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# MCQs on Equilibrium in Three Dimensions

A force is developed by a support that not allows the ________ of its attached member.

a) Translation

b) Rotation

c) Addition

d) Subtraction

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Answer: a

Explanation: The force developed by a support doesn’t allow the translation of its attached member. This is the basic condition for the equilibrium of the forces in any dimension. This rule is applied when the support reactions are taken into the account for the equilibrium of the body.

In the diagram given below, coordinates of D is (1, -2, 2), C (-2, 0, 0) and B are as shown. The dark region is the cables holding the weight of 600N at the origin. Find the tension in the AD section.

a) 900N

b) 693N

c) 646N

d) 0N

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Answer: a

Explanation: As the system is in equilibrium so we need to balance the forces. So when applying the condition of net force to be zero in the z direction, we get (2/3)FAD = 600N. This gives us force along AD be 900N.

A couple moment is developed when _______ of the attached member is prevented.

a) Translation

b) Rotation

c) Addition

d) Subtraction

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Answer: b

Explanation: The development of the couple moment is when there is a prevention of the rotation of the attached member. This is the basic condition for the equilibrium of the couple moments in any dimension. This rule is applied when the couple moments are taken into the account for the equilibrium of the body.

We first make equilibrium equations of the body by considering all the three dimensional forces and then the free body diagram is made and solved.

a) The first part of the statement is false and other part is true

b) The first part of the statement is false and other part is false too

c) The first part of the statement is true and other part is false

d) The first part of the statement is true and other part is true too

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Answer: d

Explanation: We first make the free body diagram and then we make the equilibrium equations to satisfy the given conditions. This helps us to solve the question easily. As this reduces the part of imagination and increases accuracy too.

∑Fx=0, ∑Fy=0 and ∑Fz=0 are vector equations for the three dimensions. They are satisfied when the body is achieved its state of equilibrium.

a) True

b) False

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Answer: b

Explanation: The answer is false as the equations asked are scalars. As we make the net sum of the forces along the axis equal to zero. Of course this equation comes from the solving the vector forms, but still the result is a scalar, hence the equations are scalar.

The supports in the 3D are having more than three reaction forces. Because they are having three axis on which the components of the forces need to be zero.

a) The first part of the statement is false and other part is true

b) The first part of the statement is false and other part is false too

c) The first part of the statement is true and other part is false

d) The first part of the statement is true and other part is true too

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Answer: d

Explanation: As 3D is defined as the three axis system, we have to consider the equilibrium in all the three axis. This will make the equilibrium go on all the axis of the 3D space. And hence will cancel all the forces.

The single pin, single bearing and single hinge resist _______

a) Force

b) Couple moments

c) Both force and couple moments

d) Inertia

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Answer: c

Explanation: The experiments have founded that the single pin, single bearing and single hinge resist both force and couple moments. This does helps in attaining the equilibrium of the body. Thus proper guiding must be taken during solving the question on the same.

If the supports are properly aligned then the reaction forces developed are adequate to support the body.

a) Statement is true only in 2D

b) Statement is true only in 3D

c) Statement is true throughout

d) Statement is true only in 1D

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Answer: c

Explanation: This is the basic nature observed during the experiments on the beams an all the support system. The dimension doesn’t affect the equilibrium conditions. The main motto is to achieve the equilibrium. It is achieved by equating the net force equal to zero.

Find the tension in the cable AC.

a) 23.6N

b) 55N

c) 89N

d) -29N

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Answer: a

Explanation: First represent the forces in their vector form. Then equate the net sum of the forces in the x, y and z directions to be zero. You will get FB = FC and 2(.848) = 40N. This gives the answer as 23.6N.

Determine the value of the q, parallel to the z axis. That is the point of intersection of the projections of the points A, B and C parallel to the xy plane. With the distance between the tri-section point and the points A, B and C be equal to 0.6m.

a) 51.9cm

b) 51.9mm

c) 51.9m

d) 5.19mm

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Explanation: The application of the equilibrium equation will yield the result. That is the resultant along the z-axis will remain zero. Which give the value of γ as 50˚. And therefore q=51.9cm.

If the supports are not properly aligned then the reaction forces developed are adequate to support the body.

a) Statement is true only in 2D

b) Statement is true only in 3D

c) Statement is false throughout

d) Statement is true only in 1D

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View Answer**

Explanation: This is the basic nature observed during the experiments on the beams an all the support system. The dimension doesn’t affect the equilibrium conditions. The main motto is to achieve the equilibrium. It is achieved by equating the net force equal to zero. But here the system is not properly aligned.