CHAPTER 4
PROBLEM 4.1
A gardener uses a 60-N wheelbarrow to transport a 250-N bag
of fertilizer. What force must she exert on each handle?
SOLUTION
Free-Body Diagram:
PROBLEM 4.2
The gardener of Problem 4.1 wishes to transport a second
250-N bag of fertilizer at the same time as the first one.
Determine the maximum allowable horizontal distance from
the axle A of the wheelbarrow to the center of gravity of the
second bag if she can hold only 75 N with each arm.
PROBLEM 4.1 A gardener uses a 60-N wheelbarrow to
transport a 250-N bag of fertilizer. What force must she exert on
each handle?
SOLUTION
Free-Body Diagram:
PROBLEM 4.3
A 2100-lb tractor is used to lift 900 lb of gravel.
Determine the reaction at each of the two (a) rear wheels
A, (b) front wheels B.
SOLUTION
PROBLEM 4.4
For the beam and loading shown, determine (a) the reaction at A,
(b) the tension in cable BC.
SOLUTION
Free–Body Diagram:
PROBLEM 4.5
A load of lumber weighing 25 kNW is being raised by a
mobile crane. The weight of the boom ABC and the
combined weight of the truck and driver are as shown.
Determine the reaction at each of the two (a) front wheels
H, (b) rear wheels K.
SOLUTION
Free-Body Diagram:
PROBLEM 4.6
A load of lumber weighing 25 kNW is being raised as
shown by a mobile crane. Knowing that the tension is 25
kN in all portions of cable AEF and that the weight of boom
ABC is 3 kN, determine (a) the tension in rod CD, (b) the
reaction at pin B.
SOLUTION
Free-Body Diagram: (boom)
PROBLEM 4.7
A T-shaped bracket supports the four loads shown. Determine the
reactions at A and B (a) if
10 in.,a
(b) if
7 in.a
SOLUTION
Free-Body Diagram:
0: 0
xx
FB
0: (40lb)(6in.) (30lb) (10lb)( 8in.) (12in.) 0
B
MaaA
(40 160)
12
a
A
(1)
PROBLEM 4.8
For the bracket and loading of Problem 4.7, determine the
smallest distance a if the bracket is not to move.
PROBLEM 4.7 A T-shaped bracket supports the four loads
shown. Determine the reactions at A and B (a) if
10 in.,a
(b) if
7 in.a
SOLUTION
Free-Body Diagram:
PROBLEM 4.9
Three loads are applied as shown to a light beam supported by
cables attached at B and D. Neglecting the weight of the beam,
determine the range of values of Q for which neither cable becomes
slack when
0.P
SOLUTION
Free-Body Diagram:
PROBLEM 4.10
Three loads are applied as shown to a light beam supported by
cables attached at B and D. Knowing that the maximum allowable
tension in each cable is 12 kN and neglecting the weight of the
beam, determine the range of values of Q for which the loading is
safe when 0.P
SOLUTION
Free-Body Diagram:
PROBLEM 4.11
For the beam of Prob. 4.10, determine the range of values of Q for
which the loading is safe when P = 5 kN.
SOLUTION
Free-Body Diagram:
PROBLEM 4.12
For the beam of Sample Prob. 4.2, determine the range of values
of P for which the beam will be safe, knowing that the maximum
allowable value of each of the reactions is 25 kips and that the
reaction at A must be directed upward.
SOLUTION
Free-Body Diagram:
PROBLEM 4.13
The maximum allowable value of each of the reactions is 180 N.
Neglecting the weight of the beam, determine the range of the
distance d for which the beam is safe.
SOLUTION
0: 0
xx
FB
y
BB
0: (50 N) (100 N)(0.45 m ) (150 N)(0.9 m ) (0.9 m ) 0
A
Md d dBd
PROBLEM 4.14
For the beam and loading shown, determine the range of
the distance a for which the reaction at B does not exceed
100 lb downward or 200 lb upward.
SOLUTION
Assume B is positive when directed .
PROBLEM 4.15
Two links AB and DE are connected by a bell crank as
shown. Knowing that the tension in link AB is 720 N,
determine (a) the tension in link DE, (b) the reaction
at C.
SOLUTION
Free-Body Diagram:
0: (100 mm) (120 mm) 0
CAB DE
MF F
5
PROBLEM 4.16
Two links AB and DE are connected by a bell crank as
shown. Determine the maximum force that may be
safely exerted by link AB on the bell crank if the
maximum allowable value for the reaction at C is
1600 N.
SOLUTION
See solution to Problem 4.15 for F.B.D. and derivation of Eq. (1).
5
6
DE AB
FF
(1)
PROBLEM 4.17
The required tension in cable AB is 200 lb. Determine (a) the
vertical force P that must be applied to the pedal, (b) the
corresponding reaction at C.
SOLUTION
Free-Body Diagram:
PROBLEM 4.18
Determine the maximum tension that can be developed in cable
AB if the maximum allowable value of the reaction at C is 250 lb.
SOLUTION
Free-Body Diagram: