Mechanics doubt
Could someone explain the Virtual Work Theorem to me? The ΣTiai = 0 thing hasn't made sense to me at all, and my teacher didn't even teach it last year. I couldn't even find it in any of my go-to books, and whenever I look up 'Virtual Work Theorem', I get the d'Alembert concept of virtual displacements, which is not what I want.
10 Replies
@Gyro Gearloose
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.U want derivation or logic behind it?
Regardless ping me when u get an apt ans pls
Both pls
Virtual work
In mechanics, virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual dis...
Yeah, this didn't helo
*help
That's why I asked
If a force acts on a particle as it moves from point A to point
B, then, for each possible trajectory that the particle may take, it is possible to compute the total work done by the force along the path. The principle of virtual work, which is the form of the principle of least action applied to these systems, states that the path actually followed by the particle is the one for which the difference between the work along this path and other nearby paths is zero (to the first order).
hmm i think there was a vertasium vid on this
althogh idk out of syllabus for me rn 🗣️
No, that's principle of least action, which I get.
But application is a different story
ahh i see
if you have simple pulley block systems then net work done by the string has to be zero
(the tension in the string)
cuz if it isnt zero then the length of the string changes
which is against the string constraint
so sum of all T.x must be zero on the system
now differentiate this two times so summation T.a = 0