1 Problem Set 1

Eng1010 - Problem Sets

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Problem Set 1 1. (2-20 Hibbeler, 11e) The plate is subjected to the forces acting on the members A and B as shown. If = 60 , determine the magnitude of the resultant of these forces and its direction measured clockwise from the positive x axis.

2. (2-49 Hibbeler, 12e) Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis.

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

4. (2-54 Hibbeler, 12e) Three forces act on the bracket. Determine the magnitude and direction of F~2 so that the resultant force is directed along the positive u axis and has magnitude of 50 lbf.


5. (2-58 Hibbeler, 12e) Express each of the three forces acting on the bracket in Cartesian vector form with respect to the x and y axes. Determine the magnitude of and direction of F~1 so that the resultant force is directed along the positive x0 axis and has magnitude FR = 600 N.

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2. (3-10 Hibbeler, 11e) The 500 lbf crate is hoisted using the ropes AB and AC. Each rope can withstand a maximum tension of 2500 lbf before it breaks. If AB always remains horizontal, determine the smallest angle to which the crate can be lifted.

3. (3-7 Hibbeler, 12e) The towing pendant AB is subjected to the force of 50 kN exerted by a tugboat. Determine the force in each of the bridles, BC and BD, if the ship is moving forward with constant velocity.

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Problem Set 2 1. (3-8 Hibbeler, 11e) The 200 kg engine is suspended from a vertical chain at A. A second chain is wrapped around the engine and held in position by the spreader bar BC. Determine the compressive force acting along the axis of the bar and the tension in segments BA and CA of the chain.


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4. (3-36 Hibbeler, 12e) The 200 lbf uniform tank is suspended by means of a 6 ft long cable, which is attached to the sides of the tank and passes over the small pulley located at O. If the cable can be attached at either points A and B, or C and D, determine which attachment produces the least amount of tension in the cable. What is this tension?

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

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

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Problem Set 3 1. (4-22 Hibbeler, 11e) Determine the clockwise direction (0 180 ) of the force F~ sothat it produces: (a) the maximum moment about A; and (b) no moment about point A. Compute the moment for part (a).


2. (4-29 Hibbeler, 11e) If the resultant moment about point A is 4800 N m clockwise, determine the magnitude of F~3 if F1 = 300 N and F2 = 400 N.

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the resultant couple moment is 450 lbf ft, conterclockwise. Where on the beam does the resultant couple moment act?

5. (4-85 Hibbeler, 11e) Two couples act on the frame. If d = 4 ft, determine the resultant couple moment. Compute the result by resolving each force into x and y components and (a) …nding the moment of each couple and (b) summing moments of all the force components about B.

3. (4-31 Hibbeler, 11e) The worker is using the bar to pull two pipes together in order to complete the connection. If he applies a horizontal force of 80 lbf to the handle of the lever, determine the moment of this force about the end A. What would be the tension T in the cable needed to cause the opposite moment about point A?

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

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


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

8. (4-126 Hibbeler, 12e) Replace the force system acting on the frame by an equivalent resultant force and specify where the line of action of the resultant intersects member BC, measured from B.

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Problem Set 4 1. (4-152 Hibbeler, 12e) Wind has blown sand over a platform such that the intensity of the load can be approximated by the function w = 0:5x3 N= m. Simplify this distributed loading to an equivalent resultant force and specify its magnitude and location measured from A.

2. (4-153 Hibbeler, 11e) Replace the distributed loading by an equivalent resultant force and specify where its line of action intersects member BC, measured from C.


3. (4-154 Hibbeler, 11e) Replace the loading by an equivalent resultant force and couple moment acting at point O.

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2. (5-27 Hibbeler, 12e) As an airplane’s brakes are applied, the nose wheel exerts two forces on the end of the landing gear as shown. Determine the horizontal and vertical components of the reaction at the pin C and the force in the strut AB.

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

3. (5-31 Hibbeler, 12e) If the force of the smooth roller at B on the bar bender is required to be 1500 lbf, determine the horizontal and vertical components of the reaction at pin A and the required magnitude of the force F~ applied to the handle.


4. (5-36 Hibbeler, 12e) Outriggers A and B are used to stabilize the crane from overturning when lifting large loads. If the load to be lifted is 3 Mg, determine the maximum boom angle so that the crane does not overturn. The crane has mass of 5 Mg and center of mass at G C , whereas the boom has mass 0:6 Mg and center of mass G B .

5. (5-37 Hibbeler, 12e) The wooden plank resting between the buildings de‡ects slightly when it supports the 50 kg boy. This de‡ection causes a triangular distribution of load at its ends, having maximum intensities wA and wB . Determine wA and wB , each measured in N= m, when the boy is standing 3 m from one end as shown. Neglect the mass of the plank.

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6. (5-47 Hibbeler, 12e) The motor has a weight of 850 lbf. Determine the force that each of the chains exerts on the supporting hooks at A, B and C. Neglect the size of the hooks and the thickness of the beam.

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


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Problem Set 6 1. (6-2 Hibbeler, 12e) The truss used to support a balcony is subjected to the loading show. Approximate each joint as a pin and determine the force in each member. State whether the members are in tension or compression. Set P1 = 600 lbf and P2 = 400 lbf.

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

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

5. (6-46 Hibbeler, 12e) Determine the force developed in members BC and CH of the roof truss and state if the members are in tension or compression.

3. (6-26 Hibbeler, 12e) A sign is subjected to a wind loading that exerts horizontal forces of 300 lbf on joints B and C of one of the side supporting trusses. Determine the force in each member of the truss and state if the members are in tension or compression. Note: In my solution on the web I forgot to include the 300 lbf at joint B, therefore, my values for FAB and FBE will be incorrect. When this note disappears the correct solution has been uploaded.


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Problem Set 7 1. (6-69 Hibbeler, 12e) Determine the force P~ required to hold the 50 kg mass in equilibrium.

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3. (6-93 Hibbeler, 12e) The wall crane supports a load of 700 lbf. Determine the horizontal and vertical components of reaction at the pins A and D. Also, what is the force in the cable at W ? The jib ABC has a weight of 100 lbf and the member BD has a weight of 40 lbf. Each member is uniform and has a center of gravity at its center.

2. (6-87 Hibbeler, 12e) The hoist supports the 125 kg engine. Determine the force the load creates in member DB and in member FB, which contains the hydraulic cylinder H. 4. (6-98 Hibbeler, 12e) A 300 kg counterweight, with center of mass at G, is mounted on the pitman crank AB of the oil pumping unit. If a force of F = 5 kN is to be developed in the …xed cable attached to the walking beam DEF, determine the torque M that must be supplied by the motor.


5. (6-106 Hibbeler, 12e) The bucket of the backhoe and its contents have a weight of 1200 lbf and a center of gravity at G. Determine the forces of the hydraulic cylinder AB and in links AC and AD in order to hold the load in the position shown. The bucket is pinned at E. Note: In my solution on the web there is a sketcho in the FBD for the bucket. For some unknown reason, I drew force F~AD acting at E. Replace that force with reactions Ex (left) and Ey (up). When this note disappears the sketcho has been …xed.

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Problem Set 8 1. (2-86 Hibbeler, 11e) The positions of point A on the building and point B on the antenna have been measured relative to the electronic distance meter (EDM) at O. Determine the distance between A and B.

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


3. (2-98 Hibbeler, 11e) The cable attached to the tractor at B exerts a force of 350 lbf on the framework. Express this force as a Cartesian vector.

4. (2-100 Hibbeler, 11e) Determine the position (x; y; 0) for …xing cable BA so that the resultant of the forces exerted on the pole is directed along its axis, from B to O and has a magnitude of 1 kN. Also, what is the magnitude of force F~3 ?

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Problem Set 9 1. (3-47 Hibbeler, 11e) Determine the stretch in each of the two springs required to hold the 20 kg crate in the equilibrium position shown. Each spring has an unstretched length of 2 m and a sti¤ness of k = 300 N= m.

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


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

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

6. (4-130 Hibbeler, 11e) A force and couple act on the pipe assembly. If F1 = 50 N and F2 = 80 N, replace the system by an equivalent resultant force and couple moment at O. Express the results in Cartesian vector form. 4. (4-45 Hibbeler, 11e) The pipe assembly is subjected to the 80 N force. Determine the moment of this force about B.


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Problem Set 10

1. (8-14 Hibbeler, 12e) Determine the minimum coe¢ cient of static friction between the uniform 50 kg spool and the wall so that the spool does not slip.

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

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

5. (F8-4 Hibbeler, 12e) If the coe¢ cient of static friction at contact points A and B is s , determine the maximum force P that can be applied without causing the 100 kg spool to move.

3. (8-29 Hibbeler, 12e) If the center of gravity of the stacked tables is at G, and the stack weighs 100 lbf, determine the smallest force P the boy must push on the stack in order to cause movement. The coe¢ cient of static friction at A and B is s = 0:3. The tables are locked together.