Patel, Kinal – Homework 9 – Due: Oct 5 2007, 7:00 pm – Inst: D Weathers
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The due time is Central
time.
001
(part 1 of 1) 10 points
A timevarying net force acting on a 1
.
9 kg
particle causes the object to have a displace
ment given by
x
=
a
+
b t
+
d t
2
+
e t
3
,
where
a
= 2
.
2 m
,
b
= 1
.
3 m
/
s
,
d
=

2
.
4 m
/
s
2
,
and
e
= 1
.
3 m
/
s
3
,
with
x
in meters and
t
in seconds.
Find the work done on the particle in the
first 2
.
9 s of motion.
Correct answer: 385
.
227 J.
Explanation:
Since the force is time dependent
W
≡
Z
x
f
x
i
~
F
·
d~x
=
Z
x
f
x
i
m a dx
=
m
Z
x
f
x
i
d v
dt
dx
=
m
Z
x
f
x
i
d v
dx
d x
dt
dx
=
m
Z
v
f
v
i
v dv
=
1
2
m v
2
f

1
2
m v
2
i
.
Therefore work done on the particle is the
change in kinetic energy. For this case,
W
= Δ
K
=
K
f

K
i
=
1
2
m
(
v
2
f

v
2
i
)
,
where the velocity is found by differentiating
the displacement:
v
=
d x
dt
=
b
+ 2
d t
+ 3
e t
2
v
i
= 1
.
3 m
/
s
,
and
(1)
v
f
= (1
.
3 m
/
s) + 2 (

2
.
4 m
/
s
2
) (2
.
9 s)
+3 (1
.
3 m
/
s
3
) (2
.
9 s)
2
= 20
.
179 m
/
s
,
(2)
where
t
i
= 0 s and
t
f
= 2
.
9 s
.
Evaluation of the velocity at the initial and
final times gives the desired result.
W
=
K
f

K
i
=
1
2
m
(
v
2
f

v
2
i
)
=
1
2
(1
.
9 kg)
h
(20
.
179 m
/
s)
2

(1
.
3 m
/
s)
2
i
= (386
.
832 J)

(1
.
6055 J)
=
385
.
227 J
.
keywords:
002
(part 1 of 1) 10 points
Robin pushes a wheelbarrow by exerting a
121 N force horizontally. Robin moves it 83 m
at a constant speed for 24 s.
What power does Robin develop?
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 Fall '07
 Weathers
 Energy, Force, Work, Correct Answer, patel

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