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Overton, Mays – Homework 27 – Due: Apr 11 2005, 4:00 am – Inst: Turner
1
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beFore answering.
The due time is Central
time.
001
(part 1 oF 3) 10 points
A uniForm rod pivoted at one end “point
O
”
is Free to swing in a vertical plane in a gravita
tional feld. However, it is held in equilibrium
by a Force
F
at its other end.
The rod makes an angle 40
◦
with the hori
zontal. The length oF the rod is 5 m. The Force
makes and angle 68
◦
with the horizontal. The
weight oF the rod is 9
.
8 N.
x
y
5
m
F
68
◦
40
O
What is the magnitude oF the Force
F
?
Correct answer: 7
.
99541 N.
Explanation:
Let :
‘
= 5 m
,
W
= 9
.
8 N
,
θ
= 40
◦
,
and
φ
= 68
◦
.
x
y
ψ
‘
W
φ
θ
O
R
Basic Concepts:
±or static equilibrium,
we have
X
i
F
xi
= 0
,
(1)
X
i
F
y i
= 0
,
and
(2)
X
i
τ
i
= 0
.
(3)
Solution:
Using the torque equation,
about point
O
, (Eq. 3 with counter clock
wise positive), we have
‘
2
W
cos
θ

‘F
cos
θ
sin
φ
+
‘F
sin
θ
cos
φ
= 0
W
2

F
sin
φ
+
F
tan
θ
cos
φ
= 0
,
so
F
=
W
2[sin
φ

cos
φ
·
tan
θ
]
(4)
=
(9
.
8 N)
2[sin68
◦

cos68
◦
·
tan40
◦
]
=
7
.
99541 N
.
Alternate Solution:
The angle between
the Force
F
and the rod is
β
=
φ

θ
= (68
◦
)

(40
◦
) = 28
◦
.
Using the torque equation,
about point
O
, (Eq. 3 with counter clockwise
positive), we have
‘
2
W
cos
θ
=
‘F
sin
β ,
so
F
=
W
2
cos
θ
sin
β
(5)
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View Full DocumentOverton, Mays – Homework 27 – Due: Apr 11 2005, 4:00 am – Inst: Turner
2
=
(9
.
8 N)
2
cos40
◦
sin28
◦
=
7
.
99541 N
.
002
(part 2 of 3) 10 points
What is the magnitude of the force the pivot
exerts on the rod at point
O
?
Correct answer: 3
.
82983 N.
Explanation:
Using the translational equations (Eqs. 1
and 2), where
R
x
and
R
y
are the horizontal
and vertical components of the force
R
at the
pivot, we have
F
x
+
R
x
= 0
,
so
(1)
R
x
=

F
x
=

F
cos
φ
=

(7
.
99541 N)cos68
◦
=

2
.
99513 N
,
and
F
y
+
R
y
=
W ,
so
(2)
R
y
=
W

F
y
=
W

F
sin
φ
= (9
.
8 N)

(7
.
99541 N)sin68
◦
= 2
.
38678 N
,
and
k
~
R
k
=
q
R
2
x
+
R
2
y
=
q
(

2
.
99513 N)
2
+ (2
.
38678 N)
2
=
3
.
82983 N
.
003
(part 3 of 3) 10 points
What is the angle (

180
◦
≥
θ
≥
+180
◦
) the
reactive force on the pivot at point
O
makes
with the positive
x
axis?
Correct answer: 141
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 Spring '08
 Turner
 Physics, Work

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