Eng1010 - Problem Sets 1

1 Problem Set 1

1. (2-20 Hibbeler, 11e) The plate is subjected tothe forces acting on the members A and B asshown. If � = 60 �, determine the magnitudeof the resultant of these forces and its directionmeasured clockwise from the positive x axis.

2. (2-49 Hibbeler, 12e) Determine the magnitudeof the resultant force and its direction measuredcounterclockwise from the positive x axis.

3. (2-43 Hibbeler, 11e) If F1 = 300N and � =10 �, determine the magnitude and direction,measured counterclockwise from the x0 axis, ofthe resultant force of the three forces acting onthe bracket.

4. (2-54 Hibbeler, 12e) Three forces act on thebracket. Determine the magnitude and direc-tion � of ~F2 so that the resultant force is di-rected along the positive u axis and has magni-tude of 50 lbf.

Eng1010 - Problem Sets 2

5. (2-58 Hibbeler, 12e) Express each of the threeforces acting on the bracket in Cartesian vectorform with respect to the x and y axes. De-termine the magnitude of and direction � of ~F1so that the resultant force is directed along thepositive x0 axis and has magnitude FR = 600N.

2 Problem Set 2

1. (3-8 Hibbeler, 11e) The 200 kg engine is sus-pended from a vertical chain at A. A secondchain is wrapped around the engine and heldin position by the spreader bar BC. Determinethe compressive force acting along the axis ofthe bar and the tension in segments BA andCA of the chain.

2. (3-10 Hibbeler, 11e) The 500 lbf crate is hoistedusing the ropes AB and AC. Each rope canwithstand a maximum tension of 2500 lbf be-fore it breaks. If AB always remains horizon-tal, determine the smallest angle � to which thecrate can be lifted.

3. (3-7 Hibbeler, 12e) The towing pendant AB issubjected to the force of 50 kN exerted by a tug-boat. Determine the force in each of the bri-dles, BC and BD, if the ship is moving forwardwith constant velocity.

Eng1010 - Problem Sets 3

4. (3-36 Hibbeler, 12e) The 200 lbf uniform tank issuspended by means of a 6 ft long cable, whichis attached to the sides of the tank and passesover the small pulley located at O. If the cablecan be attached at either points A and B, or Cand D, determine which attachment producesthe least amount of tension in the cable. Whatis this tension?

5. (3-42 Hibbeler, 12e) Determine the mass of eachof the two cylinders if they cause a sag of s =0:5m when suspended from the rings at A andB. Note that s = 0 when the cylinders areremoved.

6. (3-57 Hibbeler, 11e) The 500 lbf crate is sus-pended from the cable system shown. Deter-mine the force in each segment of the cable, i.e.AB, AC, CD, CE and CF.

3 Problem Set 3

1. (4-22 Hibbeler, 11e) Determine the clockwisedirection � (0 � � � � 180 �) of the force ~Fsothat it produces: (a) the maximum momentabout A; and (b) no moment about point A.Compute the moment for part (a).

Eng1010 - Problem Sets 4

2. (4-29 Hibbeler, 11e) If the resultant momentabout point A is 4800N�m clockwise, determinethe magnitude of ~F3 if F1 = 300N and F2 =400N.

3. (4-31 Hibbeler, 11e) The worker is using thebar to pull two pipes together in order to com-plete the connection. If he applies a horizontalforce of 80 lbf to the handle of the lever, deter-mine the moment of this force about the endA. What would be the tension T in the ca-ble needed to cause the opposite moment aboutpoint A?

4. (4-80 Hibbeler, 12e) The couples act on thebeam. Determine the magnitude of ~F so that

the resultant couple moment is 450 lbf � ft, con-terclockwise. Where on the beam does the re-sultant couple moment act?

5. (4-85 Hibbeler, 11e) Two couples act on theframe. If d = 4 ft, determine the resultant cou-ple moment. Compute the result by resolvingeach force into x and y components and (a) �nd-ing the moment of each couple and (b) summingmoments of all the force components about B.

6. (4-116 Hibbeler, 11e) Replace the loading act-ing on the beam by a single resultant force.Specify where the force acts, measured from B.

Eng1010 - Problem Sets 5

7. (4-121 Hibbeler, 11e) Replace the loading onthe frame by a single resultant force. Specifywhere its line of action intersects member CD,measured from end C.

8. (4-126 Hibbeler, 12e) Replace the force systemacting on the frame by an equivalent resultantforce and specify where the line of action of theresultant intersects member BC, measured fromB.

4 Problem Set 4

1. (4-152 Hibbeler, 12e) Wind has blown sand overa platform such that the intensity of the loadcan be approximated by the function w = 0:5x3N=m.Simplify this distributed loading to an equiva-lent resultant force and specify its magnitudeand location measured from A.

2. (4-153 Hibbeler, 11e) Replace the distributedloading by an equivalent resultant force andspecify where its line of action intersects mem-ber BC, measured from C.

Eng1010 - Problem Sets 6

3. (4-154 Hibbeler, 11e) Replace the loading by anequivalent resultant force and couple momentacting at point O.

5 Problem Set 5

1. (5-22 Hibbeler, 12e) The articulated crane boomhas a weight of 125 lbf and center of gravity atG. If it supports a load of 600 lbf, determinethe force acting at the pin A and the force inthe hydraulic cylinder BC when the boom is inthe position shown.

2. (5-27 Hibbeler, 12e) As an airplane�s brakes areapplied, the nose wheel exerts two forces on theend of the landing gear as shown. Determinethe horizontal and vertical components of thereaction at the pin C and the force in the strutAB.

3. (5-31 Hibbeler, 12e) If the force of the smoothroller at B on the bar bender is required to be1500 lbf, determine the horizontal and verticalcomponents of the reaction at pin A and therequired magnitude of the force ~F applied tothe handle.

Eng1010 - Problem Sets 7

4. (5-36 Hibbeler, 12e) Outriggers A and B areused to stabilize the crane from overturning whenlifting large loads. If the load to be lifted is 3Mg, determine the maximum boom angle � sothat the crane does not overturn. The cranehas mass of 5 Mg and center of mass at GC ,whereas the boom has mass 0:6 Mg and centerof mass GB .

5. (5-37 Hibbeler, 12e) The wooden plank restingbetween the buildings de�ects slightly when itsupports the 50 kg boy. This de�ection causes atriangular distribution of load at its ends, hav-ing maximum intensities wA and wB . Deter-mine wA and wB , each measured in N=m, whenthe boy is standing 3m from one end as shown.Neglect the mass of the plank.

6. (5-47 Hibbeler, 12e) The motor has a weight of850 lbf. Determine the force that each of thechains exerts on the supporting hooks at A, Band C. Neglect the size of the hooks and thethickness of the beam.

7. (5-50 Hibbeler, 12e) The winch cable on the towtruck is subjected to a force of T = 6kN whenthe cable is directed at � = 60 �. Determine themagnitude of the total brake frictional force ~Ffor the rear set of wheels at B and the totalnormal forces at both front wheels A and rearwheels B for equilibrium. The truck has a totalmass of 4000 kg and mass center at G.

Eng1010 - Problem Sets 8

6 Problem Set 6

1. (6-2 Hibbeler, 12e) The truss used to support abalcony is subjected to the loading show. Ap-proximate each joint as a pin and determinethe force in each member. State whether themembers are in tension or compression. SetP1 = 600 lbf and P2 = 400 lbf.

2. (6-14 Hibbeler, 12e) Determine the force in eachmember of the truss, and state if the mem-bers are in tension or compression. Set P =2500 lbf.

3. (6-26 Hibbeler, 12e) A sign is subjected to awind loading that exerts horizontal forces of300 lbf on joints B and C of one of the sidesupporting trusses. Determine the force in eachmember of the truss and state if the membersare in tension or compression. Note: In my so-lution on the web I forgot to include the 300 lbfat joint B, therefore, my values for FAB andFBE will be incorrect. When this note disap-pears the correct solution has been uploaded.

4. (6-41 Hibbeler, 12e) Determine the force in mem-bers BC, BG and HG of the truss and state ifthe members are in tension or compression.

5. (6-46 Hibbeler, 12e) Determine the force devel-oped in members BC and CH of the roof trussand state if the members are in tension or com-pression.

Eng1010 - Problem Sets 9

7 Problem Set 7

1. (6-69 Hibbeler, 12e) Determine the force ~P re-quired to hold the 50 kg mass in equilibrium.

2. (6-87 Hibbeler, 12e) The hoist supports the 125 kgengine. Determine the force the load creates inmember DB and in member FB, which containsthe hydraulic cylinder H.

3. (6-93 Hibbeler, 12e) The wall crane supports aload of 700 lbf. Determine the horizontal andvertical components of reaction at the pins Aand D. Also, what is the force in the cable atW ? The jib ABC has a weight of 100 lbf andthe member BD has a weight of 40 lbf. Eachmember is uniform and has a center of gravityat its center.

4. (6-98 Hibbeler, 12e) A 300 kg counterweight,with center of mass at G, is mounted on thepitman crank AB of the oil pumping unit. Ifa force of F = 5kN is to be developed in the�xed cable attached to the walking beam DEF,determine the torque M that must be suppliedby the motor.

Eng1010 - Problem Sets 10

5. (6-106 Hibbeler, 12e) The bucket of the backhoeand its contents have a weight of 1200 lbf anda center of gravity at G. Determine the forcesof the hydraulic cylinder AB and in links ACand AD in order to hold the load in the positionshown. The bucket is pinned at E. Note: Inmy solution on the web there is a sketcho inthe FBD for the bucket. For some unknownreason, I drew force ~FAD acting at E. Replacethat force with reactions Ex (left) and Ey (up).When this note disappears the sketcho has been�xed.

8 Problem Set 8

1. (2-86 Hibbeler, 11e) The positions of point Aon the building and point B on the antennahave been measured relative to the electronicdistance meter (EDM) at O. Determine thedistance between A and B.

2. (2-95 Hibbeler, 11e) The window is held openby the chain AB. Determine the length of thechain and express the 30N force acting at Aalong the chain as a Cartesian vector.

Eng1010 - Problem Sets 11

3. (2-98 Hibbeler, 11e) The cable attached to thetractor at B exerts a force of 350 lbf on theframework. Express this force as a Cartesianvector.

4. (2-100 Hibbeler, 11e) Determine the position(x; y; 0) for �xing cable BA so that the resul-tant of the forces exerted on the pole is directedalong its axis, from B to O and has a magni-tude of 1 kN. Also, what is the magnitude offorce ~F3?

9 Problem Set 9

1. (3-47 Hibbeler, 11e) Determine the stretch ineach of the two springs required to hold the20 kg crate in the equilibrium position shown.Each spring has an unstretched length of 2mand a sti¤ness of k = 300N=m.

2. (3-56 Hibbeler, 11e) The ends of three cablesare attached to a ring at A and to the edge ofthe uniform plate. Determine the largest massthe plate can have if each cable can support amaximum tension of 15 kN.

Eng1010 - Problem Sets 12

3. (4-41 Hibbeler, 11e) The pole supports a 22 lbftra¢ c light. Using Cartesian vectors, deter-mine the moment of the weight of the tra¢ clight about the base of the pole at A.

4. (4-45 Hibbeler, 11e) The pipe assembly is sub-jected to the 80N force. Determine the mo-ment of this force about B.

5. (4-93 Hibbeler, 11e) Express the moment of thecouple acting on the rod in Cartesian vectorform. What is the magnitude of the couplemoment?

6. (4-130 Hibbeler, 11e) A force and couple act onthe pipe assembly. If F1 = 50N and F2 = 80N,replace the system by an equivalent resultantforce and couple moment at O. Express theresults in Cartesian vector form.

Eng1010 - Problem Sets 13

10 Problem Set 10

1. (8-14 Hibbeler, 12e) Determine the minimumcoe¢ cient of static friction between the uniform50 kg spool and the wall so that the spool doesnot slip.

2. (8-18 Hibbeler, 12e) The tongs are used to liftthe 150 kg crate, whose center of mass is at G.Determine the least coe¢ cient of static frictionbetween the pivot blocks, A and B, and thecrate so that the crate can be lifted.

3. (8-29 Hibbeler, 12e) If the center of gravity ofthe stacked tables is at G, and the stack weighs100 lbf, determine the smallest force P the boymust push on the stack in order to cause move-ment. The coe¢ cient of static friction at A andB is �s = 0:3. The tables are locked together.

4. (8-58 Hibbeler, 12e) If each box weighs 150 lbf,determine the least horizontal force P that theman must exert on the top box in order to causemotion. The coe¢ cient of static friction be-tween the boxes is �s = 0:65, and the coe¢ cientof static friction between the box and the �ooris �0s = 0:35.

5. (F8-4 Hibbeler, 12e) If the coe¢ cient of staticfriction at contact points A and B is �s, deter-mine the maximum force P that can be appliedwithout causing the 100 kg spool to move.