Kinematics in 1-D.

•Chapter 2. Describing Motion:

•Kinematics deals with the concepts that •are needed to describe motion.

•Dynamics deals with the effect that forces•have on motion.

•Together, kinematics and dynamics form• the branch of physics known as Mechanics.


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Displacement•Chapter 2. Describing Motion:

Displacement: Change in Position.•Chapter 2. Describing Motion:

position initial ix

position final fx

ntdisplaceme if xxx


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m 0.3ix

m 0.9fx

m 0.6x

m 0.6m 3.0m 9.0 if xxx

• Example 1:


m 0.4fx

m 0.12ix

m 0.8x

m 0.8m .021m 4.0 if xxx

• Example 2:


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m 0.4fx

m 0.12x

m 0.12m .08m 4.0 if xxx

m 0.8ix

• Example 3:


m 0.3ix

m 0.11x

m 0.11m .0)3(m 8.0 if xxx

m 0.8fx

• Example 4:


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Speed and Velocity•Chapter 2. Describing Motion:

•Average speed is the total distance traveled divided by the time required to cover the distance.

timeElapsed

Distance speed Average

SI units for speed: meters per second (m/s)


• Example 1 Distance Run by a Jogger

• How far does a jogger run in 1.5 hours (5400 s) if his average speed is 2.22 m/s?

timeElapsed

Distance speed Average

m 12000s 5400sm 22.2

timeElapsedspeed Average Distance


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•Average velocity is the displacement divided by the elapsed time.

timeElapsed

ntDisplaceme velocityAverage

ttt if

if

xxx

v


• Example 2 The World’s Fastest Jet-Engine Car

• Andy Green in the car ThrustSSC set a world record of 341.1 m/s in 1997. To establish such a record, the driver makes two runs through the course, one in each direction, to nullify wind effects. From the data, determine the average velocity for each run.


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• Example 2 The World’s Fastest Jet-Engine Car

sm5.339s 4.740

m 1609

t

xv

sm7.342s 4.695

m 1609

t

xv


• The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.

tt

xv

0lim


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Acceleration•Chapter 2. Describing Motion:

• The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs.

Acceleration: Rate of Change in Velocity•Chapter 2. Describing Motion:

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

ttt if

if

vvv

a


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Positive Acceleration•Chapter 2. Describing Motion:

• Example 3 Acceleration and Increasing Velocity

• Determine the average acceleration of a jet plane that starts from rest and increases its velocity to 260 km/h in 29 seconds.

sm0iv

hkm260fv

s 0it s 29ft

s

hkm0.9

s 0s 29

hkm0hkm260

o

o

tt

vva

Given:


• Notice the mixed units of km/h/s.


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Negative Acceleration•Chapter 2. Describing Motion:

• Example 4 Acceleration and Decreasing Velocity

• Determine the average acceleration of a dragster that decreases its velocity of 28 m/s when time is 9.0 seconds to 13.0 m/s when the time is 12.0 seconds.

sm0.28iv

sm0.12fv

s 0.9it s 0.12ft

Given:

2sm0.5s 9s 12

sm28sm13

o

o

tt

vva


• Notice that the acceleration is a negative value.


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POSITIVE ACCELERATION

• Speeding up in a positive direction

• Slowing down in a negative direction

• Speeding up in a negative direction

• Slowing down in a positive direction

NEGATIVE ACCELERATION

Comparison of Positive & Negative Acceleration

•It is customary to dispense with the use of boldface symbols overdrawn with arrows for the displacement, velocity, and acceleration vectors. However, we will continue to conveythe directions with a plus or minus sign.

i

i

ttf

f

xx

v

i

i

tt

xxv

f

f

i

i

ttf

f

vv

a

i

i

tt

vva

f

f

o

o

tt

vva

o

o

tt

xxv


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•Five kinematic variables:

1. displacement, x

2. acceleration (constant), a

3. final velocity (at time, t ), v

4. initial velocity, vo

5. elapsed time, t

4 Kinematic Equations for Constant Acceleration•Kinematic Equations

• Equation #4• The average of initial and final velocity times by time is displacement.

o

o

tt

xxv

If we let the object be at the origin when the clock starts at zero seconds…

0ox

0ot

BUT!!!

t

xv tvx

vvv o 21 tvvx o 2

1

WHERE

THUS

THEN


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• Equation #1• The average acceleration is change in velocity divided by time.

We let the object be at the origin when the clock starts at zero seconds…

0ox

0ot

BUT!!!

Becomes

THUS

THEN

o

o

tt

vva

t

vva o

ovvat atvv o


• Equation #2• Combine Equation #1 and Equation #4.


BUT!!!

Becomes

THUS

ANDatvv o tvvx o 21

tatvvx oo 21

221 2 attvx o 2

21 attvx o


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• Equation #3• Combine Equation #1 and Equation #4.


Eqn. 1

ANDatvv o tvvx o 21

a

vvt o Plug into Eqn. 4

a

vvvvx o

o

2

1


• Equation #3 Continued• Combine Equation #1 and Equation #4.


FOIL it!

THUS

a

vvvvx o

o

2

1

a

vvx o

2

22

222 ovvax xavv o 222


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• Equation #1

xavv o 222atvv o

• Equation #2

221 attvx o

• Equation #3

• Equation #4

tvvx o 21


• Example 5 Acceleration and Displacement

• A speed boat traveling at 6.0 m/s accelerates at 2.0 m/s2 for 8.0 seconds. What is its change in position (displacement) of the speed boat?


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sm0.6iv

DKf v

s 0it s 0.8ftGiven:

2/0.2 sma

m 110

s 0.8sm0.2s 0.8sm0.6 2221

221

attvx o



• A jet accelerates at +31.0 m/s2 from rest and takes off at velocity of 62.0 m/s. What is its change in position (displacement) of the jet?


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sm0.0iv

smf /0.62v

s 0it DKftGiven:

2/0.31 sma

???x

m 62

sm312

sm0sm62

2 2

2222

a

vvx o

• 1. Make a drawing.• 2. Decide which directions are to be called positive (+) and negative (-).

• 3. Write down the values that are given for any of the five kinematic variables.

• 4. Verify that the information contains values for at least three of the five kinematic variables. Select the appropriate equation.

• 5. When the motion is divided into segments, remember that the final velocity of one segment is the initial velocity for the next.

• 6. Keep in mind that there may be two possible answers to a kinematics problem.

•Reasoning Strategy


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• Example 7 Acceleration and Velocity

• A spacecraft is traveling with a velocity of +3250 m/s. Suddenly the retrorockets are fired, and the spacecraft begins to slow down with an acceleration whose magnitude is 10.0 m/s2. What is the velocity of the spacecraft when the displacement of the craft is +215 km, relative to the point where the retrorockets began firing?



sm0.3250iv

??fv

DKt 2/0.10 sma mx 0.215000

axvv o 222 axvv o 22

sm2500

m 215000sm0.102sm3250 22

v


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Freely Falling Body•Chapter 2. Describing Motion:

• In the absence of air resistance, it is found that all bodies at the same location above the Earth fall vertically with the same acceleration. If the distance of the fall is small compared to the radius of the Earth, then the accelerationremains essentially constant throughout the descent.

• This idealized motion is called free-fall and the acceleration of a freely falling body is called the acceleration due to gravity.

22 sft2.32or sm80.9 g

4 Kinematic Equations for Constant Vertical Acceleration•Kinematic Equations

• Equation #1

ygvv o 222gtvv o

• Equation #2

221 gttvy o

• Equation #3

• Equation #4

tvvy o 21


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2sm80.9g• Why negative??• If we consider UP as positive direction (+) then DOWN is the negative direction (-).

• Since gravity pulls everything downwards, acceleration due to gravity is negative.

Acceleration Due to Gravity•Chapter 2. Describing Motion:

• Example 8 Freely Falling Body

• A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement, y, of the stone?


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Vertical Acceleration Due to Gravity•Chapter 2. Describing Motion:


sm0.0iv

NGf v

s 3.0t 2/8.9 smg my ???

m 1.44

s 00.3sm80.9s 00.3sm0 2221

221

gttvy o

Acceleration Due to Gravity•Chapter 2. Describing Motion:

• Example 9• How High Does It Go?

• The referee tosses the coin up with an initial speed of 5.00m/s. In the absence if air resistance, how high does the coin go above its point of release?


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• Example 9 How High Does It Go???

sm0.5iv

smf /0.0v

Kt D 2/8.9 smg my ???

gyvv o 222 g

vvy o

2

22

m 28.1

sm80.92

sm00.5sm0

2 2

2222

g

vvy o


• Example 9 How High Does It Go???• There are three parts to the motion of the coin. • On the way up, the coin has a vector velocity that is directed upward and has decreasing magnitude.

• At the top of its path, the coin momentarily has zero velocity.

• On the way down, the coin has downward-pointing velocity with an increasing magnitude.

• In the absence of air resistance, does the acceleration of the coin, like the velocity, change from one part to another?


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• Taking Advantage of Symmetry

• Does the ball in part a strike the ground beneath the cliff with a smaller, greater, or the same speed as the ball in part b?

Position vs. Time Graph•Graphical Analysis of Motion

• Constant Velocity


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• Constant Velocity

s 2

m 8 Slope

t

x

sm4Slope time-position v

sm4s 2

m 8 Slope

run Slope

rise

t

x

Graphical Analysis of Motion•Chapter 2. Describing Motion:

• Position vs. Time Graph


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• Constant Acceleration

Velocity vs. Time Graph•Graphical Analysis of Motion

• Constant Acceleration


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Velocity vs. Time Graph•Graphical Analysis of Motion

s 2

m/s 12 Slope

t

v

2sm6Slope time-velocity a

2sm6s 2

m/s 12 Slope

run Slope

rise

t

v

END of Chapter 2 Notes

Please make sure that your Homework Packet is completed before the unit test!

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Chapter 2 Notes - Physics3310 - homephysics3310.wikispaces.com/file/view/Chapter+2+Notes.pdf/...Physics 3310 Chapter 2 Notes Mr. Kim 7 Speed and Velocity •Chapter 2. Describing Motion: