Chapter 3 - Supplementary Problems

STATICS OF RIGID BODIES
Chapter Three
EQUILIBRIUM OF COPLANAR FORCE SYSTEMS
Supplementary Problems
01. The crate weighing 400 lb is supported by three ropes concurrent at B. Find the forces
in ropes AB and BC is P = 460 lb.
02. The 1200-car is being lowered

slowly onto the dock using hoist A
and a winch C. Determine the forces
in cables BA and BC for the position shown.
03. A homogeneous 6-m bar AB is supported

in the vertical plane by rollers at A and B
and by a cable at C. The mass of the bar is
50 kg. Determine the roller reactions at A
and B and tension in the cable at C.
04. A frame is fabricated by joining the

three bars with pin at B, C, and D. The
frame is loaded by the 1000-lb force and
the 1200-lb-ft couple. The supports
consist of a pin at A and a roller at E.
Determine the support reaction
components at A and E.
05. The homogeneous 60-kg disk supported
by the rope AB rest against a rough
vertical wall. Determine the force in the
rope and the reaction at the wall.
06. The homogeneous, 120-kg wooden beam is suspended from ropes at A and B. A power wrench applies
the 500-N · m clockwise couple to tighten a bolt at C. Determine the tensions in the ropes.
07. The 480-kg bent bar ABC of uniform cross section is supported by a pin at A and a vertical cable at C.
Determine the pin reactions and the force in the cable.
08. The bent beam ABC is attached to a pin at C and rests against a rollersupport at B. Neglecting the
weight of the beam, find the reactions at B and C caused by the 150-kg load.
09. Compute all reactions at the base A of the traffic light

standard, given that the tension in the cable BC is
T = 544 lb; and (b) T =0. The weight of the standard
is negligible compared with the 320-lb weight of the traffic light.
10. The uniform plank ABC weighs 400 N. It is
supported by a pin at A and a cable that runs
around the pulley D. Determine the tension
in the cable and the components of the pin
reaction at A. Note that the tension in the cable
is constant.
11. The telephone cable spool weighs 300 lb and

is held at rest on a 40◦ incline by the horizontal
cable. The cable is wound around the inner hub
of the spool and attached to the support at B.
Assume that G, the center of gravity of the spool,
is located at the center of the spool. Find all
forces acting on the spool.
12. The homogeneous 40-kg bar ABC is held in position by a horizontal rope attached to end C.
Neglecting friction, determine the tension in the rope.
13. The horizontal force P is applied to the handle of the

puller. Determine the resulting tension T in the chain
if P = 200 N.
14. The thin steel plate, weighing 82 lb/ft2, is being lifted slowly by the cables AC and BC. Compute the
distance x and find the corresponding tension in each of the cables
15. The mass of the uniform bar AB is 40 kg. Calculate the couple C required for equilibrium if (a) θ = 0; and
(b) θ =54◦.
16. The 90-kg man, whose center of gravity is at G,

is climbing a uniform ladder. The length of the
ladder is 5 m, and its mass is 20 kg. Friction may be
neglected.
(a) Compute the magnitudes of the reactions at
A and B for x =1.5 m.
(b) Find the distance x for which the ladder will be ready to fall.
17. The homogeneous 18-kg pulley is attached to the bar ABC with a pin at B. The mass of the bar is
negligible. The cable running over the pulley carries a tension of 600 N. Determine the magnitudes of
the support reactions at A and C.
18. Each of the sandbags piled on the 250-lb uniform beam weighs 12 lb. Determine the support reactions
at A and C.
19. The homogeneous 600-lb plate is suspended from three cables. Determine the force in each cable.
20. A machine operator produces the tension T in the control rod by applying the force P to the foot pedal.
Determine the largest P if the magnitude of the pin reaction at B is limited to 1.8 kN. Neglect the mass
of the mechanism.
21. For the trusses shown, calculate the total reactions at the supports.
PROB 22
PROB 21
PROB 23
PROB 24
25. The beam AB shown has mass of 30 kg and is
supported by a rough surface at A and a cable
at B. Determine the total surface reaction at A
and the tension in the cable.
26. Neglecting the beam weight, compute the reactions

at A and B.
27. The supporting structure of the billboard is attached

to the ground by a pin at B, and its rear leg rests on
the ground at A. Friction may be neglected. Point G is
the center of gravity of the billboard and structure,
which together weigh 2800 lb. To prevent tipping
over in high winds, a 2370-lb weight is placed on
the structure near A, as shown.
(a) Compute the magnitudes of the reactions at A
and B if the wind load on the billboard is
q =120 lb/ft.
(b) Find the smallest wind load q that would cause
the structure to just tip over.
28. The self-regulating floodgate ABC, pinned at B, is pressed against the lip of the spillway at C by the
action of the 3645-lb weight A. If the gate is to open when the water level reaches a height h =6 ft,
determine the distance x locating the weight A. Neglect the weight of the gate.
29. Determine the reactions at the fixed support for the frame loaded as shown.
30. Determine the reactions at the supports for the frames loaded as shown.
PROB 31
PROB 30
PROB 32 PROB 33
34. The cylinders in the figure have the indicated weight and dimensions. Assuming smooth contact
surfaces, determine the reactions at A, B, C, and D on the cylinders.
35. Determine the reactions R1 and R2 for the beam loaded as shown.
36. The weight W of a travelling crane is 20 tons acting as shown. To prevent the crane from tipping to the
right when carrying a load P of 20 tons, a counterweight Q is used. Determine the value and position of
Q so that the crane will remain in equilibrium both when the maximum load P is applied and when the
load P is removed.
37. Determine the support reactions for the roof truss loaded as shown.
38. A boom AB is supported in a horizontal position by a

hinge A and a cable which runs from C over a small pulley
at D as shown. Compute the tension T in the cable and the
horizontal and vertical components of the reaction at A.
Neglect the mass of the boom and the size of the pulley
at D.
39. The forces acting on a 1-ft length of a dam are shown below. The upward ground reaction varies
uniformly from an intensity p1 lb/ft at A to p2 lb/ft at B. Determine p1 and p2 and also the horizontal
resistance to sliding.
40. The uniform rod weight 420 lb and has its center of gravity at G. Determine the tension in the cable
and the reactions at the smooth surfaces at A and B.
ACKNOWLEDGEMENT:
This Instructional Material was compiled from the following references:
1. Engineering Mechanics Statics 3rdEdition Pytel & Kiusalaas
2. Engineering Mechanics 2nd Edition Ferdinand Singer
3. Engineering Mechanics Statics 13th Edition by RC Hibbeler
4. Fundamentals of Structural Analysis by Leet 5th Edition

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Chapter 3 - Supplementary Problems

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STATICS OF RIGID BODIES

02. The 1200-car is being lowered

03. A homogeneous 6-m bar AB is supported

04. A frame is fabricated by joining the

09. Compute all reactions at the base A of the traffic light

11. The telephone cable spool weighs 300 lb and

13. The horizontal force P is applied to the handle of the

16. The 90-kg man, whose center of gravity is at G,

26. Neglecting the beam weight, compute the reactions

27. The supporting structure of the billboard is attached

38. A boom AB is supported in a horizontal position by a

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