This set of Engineering Mechanics test focuses on “Simplification of a Force and Couple System – 2”.

1. What is a collinear system of forces?

a) The force system having all the forces parallel to each other

b) The force system having all the forces perpendicular to each other

c) The force system having all the forces emerging from a single point

d) Forces cannot form a collinear system of forces, it is not possible

View Answer

Explanation: The force system having all the forces emerging from a point is called the collinear system of force. This is a type of system of the force, which is easy in the simplification. This is because as the forces are the vector quantity, the vector math is applied and the simplification is done.

2. Find the total resultant force acting in the given figure consisting of a beam with various sections.

a) 350N

b) 461N

c) 250N

d) 300N

View Answer

Explanation: The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. After this the forces are a determined and are added vetorially to get the resultant force.

3. In the collinear force system, a net force is being made after all the simplification done on all the forces.

a) True

b) False

View Answer

Explanation: The answer is obviously yes. As the simplification means addition and the subtraction of the forces. This results in the simplification of the forces and thus gives us a single force. It is in a particular direction and hence the statement is true.

4. Just like the collinear forces, there are collinear couple and the net moment is taken out from it.

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

View Answer

Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

5. Just like the collinear force system, there is a system of the parallel forces.

a) True

b) False

View Answer

Explanation: There is a system so called the parallel system of the forces. This is another type of forces. The simplification of this type of the forces is also very easy. This means that the forces in a certain direction are taken as positive and in the other direction is negative and hence the simplification is done.

6. Find the total resultant moment acting in the given figure consisting of a beam with various sections.

a) 37.5Nm

b) 7.5Nm

c) 79.5Nm

d) 370.5Nm

View Answer

Explanation: The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.

7. The system of the collinear and the parallel force are simplified as ______________

a) The simplified collinear force system gives us a net force and the parallel force system gives us a simplified force, and then we add it vectorially

b) Such simplification is not possible

c) The simplification is usually done by not considering the directions of the both

d) The simplification is done by considering the rotations only

View Answer

Explanation: The simplification is easy. The simplified force system gives us a net force and the parallel force system gives us a simplified force, and then we add it vectorially. Thus the vector addition at the last can be easily done and thus both can be simplified.

8. The couple and the other two force systems can be easily simplified.

a) Statement is wrong

b) Statement is right

c) Statement is right if we remove the ‘couple’ part

d) Statement is right if we remove the ‘force’ part

View Answer

Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

9. The resultant force is equal to the _______ of all the forces.

a) Sum

b) Product

c) Subtraction

d) Division

View Answer

Explanation: As the simplification means addition and the subtraction of the forces. This results in the simplification of the forces and thus gives us a single force. It is in a particular direction. But if one is considering the direction with the magnitude of the force, we can say that the resultant is the sum of all the forces.

10. The couple is simplified easily with the help of left hand rule. But the forces simplification is not possible as there is no such system of rules so that the forces can be simplified.

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

View Answer

Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D. Forces are simplified on the basis of the algebra.

11. The forces of the parallel system and the couple can’t be simplified together as one is the cause and the other is the effect.

a) The statement is correct and the reason given is also correct

b) The statement is wrong but the reason given is also correct

c) The statement is wrong and the reason given is also wrong

d) The statement is correct but the reason given is also wrong

View Answer

Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

12. The forces of the collinear system and the couple can’t be simplified together as one is the cause and the other is the effect.

a) The statement is correct and the reason given is also correct

b) The statement is wrong but the reason given is also correct

c) The statement is wrong and the reason given is also wrong

d) The statement is correct but the reason given is also wrong

View Answer

Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

13. Find the angle between the horizontal and vertical forces acting in the given figure consisting of a beam with various sections.

a) 49.4˚

b) 9.4˚

c) 4.4˚

d) 40.4˚

View Answer

Explanation: The couple is simplified by taking the direction of the rotation of the body as positive or negative. As soon as the horizontal and the vertical forces are determined we can get the angle between them. This can be done by using the tangent trigonometry function.

14. Find the total resultant moment acting in the given figure consisting of a beam with various sections.

a) 210Nm

b) 10Nm

c) 20Nm

d) 102Nm

View Answer

Explanation: The couple is simplified by taking the direction of the rotation of the body as positive or negative. As soon as the horizontal and the vertical forces are determined we can get the angle between them. This can be done by using the tangent trigonometry function.

15. Find the total resultant force acting in the given figure consisting of a beam with various sections.

a) 157N

b) 175N

c) 15N

d) 17N

View Answer

Explanation: The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. After this, the forces are determined and are added vectorially to get the resultant force.

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