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PROBLEM 3.98
Q - * it! A 5-m-long beam is subjected to a variety of loadings. (a) Replace each
" loading with an equivalent force-couple system at end B of the beam.
,,,,,, a. .......... "gm; R) (b) Which of the loadings are equival
PROBLEM 2.46
75'
Two eables are tied together at C and are loaded as shown. Detennine the tension
(0) in cable AC, (b) in cable Be.
.c7~"_-lC
SOLUTION
.
Force Triangle
Free-Body Diagram
W=mg
= (200 kgX9.81 mI")
=1962N
Law of sines:
(a)
(b)
TAC
THe
1962 N
,
PROBLEM 2.71
\-)IX) K
Determine (a) the x, y, and z components of the 750-N force, (b) the
angles 8.", ~, and B. that the force forms with the coordinate axes.
"',
•
,
SOLUTION
Fh =Fsin 35 0
= (750 N)sin 35°
Fh =430.2 N
./
(aJ
,
F =Fcos35°
=(430.2 N) co
PROBLEM 2.99
Three cables are used to tether a balloon as shown. Determine the
vertieal force P exerted by the balloon at A knowing that the tension
in cable AD is 259 N.
,
SOLUTION
1;"
\
o
'"I.to.
The forces applied at A are:
TAB' T ,.Ie. TAD' and P
wher
PROBLEM 3.1
A foot valve for a pneumatic system is hinged at B. Knowing
that a = 28°, detennine the moment of the 16-N force about
Point B by resolving the force into horizontal and vertical
components.
SOLUTION
Note that
and
f}
F~
=a-2Do = 28"_20° =8"
=
PROBLEM 3.39
Consider the volleyball net shown.
Determine the angle formed by guy
wires AD and AC.
SOLUTION
and
AB =
~(-6.5)' + (-S)' + (2)'
AC =
First note
~(O)' + (-S)' + (6)'
= 10.5 ft
= 10 ft
AB = -{6.5 ft)I-(S ft)J + (2 ft)k
AC = -{S ft)j + (6 ft)k
B
PROBLEM 3.75
The shafts of an angle drive are acted upon by the two couples shown.
Replace tbe two couples whh a single equivl:llent COUpllC, specifYing its
magnitude and the direction of its axis.
,
SOLUTION
Based on
where
M 1 =-(81b·ft)j
M, = -{6Ib·ft)k
ZOO N
"
400 N
~ ~_.'mlllll[;,-:i2"
PROBLEM 3.102
A 4-m-long beam is loaded as shown. Detennine the loading of
Problem 3.101 which is equivalent to this loading.
N",
SOLUTION
We have
and
I:F,' -200N-4ooN=R
I:M"
or R=600Nj .
-400 N, m+ 28ooN, m -(400 N)(4m)
IIOin.~lOin.
r
7.')1)
PROBLEM 4.25
Determine the reactions at A and B when (a) a = O. (b) a = 90°,
(e) «=30°,
lb. ill.
12 in.
SOLUTION
a=O
(a)
+jI:M A =0:
B(20in.)-750Ib·in.=O
B=37.51b
.±.IF,=O: A,=O
+1 IF,=O:
A,+37.5lb=0
A, =-37.51b
A=37.5lb!
B=37.51bj<l
PROBLEM 2.46
Ropes AB and AC are thrown to a boater whose canoe had capsized.
Knowing that a = 25° and that the magnitude of the force FR exerted by
the river on the boater is 70 1b, determine the tension (a) in rope AB, (b)
in rope AC.
SOLUTION
F