Eunil Won Dept of Physics, Korea University 1

Ch04 Work, Energy and Power

What is “work” in physics?

Eunil Won Dept of Physics, Korea University 2

공지사항강의실 변경: 다음부터 아산이학관 633호

이번 주 목요일 : 휴강

연습조교: 최지훈 (3월~4월:7주)백승호 (5월~6월:5주)

숙제 : Problems 2.17, 2.29,3.1,3.16,3.26

Eunil Won Dept of Physics, Korea University 3

Work

dF •≡W

φcosFdW =090cos == οFdW

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0>⇒= WFdW

00

=⇒==

WFdWd

0,0

=⇒=⊥≠WFdWdFd

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Example 4.1

J75mN75)m0.3)(N25( =⋅=== FdW

Calculate the work done by an ambulance attendant who pushes a patient on a gurney with a horizontal force of 25 N for a distance of 3.0 m

Eunil Won Dept of Physics, Korea University 6

Example 4.2

J117.6/smkg 117.6

m) )](1.2m/s kg)(9.810[()(

22

2

=⋅=

=== dmgFdW

How much work is done in lifting a 10-kg sack of groceries 1.2 m from the floor to a table, as in the figure below?

Eunil Won Dept of Physics, Korea University 7

Example 4.3

J3.43)m0.5)(N66.8(

=== dFW h

If the proud father in the figure exerts a force of 10 N at an angle of 30o below the horizontal, how much work does he do in pushing the baby carriage a distance of 5.0 m?

Eunil Won Dept of Physics, Korea University 8

Kinetic Energy

221 mvK ≡

KKKW if ∆≡−=

Work-Energy theorem

Kinetic Energy

2212

21

)(

if

x

x

x

x

x

x

x

x

x

x

mvmvmvdv

dtdxmdvdx

dtdvm

madxdxxFW

f

i

f

i

f

i

f

i

f

i

−==

==

==

∫

∫∫

∫∫

)(J1mN1 joule=⋅

Energy: ability to do work

Kinetic Energy: work done going into causing motion

Eunil Won Dept of Physics, Korea University 9

Example 4.4

J104.5/smkg104.5

m/s)kg)(30(1000

KE

5

225

221

221

×=⋅×=

=

= mv

How much energy is required to accelerate a 1000-kg car from rest to 30 m/sec, assuming no friction?

Eunil Won Dept of Physics, Korea University 10

Example 4.5

KKKW if ∆≡−=

0221 −== mvFdW

A picture throwing a fastball steps forward. Calculate the speed of the baseball when it leaves his hand if the picture exerts an average force of 200 N for a distance of 2.50 m on a 0.5-kg baseball.

m/s7.440.500kg

50m)2(200N)(2.

2

2/1

2/1

=⎥⎦

⎤⎢⎣

⎡=

⎟⎠⎞

⎜⎝⎛=

mFdv

~158 km/h

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Internal Energy: Kinetic and potential energy of molecules (has close relation with the thermal energy)

Kinetic Energy : The Energy of Motion

Potential Energy : Energy due to its shape or position

Gravitational potential energy

Nuclear Energy

Electromagnetic Energy

Mass Energy : Mass=Energy 2mcE =

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Gravitational Potential Energy

mgh

dxmg

dxxFxU

h

x

=

−−=

−=

∫

∫

0

0

)(

)()(

.)(

221 constmghmv

xUKE=+=

+=

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Example 4.6

J368Nm368/smkg368

)m50.0)(m/s8.9)(kg75(

mghPEW

22

2

==⋅=

===

Calculate the work done by a 50-kg nurse in lifting a 25-kg child 0.50 m onto a table

Eunil Won Dept of Physics, Korea University 14

Chemical Energy: diet?

J4186kcal1 =

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Example 4.7

J460)0.1)(80()5)(100( 2

21

221

=−=

−= mvFdWf

N920.5m

J460J460

J460

===

==

df

fdWf

ft WW += KE

An ambulance attendant pushes horizontally on a gurney with a force of 100 N. He starts from rest and pushes for a distance of 5.0 m. There is friction in the wheels. The final speed is 1.0 m/s and the mass of gurney and patient is 80 kg. Calculate the amount of work done against friction and the force of friction

Eunil Won Dept of Physics, Korea University 16

Example 4.8

hr3min175

n5.7kcal/mi1000kcal

eenergy/timenergytime

≈=

=

=

If a person who normally requires an average of 3000 kcal of food energy per day instead consumes 4000 kcal per day, he will steadily gain weight. How much bicycling per day is required to work off this extra 1000 kcal?

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Example 4.9

J109.0/smkg109.0

m/s)10kg)(3.010(1.0

13

2213

283

2

×=⋅×=

××==

−

mcE

kcal102.15J4186

kcal1 J109.0 1013 ×=××

years20,000

102.7kcal3000

kcal102.15 610

≈

×=×

Calculate the amount of energy obtained from converting 1.0 g of mass into energy and compare it to the 3000 kcal of food used by a normal person in one day

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Conservation of Total Energy

Total energy in a closed system is always conserved

ttanconsOEPEKE =++

Mechanical Energy

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Example 4.10/11

m/s3.44)]100)(8.9(2[

)2(

00

2/1

2/1

221

==

=

+=+

if

fi

ghv

mvmghffii PEKEPEKE +=+

fffiii OEPEKEOEPEKE ++=++

J10600J9000J19600)30)(20()100)(8.9(20

TE

TE000

221

221

221

=−=−=

−=

++=++

fi

fi

mvmgh

mvmgh

20 kg

100 m

Velocity of sled at the bottom?(no friction)

Thermal Energy by friction if velocity at the bottom is 30 m/s?

Eunil Won Dept of Physics, Korea University 20

Power and Efficiency

1J/s]W1[ =≡t

WPinoutEff ≡

inout

iout

inout

PP

EEEW

/EffPower

/EffEnergy/EffWork

=

==

The time rate of doing Work

Eunil Won Dept of Physics, Korea University 21

Example 4.12

0.225hp(1hp/746W)168)(

168W0.7

)0.2)(8.9)(60(0.7

=×=

==

== mght

WP

0.788hp(1hp/746W)8)58(

8W580.2

11760.2

=×=

==

=′

=′ mghtWP

a) Calculate the amount of power generated by a 60-kg person climbing a 2.0-m-high flight of stairs in 7.0 s b) Repeat the calculation for the same person running up the stairs in 2.0 s

Eunil Won Dept of Physics, Korea University 22

Example 4.13/4.14

1.40kcal186J)J)(1kcal/45880(

2.0)0.2)(8.9)(60(

2.02.0

==

=

== mghWEin 4704J1176J5880FETE

=−=−=Jmgh

2.0/Eff == inout EW ffii TEPEFEPE +=+

W23502.0s

4704JTE

672W7.0s

4704JTE

===

===

tP

tP

The efficiency of the human body in converting food energy to work ~ 20%. What is the food energy needed to climb one flight of stairs in Example 4.12?

a) Thermal energy by the person climbing the stairs?b) Rate of thermal energy when the person walks up?c) Rate of thermal energy when the person runs up?

Eunil Won Dept of Physics, Korea University 23

Example 4.15

MW 2857MW)/0.35 (1000

Eff//Eff

outin

inout

====PP

PP

MW 1857 MW 1000-MW 8572

outinwaste

wasteoutin

==

−=+=

PPPPPP

A large number nuclear power plant has an efficiency of 35% and generates 1000 MW of electric power. What is the plant’s rate of production waste thermal energy in megawatts?

Eunil Won Dept of Physics, Korea University 24

Example 4.16

kWh 90Wh90,000

days)h/day)(30 W)(6.0500(

==== PtE

The cost of electric energy varies around the country, but 50 won per kilowatt-hour is typical. What is the cost of running a 500-W color TV set 6.0 hr per day for 30 days?

wons500,4hkW

50wonsh)kW 90(cost =⎟

⎠⎞

⎜⎝⎛

⋅⋅=

Eunil Won Dept of Physics, Korea University 25

Basal Metabolic Rate (BMR)

personal BMR thyroid (갑상선) activity

Consumption of Oxygen 1 liter 4.9 kcal

(기초신진대사율)

Eunil Won Dept of Physics, Korea University 26

Warm-blooded animal BMR vs. mass

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Example 4.17

29kg/yearfat g809.3kcal

fat 1.0g743kcal gain Mass

743kcal57kcal172500kcalay1757kcal/dday)/hr)(24hr/min)(60min(1.22kcal/

⇒=×=

==

-

How many grams of fat will an idle person gain in a day by consuming 2500 kcal of food?