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Equilibrium of Concurrent Force Systems

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Problem 1 (Tension in Cables):

Determine the tension in cables AB and BC necessary to support the 60-kg cylinder.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 1 (Tension in Cables): – Diagram

Problem 2 (Tension in Cables):

Determine the tension in cables AB, BC, and CD necessary to support the 10-kg and 15-kg traffic lights at B and C, respectively. Also, find the angle θ.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 2 (Tension in Cables): – Diagram

Problem 3 (Tension in Springs):

Determine the required length of cord AC so that the 8-kg lamp can be suspended in the position shown. The unstretched length of spring AB is 0.4m, and the spring has a stiffness of kAB=300N/m

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 3 (Tension in Springs): – Diagram

Problem 4:

A concrete block of weight W holds a ring anchor bolt fastened to two guy wires as shown.
1. Calculate the resultant force acting on the bolt.
2. Determine the angle which the resultant pull makes with the horizontal.
3. To prevent uplift, what is the minimum weight of the concrete block W if the required factor of safety is 1.3?

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram

Problem 5:

A boom supports a 100N load as shown below. If the tension in the cable is 200N,
1. Find the angle α.
2. Find the angle θ.
3. Find the force in the boom.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram

Problem 6:

Refer to the image shown. Cylinder 1 weighs 20kN, cylinder 2 weighs 40kN, and cylinder 3 weighs 30kN. The surface along point D is inclined 60º with the horizontal.
1. Determine the reaction at A.
2. Determine the reaction at D.
3. Determine the reaction at C.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram

Problem 7:

Force A = 6kN
Force B = 2.4kN
Angle β = 30°
1. The resultant of the three forces, A, B, and C is 3.6kN and it acts along the y-axis. What is the angle θ?
2. If the resultant of the three forces A, B, and C is 5.4kN and it acts along the y-axis, what is the value of C if θ=45°?
3. If the angle θ=60° and the force C = 3kN, how much is the resultant pulling force on the eyebolt?

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram

Problem 8:

A hollow right circular cylinder of radius 0.5m is open at both ends and rests on a smooth horizontal plane. Inside the cylinder are two spheres having weights w1=10kN and w2=15kN and radius r1=0.20m and r2=0.40m, respectively, as shown. Neglect friction.
a. Determine the horizontal reaction of w1 on the side of the cylinder.
b. Determine the vertical reaction of w2 at the horizontal plane.
c. Determine the minimum weight Q of the cylinder in order for it not to tip over.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram

Problem 9:

A suspension cable is supported at A and B, 120m horizontally apart, with B higher than A by 15m. A concentrated load of 100kN is applied at a distance of 60m horizontally from A. The cable sags a distance of 10m from the chord joining A and B at the center.

a. What is the maximum tension in the cable?
b. What is the minimum tension in the cable?
c. What is the horizontal reaction at the supports?

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram

Problem 10:

Forces F, P, and T are concurrent and acting in the direction as shown. If the resultant is zero, find α and β.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 10: – Diagram

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Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 10: – Diagram

Problem 11:

The 60kN weight is suspended from a small pulley that is free to roll on the cable. The length of the cable ABC is 18m. Determine the horizontal force P that would hold the pulley in equilibrium in the position x=4m.

Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 11: – Diagram
Equilibrium of Concurrent Force Systems | Statics of Rigid Bodies – Problem 11: – Diagram
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