PROBLEM 4.68 (Continued)
Force Triangle
PROBLEM 4.69
A 50-kg crate is attached to the trolley-beam system shown.
Knowing that
1.5 m,a
determine (a) the tension in cable CD,
(b) the reaction at B.
SOLUTION
Three-force body:
W
and CD
T
intersect at E.
0.7497 m
tan 1.5 m
PROBLEM 4.70
One end of rod AB rests in the corner A and the other end is attached to
cord BD. If the rod supports a 150-N load at its midpoint C, find the
reaction at A and the tension in the cord.
SOLUTION
Free-Body Diagram:
(Three-force body) Dimensions in mm
PROBLEM 4.71
For the boom and loading shown, determine (a) the tension in cord
BD, (b) the reaction at C.
SOLUTION
Three-force body: 3-kip load and T intersect at E.
Geometry:
Free-Body Diagram:
PROBLEM 4.72
A 40-lb roller, of diameter 8 in., which is to be used on a tile floor, is
resting directly on the subflooring as shown. Knowing that the thickness
of each tile is 0.3 in., determine the force
P
required to move the roller
onto the tiles if the roller is (a) pushed to the left, (b) pulled to the right.
SOLUTION
Geometry: For each case as roller comes into contact with
tile,
1
3.7 in.
cos 4 in.
PROBLEM 4.73
A T-shaped bracket supports a 300-N load as shown. Determine
the reactions at A and C when α 45°.
SOLUTION
Free-Body Diagram:
(Three-force body)
PROBLEM 4.73 (Continued)
Force Triangle
PROBLEM 4.74
A T-shaped bracket supports a 300-N load as shown. Determine
the reactions at A and C when α 60°.
SOLUTION
Free-Body Diagram:
PROBLEM 4.74 (Continued)
Force Triangle
PROBLEM 4.75
Rod AB is supported by a pin and bracket at A and rests against a frictionless
peg at C. Determine the reactions at A and C when a 170-N vertical force is
applied at B.
SOLUTION
The reaction at A must pass through D where
C
and the 170-N force intersect.
160 mm
tan 300 mm
Free-Body Diagram:
(Three-force body)
PROBLEM 4.76
Solve Problem 4.75, assuming that the 170-N force applied at B is horizontal
and directed to the left.
PROBLEM 4.75
Rod AB is supported by a pin and bracket at A and rests
against a frictionless peg at C. Determine the reactions at A and C when a
170-N vertical force is applied at B.
SOLUTION
Free-Body Diagram:
(Three-Force body)
PROBLEM 4.77
Member ABC is supported by a pin and bracket at B and by an
inextensible cord attached at A and C and passing over a
frictionless pulley at D. The tension may be assumed to be the
same in portions AD and CD of the cord. For the loading shown
and neglecting the size of the pulley, determine the tension in the
cord and the reaction at B.
SOLUTION
Reaction at B must pass through D.
7 in.
tan 12 in.
30.256
Free-Body Diagram:
PROBLEM 4.78
Using the method of Section 4.7, solve Problem 4.22.
PROBLEM 4.22
A lever AB is hinged at C and attached to a
control cable at A. If the lever is subjected to a 500-N horizontal
force at B, determine (a) the tension in the cable, (b) the
reaction at C.
SOLUTION
Reaction at C must pass through E, where
F
AD
and 500-N force intersect.
Since 250 mm,AC CD triangle
ACD
is isosceles.
We have 90 30 120C
Free-Body Diagram:
(Three-Force body)
PROBLEM 4.79
Knowing that
30, determine the reaction (a) at B, (b) at C.
SOLUTION
Reaction at C must pass through D where force
P
and reaction at B intersect.
In CDE: (3 1)
tan
R
R
Free-Body Diagram:
(Three-force body)
PROBLEM 4.80
Knowing that
60, determine the reaction (a) at B, (b) at C.
SOLUTION
Reaction at C must pass through D where force
P
and reaction at B intersect.
In CDE:
3
tan
R
R
R
Free-Body Diagram:
(Three-force body)
PROBLEM 4.81
Determine the reactions at A and B when 50°.
SOLUTION
Free-Body Diagram:
(Three-force body)
Reaction
A
must pass through Point D where the 100-N force
and
B
intersect.
In right BCD:
PROBLEM 4.82
Determine the reactions at A and B when
80.
SOLUTION
Free-Body Diagram:
(Three-force body)
PROBLEM 4.82 (Continued)
Force Triangle
PROBLEM 4.83
Rod AB is bent into the shape of an arc of circle and is lodged between two
pegs D and E. It supports a load
P
at end B. Neglecting friction and the weight
of the rod, determine the distance c corresponding to equilibrium when a 20
mm and R 100 mm.
SOLUTION
Free-Body Diagram:
Since
,
ED ED
yxa
slope of ED is
45 ;
slope of HC is
45 .
PROBLEM 4.84
A slender rod of length L is attached to collars that can slide freely along
the guides shown. Knowing that the rod is in equilibrium, derive an
expression for the angle
in terms of the angle
.
SOLUTION
As shown in the free-body diagram of the slender rod AB, the three forces intersect at C. From the force
geometry:
Free-Body Diagram:
tan
GB
AB
x
y