Applied Mechanics

Q1: When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as

A imaginary work

B negative work

C virtual work

D none of these.

ANS:C - virtual work

Depending on the value of angle θ, work is categorized into three types, They are

Positive Work.
Zero Work.
Negative Work.

Positive Work:
Positive work is defined when the force acting on the system and the displacement of the body both are in the same direction. Here, the value of angle θ lies in the range, 0 ≤ θ < 90°

E.g. Work done by Gravity on a body during free fall.

Negative Work:
Negative work is defined when the force acting on the system and the displacement of the body both vectors are in the opposite direction to each other.

Here, the value of angle θ lies in the range, of 90 < θ ≤ 180°.

E.g. Work done by Gravity when something is thrown vertically upward.

Zero Work:
There are three entities involved in the formula for work. Even if any one of the entities becomes 0 the work done will come to be zero.

This gives rise to the three cases of zero work:

The force and displacement vector are perpendicular to each other, which means, θ = 90° and Cos 90° will come to be 0.
The net displacement of the system is zero.
The value of applied force is 0. Virtual work is the total work done by the applied forces and the inertial forces of a mechanical system as it moves through a set of virtual displacements. When considering forces applied to a body in static equilibrium, the principle of least action requires the virtual work of these forces to be zero.



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