alexander (jra2623) – oldhomework 14 – Turner – (92510)
1
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printout
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11
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Multiplechoice questions may continue on
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before answering.
001
(part 1 of 2) 10.0 points
A car of weight 2060 N operating at a rate of
172 kW develops a maximum speed of 25 m
/
s
on a level, horizontal road.
Assuming that the resistive force (due to
friction and air resistance) remains constant,
what is the car’s maximum speed on an incline
of 1 in 20;
i.e.
, if
θ
is the angle of the incline
with the horizontal, sin
θ
= 1
/
20 ?
Correct answer: 24
.
6312 m
/
s.
Explanation:
If
f
is the resisting force on a horizontal
road, then the power
P
is
P
=
f v
horizontal
.
so that
f
=
P
v
h
=
1
.
72
×
10
5
W
25 m
/
s
= 6880 N
.
On the incline, the resisting force is
F
=
f
+
m g
sin
θ
=
f
+
W
20
=
P
v
h
+
W
20
.
And,
F v
=
P ,
so
v
=
P
F
=
P
P
v
h
+
W
20
=
1
.
72
×
10
5
W
1
.
72
×
10
5
W
25 m
/
s
+
2060 N
20
= 24
.
6312 m
/
s
.
002
(part 2 of 2) 10.0 points
What is its power output on a 1in10 incline
if the car is traveling at 14 m
/
s?
Correct answer: 99204 W.
Explanation:
On the reduced incline, we again have,
P
=
F v
= (
f
+
m g
sin
θ
)
v
The only change from the previous problem is
sin
θ
=
1
10
,
so
P
=
parenleftbigg
f
+
W
10
parenrightbigg
v
=
parenleftbigg
p
v
h
+
W
10
parenrightbigg
v
=
parenleftbigg
1
.
72
×
10
5
W
25 m
/
s
+
2060 N
10
parenrightbigg
(14 m
/
s)
= 99204 W
.
003
10.0 points
A certain waterfall is 118
.
7 m high and has
water flow rate of 30
.
2 m
3
/
s.
The acceleration of gravity is 9
.
8 m
/
s
2
.
Find the maximum electric power that can
be generated by these falls assuming 100%
conversion of mechanical energy to electric
energy.
(Take the density of water to be
1
.
00
×
10
3
kg
/
m
3
)
Correct answer: 3
.
51305
×
10
7
W.
Explanation:
Basic Concepts:
Potential Energy and Power
Solution:
When water falls from a high place, its
potential energy decreases; for the waterfall,
the variation of potential energy per second is
Δ
U
= (
ρr
)
g h
= (1000 kg
/
m
3
) (30
.
2 m
3
/
s)
×
(9
.
8 m
/
s
2
) (118
.
7 m)
= 3
.
51305
×
10
7
J
/
s
.
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alexander (jra2623) – oldhomework 14 – Turner – (92510)
2
When
converted
into
electric
energy,
the
power is
P
= Δ
U
= 3
.
51305
×
10
7
W
.
004
10.0 points
A 103 kg physics professor has fallen into
the Grand Canyon.
Luckily, he managed
to grab a branch and is now hanging 98 m
below the rim.
A student (majoring in lin
guistics and physics) decides to perform a
rescue/experiment using a nearby horse. Af
ter lowering a rope to her fallen hero and
attaching the other end to the horse, the stu
dent measures how long it takes for the horse
to pull the fallen physicist to the rim of the
Grand Canyon.
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 Summer '08
 Kaplunovsky
 Potential Energy, Power, Work, Correct Answer, Alexander, Ferris Wheel

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