Free Bachelor of Mechanical Engineering Advanced Mechanics Questions and Answers

Question 1

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

Accepted Answer

∑F≠0

Answer

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 .

Accepted Answer

Flexible

Answer

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:

Accepted Answer

Depends on the angle between them

Answer

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 .

Accepted Answer

Line

Answer

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?

Accepted Answer

Flexibility property

Answer

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.

BME - Bachelor of Mechanical Engineering Practice Test

BME - Bachelor of Mechanical Engineering Practice Test

Free Bachelor of Mechanical Engineering Advanced Mechanics Questions and Answers