Physics E1a
Homework Assignment #5 Solutions
Fall 2011
1.
The runner's work is positive, the wind's work is negative and
!
PE
=
0
. Therefore the runner's
work plus the wind's work equal a change in kinetic energy.
F
runner
d
!
F
wind
d
=
"
KE
#
F
runner
25
m
( )
!
30.0
N
( )
25
m
( ) =
1
2
60
kg
( )
(8
m s
)
2
!
1
2
60
kg
( )
2
m s
( )
2
.
Solving for the runners force
F
runner
=
30 m
2
2
( )
60kg
+
30N
( )
25m
( )
25m
=
102N
2.
At the two extreme positions (at the bottom when the spring is fully compressed and at the top
when he has reached his maximum height) the Kinetic Energy is zero Therefore,
PE
elastic
=
PE
gravitational
1
2
kx
2
=
mgh
!
h
=
1 2
( )
kx
2
mg
=
( )
2.5
"
10
4
N
( )
0.12m
( )
40kg
( )
2
( )
=
0.46m
3.
(a) PE
Top
= KE
Bottom
or
mgh
=
1
2
mv
2
!
v
=
2gh
=
2
( )
35m
( )
=
With constant acceleration the average velocity for the run is,
v
=
v
0
+
v
f
2
=
26.2m s
2
=
and the time for the run is
t
=
d
=
70m
13.1m s
=
5.3s
(b) PE
Top
+ KE
Top
= KE
Bottom
or
mgh
+
1
2
0
2
=
1
2
f
2
!
v
=
v
0
2
+
2gh
=
2.5m
( ) +
2 9.8 m s
2
( )
35m
( )
=
With constant acceleration the average velocity for the run is,
=
v
0
+
v
f
2
=
+
26.3m s
2
=
and the time for the run is
t
=
d
=
70m
14.4 m s
=
4.86s
4.
(a)
Power
=
work
time
=
6
!
10
6
J
8hr
!
1hr
3600s
=
208Watts
(b) The work required = mgh =
2000kg
( )
2
( )
1.5m
( ) =
2.9
!
10
4
J
The time =
Work
Power
=
2.9
!
10
4
J
208Watts
=
141s or 2 min 21sec
5.
W
NC
=
!
KE
+
PE
with PE = 0
we have,
!
F
f
"
d
=
!
1
2
2
#
d
=
2
2F
f
With,
F
f
= μ
F
N
= μ
mg
then
d
=
2
2
μ
mg
=
v
2
2
μ
g
6.
K.E.
bottom
=
K.E.
top
+
P.E.
or
1
2
/
m v
0
2
=
1
2
m v
x
2
+
m gh
!
v
0
2
=
v
x
2
+
2gh
v
0
2
=
6.5m s
( )
2
+
2
( )
1.1m
( ) =
63.81m
2
2
v
0
=
V
0
= ?
h = 1.1m
V
x
= 6.5m/s
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7.
We have nonconservative forces (air friction) acting on the cyclist as she descends and climbs
the hill.
Down the hill, the work done on the cyclist is,
W
NC
=
!
K.E.
+
!
P.E.
With constant velocity we
know that
∆
K.E. = 0
so
W
=
!
P.E.
=
mgh
=
mgLsin
"
.
Now the nonconservative work done on the cyclist is due to air friction so,
W
=
F
f
air
!
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 Fall '11
 WolfgangRueckner
 mechanics, Energy, Force, Kinetic Energy, Potential Energy, Work, Wnc, Average Force

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