Chapter 10 - University of North Floridan00006757/physicslectures/Knight 2e/10_lect_outline/ja... · College Physics: A Strategic ... Answer Slide 10-17 ... •We are, for now, ignoring

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© 2010 Pearson Education, Inc.

PowerPoint® Lectures forCollege Physics: A Strategic Approach, Second Edition

Chapter 10

Energy andWork

© 2010 Pearson Education, Inc. Slide 10-2

10 Energy and Work


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Reading Quiz1. If a system is isolated, the total energy of the system

A. increases constantly.B. decreases constantly.C. is constant.D. depends on work into the system.E. depends on work out of the system.

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Answer1. If a system is isolated, the total energy of the system

A. increases constantly.B. decreases constantly.C. is constant.D. depends on work into the system.E. depends on work out of the system.

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Reading Quiz2. Which of the following is an energy transfer?

A. Kinetic energyB. HeatC. Potential energyD. Chemical energyE. Thermal energy

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Answer2. Which of the following is an energy transfer?

A. Kinetic energyB. HeatC. Potential energyD. Chemical energyE. Thermal energy

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Reading Quiz3. If you raise an object to a greater height, you are increasing

A. kinetic energy.B. heat.C. potential energy.D. chemical energy.E. thermal energy.

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Answer3. If you raise an object to a greater height, you are increasing

A. kinetic energy.B. heat.C. potential energy.D. chemical energy.E. thermal energy.

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Forms of EnergyMechanical Energy

ThermalEnergy

Other forms include

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The Basic Energy Model

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Energy Transformations

Kinetic energy K = energy of motion

Potential energy U = energy of position

Thermal energy Eth = energy associated withtemperature

System energy E = K + U + Eth + Echem + ...

Within the System, all interactions are internal

Energy can be transformed within the systemwithout loss.

Energy is a property of a system.

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Some Energy Transformations

Echem Ug KEth

Echem Eth Us KUg

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Here’s another example…

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Checking UnderstandingA skier is moving down a slope at a constant speed. Whatenergy transformation is taking place?

A. K Ug

B. Ug Eth

C. Us Ug

D. Ug K

E. K Eth

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A skier is moving down a slope at a constant speed. Whatenergy transformation is taking place?

A. K Ug

B. Ug Eth

C. Us Ug

D. Ug K

E. K Eth

Answer

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Checking UnderstandingA child is on a playground swing, motionless at the highestpoint of his arc. As he swings back down to the lowest point ofhis motion, what energy transformation is taking place?

A. K Ug

B. Ug Eth

C. Us Ug

D. Ug K

E. K Eth

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AnswerA child is on a playground swing, motionless at the highestpoint of his arc. As he swings back down to the lowest point ofhis motion, what energy transformation is taking place?

A. K Ug

B. Ug Eth

C. Us Ug

D. Ug K

E. K Eth

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Energy Transfers

These change the energy of the systemthrough interactions with the environment.

Work is the mechanical transfer of energyto or from a system via pushes and pulls.

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A few things to note:•Work can be positive (work in) or negative (work out)•We are, for now, ignoring heat…we will deal with it in Chapter 11…•Thermal energy is…special. When energy changes to thermal energy, thechange is irreversible.


Energy Transfers: Work

W K W Eth

W Us

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The Work-Energy Equation

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− + − + − =mechanical energy = + +Δ + Δ + Δ =

+ + = + + +


The Law of Conservation of Energy

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Conservation of Mechanical Energy

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− + − + − = 0Δ + Δ + Δ = 0

+ + = + +However…Remember that conservation of energy applies to all forms

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Conceptual Example ProblemA car sits at rest at the top of a hill. A small push sends it rollingdown a hill. After its height has dropped by 5.0 m, it is moving ata good clip. Write down the equation for conservation of energy,noting the choice of system, the initial and final states, and whatenergy transformation has taken place.

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Conceptual Example ProblemA car sits at rest at the top of a hill. A small push sends it rollingdown a hill. After its height has dropped by 5.0 m, it is moving ata good clip. Write down the equation for conservation of energy,noting the choice of system, the initial and final states, and whatenergy transformation has taken place.

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Checking UnderstandingThree balls are thrown off a cliff with the same speed, but indifferent directions. Which ball has the greatest speed justbefore it hits the ground?

A. Ball AB. Ball BC. Ball CD. All balls have

the same speed

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AnswerThree balls are thrown off a cliff with the same speed, but indifferent directions. Which ball has the greatest speed justbefore it hits the ground?

A. Ball AB. Ball BC. Ball CD. All balls have

the same speed

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AnswerThree balls are thrown off a cliff with the same speed, but indifferent directions. Which ball has the greatest speed justbefore it hits the ground?

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The balls have the same speed because they start fromthe same height with the same . As each of themfalls from that height, it adds an additional amount ofkinetic energy equal to the (relative to theground) it had to begin with, so that the kinetic energyjust before it hits is = + . (If they had beendropped from rest they would have gained the sameadditional amount of kinetic energy.) Ball C is a littledifferent. It rises to a height higher than the top of thecliff as its is transformed to additional : → Δ .Then it falls, converting Δ → by the time itreaches the height of the cliff. After that it falls just likethe other two balls.


Quantifying Work

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Work Done by Force at an Angle to Displacement

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Energy Equations

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= Δ = −Consider the work done by wind on the sailboard:

= += = ⇒ =2 = −= 12 − 12


Energy Equations

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It has a kinetic energy given byConsider a point particle in a rotating object:= 12 = 12Sum up the for all the point particles in the object to get the rotational kinetic energy:= 12 + 12 + ⋯ = 12 ∑

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Energy Equations

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Consider an object being lifted:Work is being done against gravity:= Δ = −Δ = −Δ = −− = −


Energy Equations

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Consider a spring being compressed (or stretched):= Δ = − 0= ( )The problem here is that is not constant, so use average:= +2 = 0 +2 = 12= 12 = ( )


Each of the boxes, with masses noted, is pulled for 10 m acrossa level, frictionless floor by the noted force. Which boxexperiences the largest change in kinetic energy?

Checking Understanding

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AnswerEach of the boxes, with masses noted, is pulled for 10 m acrossa level, frictionless floor by the noted force. Which boxexperiences the largest change in kinetic energy?

D.

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Each of the boxes, with masses noted, is pulled for 10 m acrossa level, frictionless floor by the noted force. Which boxexperiences the smallest change in kinetic energy?


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AnswerEach of the boxes, with masses noted, is pulled for 10 m acrossa level, frictionless floor by the noted force. Which boxexperiences the smallest change in kinetic energy?

C.

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Each of the boxes, with masses noted, is pulled for 10 m acrossa level, frictionless floor by the noted force. Which boxexperiences the largest change in speed?


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AnswerEach of the boxes, with masses noted, is pulled for 10 m acrossa level, frictionless floor by the noted force. Which boxexperiences the largest change in speed?

C.

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Example ProblemA 200 g block on a frictionless surface is pushed against a springwith spring constant 500 N/m, compressing the spring by 2.0 cm.When the block is released, at what speed does it shoot awayfrom the spring?

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= ( )12 = 12 Δ ⇒ = Δ= Δ ⇒ = Δ = 500 N/m 0.020 m0.200 kg = 1.0 m/s

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A 2.0 g desert locust can achieve a takeoffspeed of 3.6 m/s (comparable to the besthuman jumpers) by using energy storedin an internal “spring” near the knee joint.

A. When the locust jumps, whatenergy transformation takes place?

B. What is the minimum amount ofenergy stored in the internal spring?

C. If the locust were to make a verticalleap, how high could it jump? Ignoreair resistance and use conservationof energy concepts to solve thisproblem.

D. If 50% of the initial kinetic energy istransformed to thermal energybecause of air resistance, how highwill the locust jump?

Example Problem

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A. The initial energy transformation isB. There must be at least as much elastic energyin the spring as the bug’s kinetic energymoving at takeoff speed:

C. In a vertical leap the locust’s takeoff at thebottom would transform to at the top:

D. If 50% of is lost to air resistance:A 2.0 g desert locust can achieve a takeoff speed of 3.6 m/s(comparable to the best human jumpers) by using energystored in an internal “spring” near the knee joint.

A. When the locust jumps, what energytransformation takes place?

B. What is the minimum amount of energy storedin the internal spring?

C. If the locust were to make a vertical leap, howhigh could it jump? Ignore air resistance anduse conservation of energy concepts to solvethis problem.

D. If 50% of the initial kinetic energy istransformed to thermal energy because of airresistance, how high will the locust jump?

Example Problem

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→== 12 2.0 × 10 kg 3.6 m/s= 1.3 × 10 J

=Δ = 1.3 × 10 JΔ = 1.3 × 10 J2.0 × 10 kg 9.8 m/s = 0.66 m= 0.50Δ = 0.65 × 10 JΔ = 0.33 m


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Elastic Collisions

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Using conservation of momentum and conservation of energy you get:


Power

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Power• Same mass...• Both reach 60 mph...

Same final kinetic energy, butdifferent times mean differentpowers.

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Five toy cars accelerate from rest to their top speed in a certainamount of time. The masses of the cars, the final speeds, and thetime to reach this speed are noted in the table. Which car has thegreatest power?

Car Mass (g) Speed (m/s) Time (s)

A 100 3 2

B 200 2 2

C 200 2 3

D 300 2 3

E 300 1 4


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AnswerFive toy cars accelerate from rest to their top speed in a certainamount of time. The masses of the cars, the final speeds, and thetime to reach this speed are noted in the table. Which car has thegreatest power?


A 100 3 2

B 200 2 2

C 200 2 3

D 300 2 3

E 300 1 4

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Five toy cars accelerate from rest to their top speed in a certainamount of time. The masses of the cars, the final speeds, and thetime to reach this speed are noted in the table. Which car has thesmallest power?


A 100 3 2

B 200 2 2

C 200 2 3

D 300 2 3

E 300 1 4


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AnswerFour toy cars accelerate from rest to their top speed in a certainamount of time. The masses of the cars, the final speeds, and thetime to reach this speed are noted in the table. Which car has thesmallest power?


A 100 3 2

B 200 2 2

C 200 2 3

D 300 2 3

E 300 1 4

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In a typical tee shot, a golf ball is hit by the 300 g head of a clubmoving at a speed of 40 m/s. The collision with the ball happensso fast that the collision can be treated as the collision of a 300 gmass with a stationary ball—the shaft of the club and the golfercan be ignored. The 46 g ball takes off with a speed of 70 m/s.

A. What is the change in momentum of the ball?

B. What is the speed of the club head immediately after thecollision?

C. What fraction of the club’s kinetic energy is transferred tothe ball?

D. What fraction of the club’s kinetic energy is “lost” tothermal energy?

Example Problem

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In a typical tee shot, a golf ball is hit by the300 g head of a club moving at a speed of40 m/s. The collision with the ball happensso fast that the collision can be treated asthe collision of a 300 g mass with astationary ball—the shaft of the club andthe golfer can be ignored. The 46 g balltakes off with a speed of 70 m/s.

A. What is the change inmomentum of the ball?

B. What is the speed of theclub head immediatelyafter the collision?

C. What fraction of the club’skinetic energy istransferred to the ball?

D. What fraction of the club’skinetic energy is “lost” tothermal energy?

Example Problem

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(A) Change in momentum of ball:(B) Conservation of momentum gives:

(C)(D) The amount of lost as is the difference between theclub’s initial and the total of club and ball:

Δ = − 0 =Δ = 0.046 kg 70 ms = 3.2 kg ⋅ ms+ == −= −

= 0.300 kg 40 ms − 0.046 kg 70 ms0.300 kg = 29 ms= 1212 = = 0.046 kg 70 ms0.300 kg 40 ms = 0.47

− = 12 − 12 − 1212 = 240 J − 126 J − 113 J240 J = 0.0048

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A typical human head has a mass of 5.0 kg. If the head is movingat some speed and strikes a fixed surface, it will come to rest. Ahelmet can help protect against injury; the foam in the helmetallows the head to come to rest over a longer distance, reducingthe force on the head. The foam in helmets is generally designedto fail at a certain large force below the threshold of damage tothe head. If this force is exceeded, the foam begins to compress.

If the foam in a helmet compresses by 1.5 cm under a force of2500 N (below the threshold for damage to the head), what is themaximum speed the head could have on impact withoutcompressing the foam?

Use energy concepts to solve this problem.

Example Problem

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A typical human head has a mass of5.0 kg. If the head is moving at somespeed and strikes a fixed surface, itwill come to rest. A helmet can helpprotect against injury; the foam in thehelmet allows the head to come torest over a longer distance, reducingthe force on the head. The foam inhelmets is generally designed to failat a certain large force below thethreshold of damage to the head. Ifthis force is exceeded, the foambegins to compress.

If the foam in a helmet compressesby 1.5 cm under a force of 2500 N(below the threshold for damage tothe head), what is the maximumspeed the head could have on impactwithout compressing the foam?

Use energy concepts to solve thisproblem.

Example Problem

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Data for one stage of the 2004 Tour de France show that LanceArmstrong’s average speed was 15 m/s, and that keeping Lanceand his bike moving at this zippy pace required a power of 450 W.

A. What was the average forward force keeping Lance andhis bike moving forward?

B. To put this in perspective, compute what mass wouldhave this weight.

Example Problem

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Summary

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Summary

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Trucks with the noted masses moving at the noted speeds crashinto barriers that bring them to rest with a constant force. Whichtruck compresses the barrier by the largest distance?

Additional Questions

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Trucks with the noted masses moving at the noted speeds crashinto barriers that bring them to rest with a constant force. Whichtruck compresses the barrier by the largest distance?

Answer

E.

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Trucks with the noted masses moving at the noted speeds crashinto barriers that bring them to rest with a constant force. Whichtruck compresses the barrier by the smallest distance?


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Trucks with the noted masses moving at the noted speeds crashinto barriers that bring them to rest with a constant force. Whichtruck compresses the barrier by the smallest distance?

Answer

B.

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A 20-cm-long spring is attached to a wall. When pulledhorizontally with a force of 100 N, the spring stretches to alength of 22 cm. What is the value of the spring constant?

A. 5000 N/m

B. 500 N/m

C. 454 N/m


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AnswerA 20-cm-long spring is attached to a wall. When pulledhorizontally with a force of 100 N, the spring stretches to alength of 22 cm. What is the value of the spring constant?

A. 5000 N/mB. 500 N/m

C. 454 N/m

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I swing a ball around my head at constant speed in a circle withcircumference 3 m. What is the work done on the ball by the 10 Ntension force in the string during one revolution of the ball?

A. 30 J

B. 20 J

C. 10 J

D. 0 J


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AnswerI swing a ball around my head at constant speed in a circle withcircumference 3 m. What is the work done on the ball by the 10 Ntension force in the string during one revolution of the ball?

A. 30 J

B. 20 J

C. 10 J

D. 0 J

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Chapter 10 - University of North Floridan00006757/physicslectures/Knight 2e/10_lect_outline/ja... · College Physics: A Strategic ... Answer Slide 10-17 ... •We are, for now, ignoring