PROBLEM 3.70
Two 80-N forces are applied as shown to the corners B and D of
a rectangular plate. (a) Determine the moment of the couple
formed by the two forces by resolving each force into horizontal
and vertical components and adding the moments of the two
resulting couples. (b) Use the result obtained to determine the
perpendicular distance between lines BE and DF.
SOLUTION
(a)
Resolving forces into components:
P (80 N)sin 50
61.284 N
Q (80 N)cos50
M
(51.423 N)(0.5 m) (61.284 N)(0.3 m)
7.3263 N m
M
(b)
51.423 N
7.33 N m
Distance between lines BE and DF
M
or
Fd
7.3263 N m=(80 N)d
d
0.091579 m
d
91.6 mm
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PROBLEM 3.72
Four 1 12 -in.-diameter pegs are attached to a board as shown.
Two strings are passed around the pegs and pulled with the
forces indicated. (a) Determine the resultant couple acting on
the board. (b) If only one string is used, around which pegs
should it pass and in what directions should it be pulled to
create the same couple with the minimum tension in the string?
(c) What is the value of that minimum tension?
SOLUTION
M
(a)
(60 lb)(10.5 in.) (40 lb)(13.5 in.)
630 lb in. 540 lb in.
M
(b)
1170 lb in.
With only one string, pegs A and D, or B and C should be used. We
have
tan
9
12
36.9
90
53.1
Direction of forces:
(c)
With pegs A and D:
53.1
With pegs B and C:
53.1
The distance between the centers of the two pegs is
122
92
15 in.
Therefore, the perpendicular distance d between the forces is
d
15 in. 2
3
in.
4
16.5 in.
We must have
M
Fd 1170 lb in. F (16.5 in.)
F
70.9 lb
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PROBLEM 3.74
A piece of plywood in which several holes are being drilled
successively has been secured to a workbench by means of two
nails. Knowing that the drill exerts a 12-N·m couple on the
piece of plywood, determine the magnitude of the resulting
forces applied to the nails if they are located (a) at A and B,
(b) at B and C, (c) at A and C.
SOLUTION
(a)
(b)
(c)
M
12 N m
M
12 N m
M
Fd
Fd
F (0.45 m)
F
26.7 N
F
50.0 N
F
23.5 N
Fd
F (0.24 m)
d
(0.45 m) 2
(0.24 m) 2
0.510 m
12 N m
F (0.510 m)
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PROBLEM 3.78
Replace the two couples shown with a single equivalent
couple, specifying its magnitude and the direction of its axis.
SOLUTION
Replace the couple in the ABCD plane with two couples P and Q shown:
P
(50 N)
CD
CG
(50 N)
160 mm
200 mm
40 N
Q
(50 N)
CF
CG
(50 N)
120 mm
200 mm
30 N
Couple vector M1 perpendicular to plane ABCD:
M1
(40 N)(0.24 m) (30 N)(0.16 m)
4.80 N m
Couple vector M2 in the xy plane:
M2
tan
M1
M2
M
(12.5 N)(0.192 m)
2.40 N m
144 mm
36.870
192 mm
(4.80 cos 36.870 ) j (4.80 sin 36.870 )k
3.84 j 2.88k
2.40 j
M1
M2
M
1.44 j 2.88k
3.22 N m;
x
90.0 ,
y
53.1 ,
z
36.9
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