Eng1010 - Examples 1

1 Particles

1. (#1 Test 1, 2010) Masses m1 = 20 kg andm2 = 50 kg are suspended by spring AB,and cables BC and CD. The linear springconstant for spring AB is k = 196 N/m. De-termine the tensions in cables BC and CD(TBC and TCD), the dimension h (the heightof A above B), and the unstretched lengthof spring AB (lAB,o).

2 Moments, Couples and ForceResultant Systems

1. (4-20 Hibbeler, 11e) The boom has lengthof 30 ft, a weight of 800 lb, and mass centerat G. If the maximum moment that canbe developed by the motor at A is ~M =20, 000 lb·ft, determine the maximum loadW , having mass center at G′, that can belifted. Take θ = 30◦.

2. Ignoring the distributed load on the left sideof the structure, determine the magnitude of

the couple forces, F , such that the resultantcouple moment at A is zero. If F = 250 kN,determine the magnitude and direction of ahorizontal force ~FB applied at point B lo-cated on the left side of the column, 3 mvertically above A, such that the resultantcouple moment at A is zero. What is theresultant force at A when ~FB is applied?

3. (4-117 Hibbeler, 11e) Replace the loadingsystem on the beam by an equivalent resul-tant force and couple moment at point O.Replace the resultant force and couple mo-ment at point O with a single force ~F ap-plied to the upper surface of the beam.

4. (4-76 Hibbeler, 11e) The floor causes a cou-ple moment of ~MA = 40 N·m ←↩ and ~MB =

Eng1010 - Examples 2

30 N·m ↪→ on the brushes of the polishingmachine. Determine the magnitude of thecouple forces, F , that must be developedby the operator on the handles so that theresultant couple moment on the polisher iszero. What is the magnitude of these forcesif the brush at B suddenly stops so thatMB = 0?

3 Rigid Bodies

1. (5-23 Hibbeler, 11e) The ramp of a ship hasa weight of 200 lb and a centre of gravity atG. Determine the cable force in CD neededto just start lifting the ramp, (i.e. so the re-action at B becomes zero). Also, determinethe vertical and horizontal components offorce at the hinge (pin) at A.

2. (5-43 Hibbeler, 11e) The upper portion ofthe crane boom consists of the jib AB, which

is supported by the pin at A, the guy lineBC, and the backstay CD, each cable be-ing separately attached to the mast at C. Ifthe 5 kN load is supported by the hoist line,which passes over the pulley at B, determinethe magnitude of the resultant force the pinexerts on the jib at A for equilibrium, thetension in the guy line BC, and the tensionT in the hoist line. Neglect the weight of thejib. The pulley at B has a radius of 0.1 m.

3. (5-40 Hibbeler, 11e) Soil pressure acting onthe concrete retaining wall is represented asa loading per foot length of wall. If con-crete has a specific weight of γ = 150 lb/ft3,determine the magnitude of the soil distri-bution, w1 and w2, and the frictional force~F for equilibrium.

Eng1010 - Examples 3

4. (5-51 Hibbeler, 11e) The toggle switch con-sists of a cocking lever that is pinned to afixed frame at A and held in place by thespring which has an unstretched length of200 mm. Determine the magnitude of theresultant force at A and the normal forceon the peg at B when the lever is in theposition shown. Note: use k = 5 kN/m.

5. The rubber-tired four wheel drive tractorhas a mass of 13,500 kg with center of massat G and is used for pushing or pullingheavy loads. Determine the maximum loadP which the tractor can pull at a constantspeed of 5 km/h up the 15% grade if thedriving force exerted by the ground on eachof its four wheels is 80% of the normal forceunder that wheel. What are the normalforces under each pair of wheels (i.e. bothwheels at each location)?

4 Trusses

1. (6-1 Hibbeler, 11e) Determine the force ineach member of the truss and state if themembers are in tension or compression. SetP1 = 7 kN, P2 = 7 kN.

2. (6-14 Hibbeler, 11e) Determine the force ineach member of the truss and state if themembers are in tension or compression. SetP1 = 100 lb, P2 = 200 lb, P3 = 300 lb.

Eng1010 - Examples 4

3. (6-39 Hibbeler, 11e) Determine the forces inmembers BC, FC and FE, and state if thememebers are in tension or compression.

4. (6-42 Hibbeler, 11e) Determine the force inmembers BC, HC and HG. After the trussis sectioned use a single equation of equilib-rium for the calculation of each force. Stateif these members are in tension or compres-sion.

5 Frames and Machines

1. (6-70 Hibbeler, 11e) The 150 lb man at-tempts to lift himself and the 10 lb seat us-ing the rope and pulley system shown. De-termine the force at A needed to do so, andalso find his reaction on the seat.

2. (6-94 Hibbeler, 11e) The tongs consist oftwo jaws pinned to links at A, B, C andD. Determine the horizontal force exertedon the 500 lb stone at F and G in order tolift it.

Eng1010 - Examples 5

3. (6-108 Hibbeler, 11e) If a force of 10 lb isapplied to the grip of the clamp, determinethe compressive force F that the wood blockexerts on the clamp.

4. (6-78 Hibbeler, 11e) Determine the hori-zontal and vertical components of force atC which member ABC exerts on memberCEF .

5. (4-114 Meriam & Kraige, 7e) The elementsof the rear suspension for a front wheel drivecar are shown in the figure. Determine themagnitude of the force in each joint if thenormal force F exerted on the tire is 3600 N.

6. (4-119 Meriam & Kraige, 7e) Determine thecompressive force C exerted on the can foran applied force P = 50 N when the cancrusher is in the position shown. Note:there are two links AB and two links AOD,with one pair of linkages on each side of thestationary portion of the crusher. Also, pinB is on the vertical centerline of the can.Finally, note that the small square projec-tions E of the moving jaw move in recessedslots of the fixed frame.

Eng1010 - Examples 6

7. (4-116 Meriam & Kraige, 7e) The truckshown is used to deliver food to aircraft.The elevated unit has a mass of 1000 kg withcenter of mass at G. Determine the requiredforce in the hydraulic cylinder AB.

8. The car hoist allows the car to be drivenonto the platform, after which the rearwheels are raised. If the loading from bothrear wheels is 6 kN, determine the force inthe hydraulic cylinder AB. Member BCD isa right-angle bell crank pinned to the rampat C.

6 Rigid Bodies: Friction

1. Determine the magnitude of the frictionforce acting on the 100 kg block if: (a)P = 500 N; and (b) P = 100 N. The coef-ficient of static friction is µs = 0.2, and thecoefficient of kinetic friction is µk = 0.17.The forces are applied with the block ini-tially at rest.

2. (8-15 Hibbeler, 12e) The spool has mass of200 kg and rests against the wall and on thefloor. If the coefficient of static friction at Bis µs,B = 0.3, the coefficient of kinetic fric-tion is µk,B = 0.2, and the wall is smooth,determine the friction force developed at Bwhen the vertical force applied to the cableis P = 800 N.

3. (8-18 Hibbeler, 12e) The tongs are used tolift the 150 kg crate, whose center of massis at G. Determine the least coefficient ofstatic friction at the pivot blocks so that thecrate can be lifted.

Eng1010 - Examples 7

4. (8-27 Hibbeler, 12e) The refrigerator hasa weight of 180 lb and rests on a floor forwhich µs,R = 0.25. Also, the man has aweight of 150 lb and the coefficient of staticfriction between the floor and his shoes isµs,M = 0.6. If he pushes horizontally on therefrigerator, determine if he can move it. Ifso, does the refrigerator slip or tip?

5. (8-6 Hibbeler, 12e) The 180 lb man climbsup the ladder and stops at the positionshown after he senses that the ladder is onthe verge of slipping. Determine the coeffi-cient of static friction between the frictionpad at A and ground if the inclination ofthe ladder is θ = 60◦ and the wall at B issmooth. The center of gravity for the manis at G. Neglect the weight of the ladder.

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6. (8-35 Hibbeler, 12e) A roll of paper has auniform weight of 0.75 lb and is suspendedfrom the wire hanger so that it rests againstthe wall. If the hanger has a negligibleweight and the bearing at O can be con-sidered frictionless, determine the force Pneeded to start turning the roll if θ = 30◦.The coefficient of static friction between thewall and the paper is µs = 0.25.

7. (8-30 Hibbeler, 12e) The tractor has aweight of 8000 lb with center of gravity atG. Determine if it can push the 550 lblog up the incline. The coefficient of staticfriction between the log and the ground isµs,C = 0.5, and between the rear wheels ofthe tractor and the ground µs,A = 0.8. Thefront wheels are free to roll. Assume the en-gine can develop enough torque to cause therear wheels to slip.

8. (8-31 Hibbeler, 12e) The tractor has aweight of 8000 lb with center of gravity atG. Determine the greatest weight of the logthat can be pushed up the incline. The coef-ficient of static friction between the log andthe ground is µs,C = 0.5, and between therear wheels of the tractor and the groundµs,A = 0.7. The front wheels are free toroll. Assume the engine can develop enoughtorque to cause the rear wheels to slip.

Eng1010 - Examples 8