eunil won dept of physics, korea university 1 ch04 work, energy...
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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
Eunil Won Dept of Physics, Korea University 4
0>⇒= WFdW
00
=⇒==
WFdWd
0,0
=⇒=⊥≠WFdWdFd
Eunil Won Dept of Physics, Korea University 5
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
Eunil Won Dept of Physics, Korea University 11
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 =
Eunil Won Dept of Physics, Korea University 12
Gravitational Potential Energy
mgh
dxmg
dxxFxU
h
x
=
−−=
−=
∫
∫
0
0
)(
)()(
.)(
221 constmghmv
xUKE=+=
+=
Eunil Won Dept of Physics, Korea University 13
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 =
Eunil Won Dept of Physics, Korea University 15
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?
Eunil Won Dept of Physics, Korea University 17
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
Eunil Won Dept of Physics, Korea University 18
Conservation of Total Energy
Total energy in a closed system is always conserved
ttanconsOEPEKE =++
Mechanical Energy
Eunil Won Dept of Physics, Korea University 19
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
Eunil Won Dept of Physics, Korea University 27
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?
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