PROBLEM 3.90
A rectangular plate is acted upon by the force and couple
shown. This system is to be replaced with a single equivalent
force. (a) For
40 , specify the magnitude and the line of
action of the equivalent force. (b) Specify the value of if the line
of action of the equivalent force is to intersect line CD 300 mm
to the right of D.
SOLUTION
(a)
The given force-couple system (F, M ) at B is
and
F
48 N
M
MB
(0.4 m)(15 N) cos 40
or
M
(0.24 m)(15 N) sin 40
6.9103 N m
The single equivalent force F is equal to F. Further for equivalence
MB: M
or
6.9103 N m
or
d
dF
d 48 N
0.14396 m
F
48.0 N
and the line of action of F intersects line AB 144.0 mm to the right of A.
(b)
Following the solution to Part a but with d
0.1 m and
M B : (0.4 m)(15 N) cos
unknown, have
(0.24 m)(15 N)sin
(0.1 m)(48 N)
or
5cos
3sin
4
25 cos 2
Rearranging and squaring
Using cos 2
1 sin 2
(4 3 sin
and expanding
25(1 sin 2 ) 16 24 sin
or
Then
34 sin 2
)2
24 sin
9
sin
sin
9 sin 2
0
( 24) 2 4(34)( 9)
2(34)
0.97686 or sin
0.27098
24
77.7
or
15.72
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PROBLEM 3.105
The weights of two children sitting at ends A and B of a
seesaw are 84 lb and 64 lb, respectively. Where should a
third child sit so that the resultant of the weights of the
three children will pass through C if she weighs (a) 60 lb,
(b) 52 lb.
SOLUTION
(a)
For the resultant weight to act at C,
Then
(b)
0 WC
(84 lb)(6 ft) 60 lb(d ) 64 lb(6 ft)
For the resultant weight to act at C,
Then
MC
MC
0 WC
(84 lb)(6 ft) 52 lb(d ) 64 lb(6 ft)
60 lb
0
d
2.00 ft to the right of C
d
2.31 ft to the right of C
52 lb
0
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PROBLEM 3.113
A truss supports the loading shown. Determine the
equivalent force acting on the truss and the point of
intersection of its line of action with a line drawn through
Points A and G.
SOLUTION
We have
R
R
F
(240 lb)(cos 70 i sin 70 j) (160 lb) j
(300 lb)( cos 40 i sin 40 j) (180 lb) j
R
(147.728 lb)i (758.36 lb) j
R
Rx2
Ry2
(147.728) 2
(758.36)2
772.62 lb
tan
1
tan
1
Ry
Rx
758.36
147.728
78.977
We have
MA
where
MA
or
R
773 lb
79.0
dR y
[240 lb cos 70 ](6 ft) [240 lb sin 70 ](4 ft)
(160 lb)(12 ft) [300 lb cos 40 ](6 ft)
[300 lb sin 40 ](20 ft) (180 lb)(8 ft)
7232.5 lb ft
d
7232.5 lb ft
758.36 lb
9.5370 ft
or
d
9.54 ft to the right of A
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