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The
x
and
y
applications of Newton's second law provide two equations:
F
1
cos
θ
–
f
k
–
mg
sin
=
ma
F
N
–
F
1
sin
–
mg
cos
= 0.
(a) The trunk is moving up the incline at constant velocity, so
a
= 0. Using
f
k
=
μ
k
F
N
, we
solve for the pushforce
F
1
and obtain
F
mg
k
k
1
=
+
−
sin
cos
cos
sin
.
bg
The work done by the pushforce
G
F
1
as the trunk is pushed through a distance
A
up the
inclined plane is therefore
()
(
)
(
)
(
)
11
k
2
3
cos
sin
cos
cos
cos
sin
50 kg 9.8 m s
6.0 m cos30
sin30
0.20 cos30
cos30
0.20 sin30
2.2 10 J.
k
mg
WF
θθ
θμ θ
+
==
−
°°
+
°
=
°−
°
=×
A
A
(b) The increase in the gravitational potential energy of the trunk is
23
sin
(50kg)(9.8m/s )(6.0m)sin30
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 Spring '08
 Any
 Physics

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