Free Bachelor of Mechanical Engineering Advanced Mechanics Questions and Answers — Questions and Answers

Question 1: What doesn't make a cable susceptible to its own weight balance in a three-dimensional system of axes?

∑F≠0 (Correct answer)
∑Fz=0
∑Fy=0
∑Fx=0

Correct answer: ∑F≠0

For a cable to be in a state of balance or equilibrium under its own weight in a three-dimensional system, the net force acting on any part of it must be zero. This means that the sum of all forces in the x, y, and z directions must individually be zero (∑Fx=0, ∑Fy=0, ∑Fz=0). If ∑F≠0, there is a net force, and the cable would be accelerating, thus not in balance.

Question 2: The cable is assumed to be subject to its own weight for the computations. One of the presumptions in this is that the cable is .

Static
Flexible (Correct answer)
Non-flexible
Extensible

Correct answer: Flexible

A key assumption in the analysis of cables subjected to their own weight is that the cable is perfectly flexible. This property means the cable offers no resistance to bending, and consequently, the internal force (tension) at any point within the cable is always purely tangential to its curve. This flexibility allows the cable to conform to a specific shape under gravity.

Question 3: In calculations for cable exposed to its own weight, the magnitude of the resultant of the two vectors is always:

Axis we choose to calculate the magnitude
Depends on the angle between them (Correct answer)
Smaller than one of the vector’s magnitude
Greater than one of the vector’s magnitude

Correct answer: Depends on the angle between them

When combining two vector forces, such as tensions in a cable, the magnitude of their resultant vector is not simply the sum of their magnitudes. Instead, it depends on both the magnitudes of the individual vectors and the angle between them. This relationship is precisely described by the law of cosines for vector addition, where the angle significantly influences the final resultant magnitude.

Question 4: When loaded, cable that is supporting its own weight has the shape of a .

Line (Correct answer)
Helix
Complex figure
Spring

Correct answer: Line

While a cable supporting its own weight typically forms a catenary curve (or a parabola under a uniformly distributed horizontal load), in many simplified engineering analyses, especially when the sag is very small compared to the span, the cable's shape can be idealized as a straight 'line'. This approximation is often used for initial calculations or in contexts where the curvature is considered negligible for practical purposes.

Question 5: What quality of the cable causes it to have no resistance to bending while it is under its own weight?

Static property
Flexibility property (Correct answer)
Extensible property
Non-flexible property

Correct answer: Flexibility property

The flexibility property of a cable is its characteristic that allows it to bend freely without developing internal bending moments. This means that the cable offers no resistance to changes in its curvature. Consequently, the internal force within the cable is always purely tensile and acts tangentially to its curve, which is a fundamental assumption in cable analysis.

Question 6: Which direction is the tensile force acting on the cable under the weight w.r.t the cable?

Parallel
Tangential (Correct answer)
Perpendicular
At an angle of 2 radians

Correct answer: Tangential

Due to a cable's inherent flexibility, it cannot sustain bending moments or shear forces. Therefore, the internal tensile force at any point along the cable must always act purely in the direction of the cable itself. This means the tensile force is always tangential to the curve formed by the cable at that specific point, ensuring no resistance to bending.

Question 7: The loading in the cable under its own weight has little effect on the cables' Integrity.

Point at which the shear stress is zero
Bending moment
Colour
Geometry (Correct answer)

Correct answer: Geometry

The geometry of a cable, specifically its sag and the overall curve it forms (e.g., catenary or parabolic), is directly and significantly influenced by the distribution of its own weight. This resulting geometric configuration dictates the internal tensile forces and is crucial for understanding the cable's structural behavior and ensuring its integrity under load.

Question 8: What number of equations are necessary to solve all the unknown variables for cable subjected to its own weight if the unknown variables in the computations are greater than the known quantities?

Infinite
Not possible
Finite (Correct answer)
Question fault

Correct answer: Finite

In structural mechanics, when analyzing a cable subjected to its own weight, the number of equations required to solve for unknown variables (such as tensions and reaction forces) is always finite. These equations are derived from equilibrium conditions (sum of forces and moments equal to zero) and geometric compatibility, forming a solvable, albeit sometimes complex, system.

Question 9: The following rules apply to computations involving cable that is subject to its own weight:

Parallelogram law of addition of square of their magnitudes
Parallelogram law of addition (Correct answer)
Parallelogram law of multiplication
Parallelogram law of addition of square root of their magnitudes

Correct answer: Parallelogram law of addition

The Parallelogram Law of Addition is a fundamental principle in vector mechanics used to determine the resultant of two or more forces (vectors) acting at a common point. In cable computations, this law is essential for resolving and combining the various tensile forces and external loads acting on the cable segments to ensure equilibrium and analyze its behavior.

Question 10: What angle is the resultant force acting at in comparison to one of the vectors when two equal vector forces are mutually perpendicular in a cable subjected to its own weight?

0 degree
45 degree (Correct answer)
90 degree
180 degree

Correct answer: 45 degree

When two equal vector forces are mutually perpendicular, their resultant force will always bisect the angle between them. Since the angle between two perpendicular vectors is 90 degrees, the resultant force will act at an angle of 45 degrees relative to each of the original vectors. This is a direct consequence of the parallelogram law of vector addition.

Question 11: Which of the following describes a frictional property?

It is an active force
Always acts in the direction of applied force
Not a self-adjusting force
Always acts in the direction opposite to the applied force (Correct answer)

Correct answer: Always acts in the direction opposite to the applied force

Friction is a resistive force that inherently opposes relative motion or the tendency of relative motion between two contacting surfaces. Consequently, its direction is always opposite to the direction of the applied force that is attempting to cause movement, working to impede or prevent that motion.

Question 12: Which of the following forces develops when there is no relative force between two contacting surfaces?

Static friction (Correct answer)
Fluid friction
Dynamic friction
Dry friction

Correct answer: Static friction

Static friction is the specific type of frictional force that develops when two surfaces are in contact and at rest relative to each other, but an external force is attempting to cause motion. It acts to prevent the initiation of relative movement, meaning it exists even when there is no actual sliding or 'relative force' (motion) between the surfaces.

Question 13: There is some resistance to sliding between two bodies' surfaces when they come into touch; this is called .

Attraction force
Lubrication
Friction (Correct answer)
Internal forces

Correct answer: Friction

Friction is the general term for the force that resists the relative motion or the tendency of relative motion between two surfaces in contact. This resistance arises from microscopic irregularities, adhesion, and interlocking between the surfaces, making it harder for them to slide past each other.

Question 14: The frictional force is not affected by which of the following?

Force tending cause motion
Area of contact (Correct answer)
Surface roughness
Reaction of surface

Correct answer: Area of contact

Frictional force primarily depends on the normal force pressing the surfaces together and the coefficient of friction between those surfaces, which accounts for surface roughness. According to Amontons's Laws of Friction, the area of contact does not affect the magnitude of the frictional force. This is because while a larger area might distribute the normal force over more points, the actual microscopic contact area remains roughly proportional to the normal force, leading to a constant frictional force per unit normal force.

Question 15: Which of the following statements holds true if two forces are represented by two triangle sides in that order?

The resultant’s magnitude is greatest
The resultant’s magnitude is zero
The resultant of two forces is represented by the third side in reverse order (Correct answer)
The resultant of two forces is represented by the third side in the same sequence

Correct answer: The resultant of two forces is represented by the third side in reverse order

This question describes the Triangle Law of Vector Addition. If two forces are represented by two sides of a triangle taken in the same sequential order, their resultant is given by the third side. Crucially, the resultant vector must be drawn from the tail of the first vector to the head of the second vector, meaning it closes the triangle and is therefore taken in the reverse order relative to the other two sides.

Question 16: If there are three concurrent forces acting on a body, according to Lami's theorem, what is the connection between each force?

Inversely proportional to the sine of the angle between the other two forces
Directly proportional to the cosine of the angle between the other two forces
Inversely proportional to the cosine of the angle between the other two forces
Directly proportional to the sine of the angle between the other two forces (Correct answer)

Correct answer: Directly proportional to the sine of the angle between the other two forces

Lami's theorem applies to three concurrent forces that are in equilibrium. It states that for such a system, each force is directly proportional to the sine of the angle formed between the other two forces. This theorem provides a convenient way to analyze forces in equilibrium when their directions and one force's magnitude are known.

Free Bachelor of Mechanical Engineering Advanced Mechanics Questions and Answers

What doesn't make a cable susceptible to its own weight balance in a three-dimensional system of axes?