211
The total potential energy of an object is to be determined.
Analysis
Substituting the given data into the potential energy expression gives
kJ
19.6
2
2
2
/s
m
1000
kJ/kg
1
m)
20
)(
m/s
8
.
9
(
kg)
(100
PE
mgz
217
A river flowing steadily at a specified flow rate is considered for hydroelectric power generation by
collecting the water in a dam. For a specified water height, the power generation potential is to be
determined.
Assumptions
1
The elevation given is the elevation of the free surface of the river.
2
The mechanical
energy of water at the turbine exit is negligible.
Properties
We take the density of water to be
= 1000 kg/m
3
.
Analysis
The total mechanical energy the water in a dam
possesses is equivalent to the potential energy of water at the free
surface of the dam (relative to free surface of discharge water),
and it can be converted to work entirely. Therefore, the power
potential of water is its potential energy, which is
gz
per unit
mass, and
gz
m
for a given mass flow rate.
kJ/kg
4905
.
0
/s
m
1000
kJ/kg
1
m)
50
)(
m/s
(9.81
2
2
2
mech
gz
pe
e
The mass flow rate is
kg/s
0,000
24
/s)
m
0
)(24
kg/m
1000
(
3
3
V
m
Then the power generation potential becomes
MW
118
kJ/s
1000
MW
1
kJ/kg)
905
kg/s)(0.4
000
,
240
(
mech
mech
max
e
m
E
W
Therefore, 118 MW of power can be generated from this river if its power potential can be recovered completely.
Discussion
Note that the power output of an actual turbine will be less than 118 MW because of losses
and inefficiencies.
219C
Energy can cross the boundaries of a closed system in two forms: heat and work.
231
A car is accelerated from rest to 100 km/h. The work needed to achieve this is to be determined.
Analysis
The work needed to accelerate a body the change in kinetic energy of the body,
kJ
309
2
2
2
2
1
2
2
/s
m
kg
1000
kJ
1
0
s
3600
m
100,000
kg)
(800
2
1
)
(
2
1
V
V
m
W
a
River
50 m
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233
A man is pushing a cart with its contents up a ramp that is inclined at an angle of 20° from the
horizontal. The work needed to move along this ramp is to be determined considering (a) the man and
(b) the cart and its contents as the system.
Analysis
(
a
) Considering the man as the system, letting
l
be the displacement along the ramp, and letting
be the inclination angle of the ramp,
kJ
67.0
2
2
2
/s
m
1000
kJ/kg
1
m)sin(20)
100
(
)
m/s
8
.
9
)(
kg
100
100
(
sin
sin
mgl
Fl
W
This is work that the man must do to raise the weight of the cart and contents, plus his own weight, a
distance of
l
sin
.
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 Summer '07
 RAMUSSEN
 Energy, Potential Energy, electrical energy

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