This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Three Dimensional Force System”.

1. What is not the condition for the equilibrium in three dimensional system of axis?

a) ∑Fx=0

b) ∑Fy=0

c) ∑Fz=0

d) ∑F≠0

View Answer

Explanation: For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also, we have the summation of the forces equal to zero. Which is not a non-zero value.

2. We first make equilibrium equations and then the free body diagram and then solve the question.

a) True

b) False

View Answer

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.

3. 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

View Answer

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.

4. 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 origin. Find the tension in the AB section.

a) 900N

b) 693N

c) 646N

d) 0N

View Answer

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 y direction, we get FAB cos30 = (2/3)*900. This gives us force along AB be 693N.

5. Find the tension in the cable AC.

a) 23.6N

b) 55N

c) 89N

d) -29N

View Answer

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.

6. 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

View Answer

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.

7. ∑Fx=0, ∑Fy=0 and ∑Fz=0 are vector equations.

a) True

b) False

View Answer

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.

8. When the body is in equilibrium then which of the following is true?

a) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude

b) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude square

c) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude square root

d) We equate all the components of the forces acting on the body equal to zero

View Answer

Explanation: Yes, we equate all the components of the three axis equal to zero. That is the resultant of the forces along the three axis are being equated to zero. This brings in that there is no net force in any direction. Hence equilibrium.

9. If solving the question in 3D calculations is difficult, then use the 2D system and then equate the total net force to zero.

a) True

b) False

View Answer

Explanation: The answer is obviously yes. If we are having any difficulty in making the vector components, then we can go in 2D. As if the particle is in equilibrium, the net force will be zero. No matter where you see first. Net force is zero.

10. If the resolved force or the force which you get as the answer after solving the question is negative, then what does this implies?

a) The force is in the reverse direction w.r.t the direction set in the free body diagram

b) The force is not in the reverse direction w.r.t the direction set in the free body diagram

c) The force component is not possible

d) The force is possible, but in the direction perpendicular to the resultant force

View Answer

Explanation: The negative sign implies things in the opposite manner. If the force is coming negative this doesn’t mean that it is impossible. But it means that the force is in the opposite direction w.r.t the direction set by you in the free body diagram.

11. An electromagnet crane is carrying the electromagnet with the help of the three cables. But the electromagnet is not stable because of the wind. What is science behind the cause?

a) The wind is making the net force of the body equal to a non-zero value

b) The wind is making the net force of the body equal to zero value

c) The wind is making the net force of the body equal to a non-zero value but is supporting the equilibrium

d) The wind is making the net force of the body equal to zero value and supporting equilibrium

View Answer

Explanation: Anybody is in equilibrium only if the net force along the three axis is zero. But in this case, the wind is not helping the body to do so. The science behind this is that the resultant forces are being equated to a non-zero value by the wind. Hence unstable.

12. If anybody is tied to three or more ropes, and then is allowed to achieve its equilibrium. Then the equilibrium achieved is achieved w.r.t what?

a) The three axis of the body

b) The ground

c) The ropes direction

d) The weight direction

View Answer

Explanation: Yes, the equilibrium is being achieved w.r.t the ground. Like the motion, w.r.t ground need be zero. That is the relative velocity of the object or the body must be zero w.r.t the ground. This means motion is in equilibrium.

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