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Work ii.
É
→ Work is done when
object moves
=
parallel to The direction of friction = 20N
applied force.
Workdone
against friction
Definition : It is the
product of force W= Fxs
and
displacement parallel to
force.
W -
-
20×2
W =
40 J
W =
Fxs •
SI Unit : Joules ( J)
•
Scalar
Quantity
"
Work done
by
"
force in the direction
F- 50N
of movement
I,
>
"
workdone
against
"
force opposite to
work done by applied force the direction
of
W : Fxs movement .
= 50×2
W =
100J
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iii.
friction -
-
low
"
'
I
.
.
.
'
'
'
g-
S
"
-
.
-
"
iz ,m
. E£••• ,
,
-
<
5cm -
i
-
i -
-
i
12cm -
V
weight
-
-40N
'
'
r
, ,
i
'
>
Weight when
something is
moving in a circle
a) Workdone
by gravity about a
point leg.
satellite
orbiting
around Earth ) ,
the centripetal force
W =
Fxs is
acting towards center but the
= 40×0.05
displacement / motion ) of satellite is
W = 2J
perependicutar 190° ) to the
force.
b) Workdone
against friction As
force and displacement are not
parallel to one another
,
NO WORK IS
W =
Fxs BEING DONE
by centripetal force.
= 10×0.13
w =
1.3J
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Energy sources of Energy
The
ability of a
body to do 1 .
Non-
Renewable Resources
work.
→
Consumption rate
of these resources
are
extremely high compared to
•
SI Unit:
Joules 1J ) °
Scalar
quantity
the
regeneration rate .
Types Forms
of energy
Coal Oil Natural Nuclear
Gas
1. Mechanical Energy
a) Kinetic Energy 2 . Renewable Resources
b) Potential Energy → Resources
regenerate at an
2. Heat Energy incredibly fast rate so consumption
3. Chemical
Energy doesnot
effect Their reserves.
4 . Sound Energy
5.
light Energy o
Solar ° Wind . Wave
6. Nuclear Energy • Tidal °
Geothermal ☐
Biogas
7. Internal Energy
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Gravitational Potential Energy Example # I
m -
-200g g-
-
9.8141kg 2,0%0=0-2kg
The
energy stored in a
body due
^
to its
position in a
gravitational Ep
-
-
mgh
field .
4µm =
1002119.811401
Ep =
78.4J
•
It is due to the
pull
• - -
v
of gravity on the Wv
µ
object in the
field .
Example # 2
.
mass
-
-
0.5kg g-
-9.81N/kg
a-
- - - -
•
Weight pulls the
ground Calculate the loss in
object downwards ,
so when the
objection -
-
Grau. Potential Energy
f-
- - - - -
i.
is released ,
it moves .
Hence it has
| am
of the ball .
some
potential .
Ep =
mgh
>
h
"Ñt A- Ep =P-
Ef -
P-
Ei
IEp=mgDh
Potential
'
✓
=
might -
mghi DEp= 0.5×9.8×6
energy mass
'
grainfield strength =
mg tht - hit
= 0.5×9.8×(4-10)
B. Ep = 29.45
DEP = -29.4J
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kinetic
Energy "
÷
"
kinetic > motion m v E
•
2m ZV E- ✗ 2×22 =
BE
•
The
energy possessed by a
body .
mz
Zv E ✗ 22=2 E
due to in motion .
| |-2
I E
EK =
Izmit >
speed
•
MI 3 2×32
=
¥8
E ✗ 3
L
zz
=
3E
Kinetic v 2 4
energy mass
EKXM EKXVZ
mass KE speed K .E
Example # I
Ek=
tgmv
"
m E v E > v
.
8m15
2m 2E 2v 12T¥ 4E -
-12160011812
3m 3E 3v (3)
'
9E m
-
-600kg
my} Ets 42 125=>44 Ek= 19200J
Mla 1=12 V3 (3)
'
Elq
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Example # 2 mass
-
-
0.6kg Law
of conservation
of Energy
initial calculate the
gain
5m15 -
in K.E. Kenagy can neither be created
,
nor
L
final -
÷
be
destroyed .
9T is
only
converted
8m15
from one
form
to another .
<
vi.
final speed
•
Total
energy of an entire closed
AEK =
Kott - K -
Ei u : initial
speed system is conserved .
L
=
Izmit
-
Izmit
☐ Ek =
tgm /v2 -
W ) v2
.az ( v
. up
closed
system means
no
energy enters
or leaves the zone .
AEK -
-
1210.61/82-54 1 .
Burning of coal
☐ Ek = 11.7J Chemical
>
Heat
+ Light
energy energy energy
+
produced to
gather
> converted into
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2.
Object falling from a
height 4. Ball
colliding
with the
ground and
( no air resistance) Ep
-
-100J
rebounding Ino loss
upon
collision )
Ek= 0
mV
Gravitational kinetic .
'
'
'
.
Potential >
energy
.
'
'
Ep-
-60J
i
Energy Ek-
-
40J
Kinetic
energy
>
Elastic
"
"
"
"
potential
>
kinetic
Ep -0
energy
VVEK -100J energy
1 ball bounces off with same speed )
3.
Object falling from a
height
1 with air resistance )
Ep
-
-100J rebounding (
energy
lost on collision )
'
'
'
Ep=goj§
" % " """
Y -
with the
gwun
, any
GPE > Kot + heat Ek -
- O
l
i
'
'
'
.
qv ( less
because
of peed )
air resistance Ek=3OJÉ
Kinetic
>
Elastic RE
"
"
"
Ep:O
'
if
•
energy + heat
vv Ex -
- 80J IÉ • Elastic P-
E > K - E + heat
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6.
Energy conversion in cell & circuit
Example # I u=o
A ball is released
from rest
,
40m
-
inimiiaiéneigy's ,
on above the
ground .
Ignoring
→
[nside
"- - - - -
"
air resistance ,
calculate the
= in cell / battery =
I v
speed of ball as it hits the
-
Electrical
energy
?
4µmground.
"
l l l l l
✓
l l l l l l l
'
,
,
,
i
,
,
1
,
P. E → K . E
light energy + heat
energy
B v
Potential
energy =
Kinetic
energy
at A at B
7. Solar Panels
nxgh =
Izmit
light energy > Electrical energy 190811401 =
Iz
v2
8. Wind Turbine +
Generator V= ✓ 2×9.8×40
✓ =
28m15
Kinetic
energy >
KE
of >
Electrical
in wind blades
energy in
If energy loss would have occurred,
+ heat
generator v would be less than 28
Mfs.
+ neat
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,
^
Power
•
Rate at which work is done .
m
4 m¥,
h
¥
•
Rate at which
energy
is converted .
running walking
P -
- Work P=
Energy ☐ same
gain
in P-
E in both cases
time time o
less time taken while running .
-
P=W_ P=
Ey
☐ more
power developed while
running,
t than while
walking .
•
SI Unit : Walt IWI °
Scalar
quantity Example # 2
lamp :P = 100W 1100J/s ) A motor
pumps 20kg of water to a
100J
of electrical
energy
is converted
height of 40m above
ground in 5min .
in 1s .
Assuming no
energy
loss,
calculate The
power rating of motor.
A more
powerful machine can do
the same work or can convert RE -
-
mgh Power-_
E- =
7840
same
energy
is less time .
=
20×9.8×40 t 5×60
P. E =
7840J Power =
26.13W
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Efficiency
Ratio
of useful output to the
required input.
•
efficiency =
useful output
required input
✗ 100
•
input =
output + waste
eft
-
-
ww÷ eff
-
-
E€,
eft-
k
Pi
eff
-
-
WOE
;
ebb =
.
eff
-
- E
Ei
ldifferent units )
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1.
2.
3.
Work, energy and Power
Past Papers - MCQs
138
0
-
✓
2000N
→
weight W= Fxs
0 =
2000×0.8
= 1600J
eff
-
-1%0×100
input → ←
output
0
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10
11
12
13
140
0
t
'
✗
¥:
:
n
108-006=1 -2m
?⃝2m W : Fxs
=
50×1-2
=
60J
0
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54.
55.
56.
149
W = Fxs
=
300×5
W =
1500J
O
O EE -
-
mgh
"
☒
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© UCLES 2018 5054/12/O/N/18
6
78 The diagram represents a geothermal power station.
cold
water
steam and
hot water
Which useful energy transformation is taking place?
A electrical energy → potential energy
B electrical energy → thermal energy
C potential energy → electrical energy
D thermal energy → electrical energy
79 A motor is used to lift a load 0.50m vertically, as shown.
0.50m
load
40N
motor
The load weighs 40N. The power of the motor is 20W and the system is 25% efficient.
How long does it take to raise the load?
A 0.040s B 0.25s C 4.0s D 40s
155
Electrical
heat
0
F-
It
or F- E-
t
8 3 .
P=
WI
1 .
Work =
f- ✗ S 20 =
Got
= 40×0.5
=
20J - .
1- =
8¥
2.
efficiency =
:# ✗ too
t -
-
us
25 =
21×100
inp
input =
202-050=805 - .
time ?
- i
0
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Answers
1.D 2.B 3.A 4.C 5.C 6.D 7.A 8.A 9.C 10.C 11.D 12.C
13.B 14.D 15.B 16.D 17.D 18.A 19.D 20.C 21.D 22.C 23.C
24.D 25.B 26.D 27.B 28.B 29.B 30.B 31.D 32.A 33.D 34.B 35.B
36.D 37.A 38.A 39.A 40.B 41.A 42.B 43.D 44.B 45.C 46.A 47.A
48.D 49.C 50.A 51.B 52.C 53.A 54.C 55.B 56.C 57.B 58.D 59.C
60.A 61.B 62.B 63.C 64.C 65. 66. 67. 68. 69. 70. 71.
72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82.
157
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160
Kinetic
energy of hands convert to heat
energy
( due to
friction)
there is more
friction force when
pressed harder
-
hence more heat
produced .
=
W =
f- ✗ s 0096J
☒
1
= 1.2×0008 2 J -
N
W = 0.096
a = 2-
11 movement )
0.096
n =
20.8
21
=
P=Wµ°e
=0;?Y-
=
0.48W
0.48W
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6
163
Chemical
energy of
the
cyclist is converted
Gravitational
Potential
Energy.
Kinetic
energy remains same as
speed is constant .
the potential energy gained
at the top of
the
hill is converted to kinetic
energy as it descends
and then to heat as it brakes to
stop.
P . E =
mgh
5400 = 60×10 ✗ h
h = 9m
9m
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14
174
W -1540N
W= F ✗ s
=
Weight ✗ h
=
(54×10)×2.8
=
1512 J
1512J
p=Wo
time
=
15¥ = 504W
504W
some energy is converted to kinetic
energy of bricks .
Some energy
is lost as heat to
surrounding.
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17
179
Solar
wind
E-
-
(6.8×109)×11×365 ✗ 24×60×60)
p=
¥ E-
-
2.14×10
"
J
E-
-
pxt
2. 14 ✗ 1017J
The
quantity of
water varies
Throughout The
air due to
rainfall or siltation.
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180
-
P-
E =
mgh
=
106×1010×10×170
=
2.72×1013 J
2.72×10135
P=¥= 2.72×101-3 off
-
-
Pont =
6.8×10
"
1×60×60 Pin ¥109
✗ 10°
P =
7.56×109 W
= 89.9
9 90%
input power
some energy
is lost as heat
some energy
is converted to K .E
of
water .
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2
3
4
5
Answers - Theory
195
<
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6
7
8
196
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10
197
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Physicsby Kashan Rashid
11
12
13
14
15
198
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16
17
199
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18
19.
20.
200
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21.
22.
23.
24
201
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25
26
202
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7.-OL-Work-Energy-And-Power.pdf

  • 1. Work ii. É → Work is done when object moves = parallel to The direction of friction = 20N applied force. Workdone against friction Definition : It is the product of force W= Fxs and displacement parallel to force. W - - 20×2 W = 40 J W = Fxs • SI Unit : Joules ( J) • Scalar Quantity " Work done by " force in the direction F- 50N of movement I, > " workdone against " force opposite to work done by applied force the direction of W : Fxs movement . = 50×2 W = 100J CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 2. iii. friction - - low " ' I . . . ' ' ' g- S " - . - " iz ,m . E£••• , , - < 5cm - i - i - - i 12cm - V weight - -40N ' ' r , , i ' > Weight when something is moving in a circle a) Workdone by gravity about a point leg. satellite orbiting around Earth ) , the centripetal force W = Fxs is acting towards center but the = 40×0.05 displacement / motion ) of satellite is W = 2J perependicutar 190° ) to the force. b) Workdone against friction As force and displacement are not parallel to one another , NO WORK IS W = Fxs BEING DONE by centripetal force. = 10×0.13 w = 1.3J CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 3. Energy sources of Energy The ability of a body to do 1 . Non- Renewable Resources work. → Consumption rate of these resources are extremely high compared to • SI Unit: Joules 1J ) ° Scalar quantity the regeneration rate . Types Forms of energy Coal Oil Natural Nuclear Gas 1. Mechanical Energy a) Kinetic Energy 2 . Renewable Resources b) Potential Energy → Resources regenerate at an 2. Heat Energy incredibly fast rate so consumption 3. Chemical Energy doesnot effect Their reserves. 4 . Sound Energy 5. light Energy o Solar ° Wind . Wave 6. Nuclear Energy • Tidal ° Geothermal ☐ Biogas 7. Internal Energy CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 4. Gravitational Potential Energy Example # I m - -200g g- - 9.8141kg 2,0%0=0-2kg The energy stored in a body due ^ to its position in a gravitational Ep - - mgh field . 4µm = 1002119.811401 Ep = 78.4J • It is due to the pull • - - v of gravity on the Wv µ object in the field . Example # 2 . mass - - 0.5kg g- -9.81N/kg a- - - - - • Weight pulls the ground Calculate the loss in object downwards , so when the objection - - Grau. Potential Energy f- - - - - - i. is released , it moves . Hence it has | am of the ball . some potential . Ep = mgh > h "Ñt A- Ep =P- Ef - P- Ei IEp=mgDh Potential ' ✓ = might - mghi DEp= 0.5×9.8×6 energy mass ' grainfield strength = mg tht - hit = 0.5×9.8×(4-10) B. Ep = 29.45 DEP = -29.4J CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 5. kinetic Energy " ÷ " kinetic > motion m v E • 2m ZV E- ✗ 2×22 = BE • The energy possessed by a body . mz Zv E ✗ 22=2 E due to in motion . | |-2 I E EK = Izmit > speed • MI 3 2×32 = ¥8 E ✗ 3 L zz = 3E Kinetic v 2 4 energy mass EKXM EKXVZ mass KE speed K .E Example # I Ek= tgmv " m E v E > v . 8m15 2m 2E 2v 12T¥ 4E - -12160011812 3m 3E 3v (3) ' 9E m - -600kg my} Ets 42 125=>44 Ek= 19200J Mla 1=12 V3 (3) ' Elq CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 6. Example # 2 mass - - 0.6kg Law of conservation of Energy initial calculate the gain 5m15 - in K.E. Kenagy can neither be created , nor L final - ÷ be destroyed . 9T is only converted 8m15 from one form to another . < vi. final speed • Total energy of an entire closed AEK = Kott - K - Ei u : initial speed system is conserved . L = Izmit - Izmit ☐ Ek = tgm /v2 - W ) v2 .az ( v . up closed system means no energy enters or leaves the zone . AEK - - 1210.61/82-54 1 . Burning of coal ☐ Ek = 11.7J Chemical > Heat + Light energy energy energy + produced to gather > converted into CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 7. 2. Object falling from a height 4. Ball colliding with the ground and ( no air resistance) Ep - -100J rebounding Ino loss upon collision ) Ek= 0 mV Gravitational kinetic . ' ' ' . Potential > energy . ' ' Ep- -60J i Energy Ek- - 40J Kinetic energy > Elastic " " " " potential > kinetic Ep -0 energy VVEK -100J energy 1 ball bounces off with same speed ) 3. Object falling from a height 1 with air resistance ) Ep - -100J rebounding ( energy lost on collision ) ' ' ' Ep=goj§ " % " """ Y - with the gwun , any GPE > Kot + heat Ek - - O l i ' ' ' . qv ( less because of peed ) air resistance Ek=3OJÉ Kinetic > Elastic RE " " " Ep:O ' if • energy + heat vv Ex - - 80J IÉ • Elastic P- E > K - E + heat CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 8. 6. Energy conversion in cell & circuit Example # I u=o A ball is released from rest , 40m - inimiiaiéneigy's , on above the ground . Ignoring → [nside "- - - - - " air resistance , calculate the = in cell / battery = I v speed of ball as it hits the - Electrical energy ? 4µmground. " l l l l l ✓ l l l l l l l ' , , , i , , 1 , P. E → K . E light energy + heat energy B v Potential energy = Kinetic energy at A at B 7. Solar Panels nxgh = Izmit light energy > Electrical energy 190811401 = Iz v2 8. Wind Turbine + Generator V= ✓ 2×9.8×40 ✓ = 28m15 Kinetic energy > KE of > Electrical in wind blades energy in If energy loss would have occurred, + heat generator v would be less than 28 Mfs. + neat CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 9. , ^ Power • Rate at which work is done . m 4 m¥, h ¥ • Rate at which energy is converted . running walking P - - Work P= Energy ☐ same gain in P- E in both cases time time o less time taken while running . - P=W_ P= Ey ☐ more power developed while running, t than while walking . • SI Unit : Walt IWI ° Scalar quantity Example # 2 lamp :P = 100W 1100J/s ) A motor pumps 20kg of water to a 100J of electrical energy is converted height of 40m above ground in 5min . in 1s . Assuming no energy loss, calculate The power rating of motor. A more powerful machine can do the same work or can convert RE - - mgh Power-_ E- = 7840 same energy is less time . = 20×9.8×40 t 5×60 P. E = 7840J Power = 26.13W CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 10. Efficiency Ratio of useful output to the required input. • efficiency = useful output required input ✗ 100 • input = output + waste eft - - ww÷ eff - - E€, eft- k Pi eff - - WOE ; ebb = . eff - - E Ei ldifferent units ) CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 11. 1. 2. 3. Work, energy and Power Past Papers - MCQs 138 0 - ✓ 2000N → weight W= Fxs 0 = 2000×0.8 = 1600J eff - -1%0×100 input → ← output 0 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 12. 10 11 12 13 140 0 t ' ✗ ¥: : n 108-006=1 -2m ?⃝2m W : Fxs = 50×1-2 = 60J 0 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 13. 54. 55. 56. 149 W = Fxs = 300×5 W = 1500J O O EE - - mgh " ☒ CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 14. © UCLES 2018 5054/12/O/N/18 6 78 The diagram represents a geothermal power station. cold water steam and hot water Which useful energy transformation is taking place? A electrical energy → potential energy B electrical energy → thermal energy C potential energy → electrical energy D thermal energy → electrical energy 79 A motor is used to lift a load 0.50m vertically, as shown. 0.50m load 40N motor The load weighs 40N. The power of the motor is 20W and the system is 25% efficient. How long does it take to raise the load? A 0.040s B 0.25s C 4.0s D 40s 155 Electrical heat 0 F- It or F- E- t 8 3 . P= WI 1 . Work = f- ✗ S 20 = Got = 40×0.5 = 20J - . 1- = 8¥ 2. efficiency = :# ✗ too t - - us 25 = 21×100 inp input = 202-050=805 - . time ? - i 0 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 15. Answers 1.D 2.B 3.A 4.C 5.C 6.D 7.A 8.A 9.C 10.C 11.D 12.C 13.B 14.D 15.B 16.D 17.D 18.A 19.D 20.C 21.D 22.C 23.C 24.D 25.B 26.D 27.B 28.B 29.B 30.B 31.D 32.A 33.D 34.B 35.B 36.D 37.A 38.A 39.A 40.B 41.A 42.B 43.D 44.B 45.C 46.A 47.A 48.D 49.C 50.A 51.B 52.C 53.A 54.C 55.B 56.C 57.B 58.D 59.C 60.A 61.B 62.B 63.C 64.C 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 157 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 16. 160 Kinetic energy of hands convert to heat energy ( due to friction) there is more friction force when pressed harder - hence more heat produced . = W = f- ✗ s 0096J ☒ 1 = 1.2×0008 2 J - N W = 0.096 a = 2- 11 movement ) 0.096 n = 20.8 21 = P=Wµ°e =0;?Y- = 0.48W 0.48W CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 17. 6 163 Chemical energy of the cyclist is converted Gravitational Potential Energy. Kinetic energy remains same as speed is constant . the potential energy gained at the top of the hill is converted to kinetic energy as it descends and then to heat as it brakes to stop. P . E = mgh 5400 = 60×10 ✗ h h = 9m 9m CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 18. 14 174 W -1540N W= F ✗ s = Weight ✗ h = (54×10)×2.8 = 1512 J 1512J p=Wo time = 15¥ = 504W 504W some energy is converted to kinetic energy of bricks . Some energy is lost as heat to surrounding. CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 19. 17 179 Solar wind E- - (6.8×109)×11×365 ✗ 24×60×60) p= ¥ E- - 2.14×10 " J E- - pxt 2. 14 ✗ 1017J The quantity of water varies Throughout The air due to rainfall or siltation. CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 20. 180 - P- E = mgh = 106×1010×10×170 = 2.72×1013 J 2.72×10135 P=¥= 2.72×101-3 off - - Pont = 6.8×10 " 1×60×60 Pin ¥109 ✗ 10° P = 7.56×109 W = 89.9 9 90% input power some energy is lost as heat some energy is converted to K .E of water . CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 21. 2 3 4 5 Answers - Theory 195 < CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 22. 6 7 8 196 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 23. 10 197 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 24. 11 12 13 14 15 198 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 25. 16 17 199 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 26. 18 19. 20. 200 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 27. 21. 22. 23. 24 201 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid
  • 28. 25 26 202 CLASSMATE YOUR PARTNER FOR PURSUING EXCELLENCE Physicsby Kashan Rashid