Hello Physicists!

I am studying Newton's Laws of Motion, and am working out some problems on Pulleys and Constrained motion. I have heard of a technique called the **Virtual Work Method**, also called the *T dot Trick* or the *Tension Trick*. I would like to learn about it, to make my problem solving effective. So please write about it in this note and attach an example problem. I'll be highly grateful.

Thanks.

*Swapnil*

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestThe crux of the Virtual Work Method is that the sum of work done by all

internal forces of a systemis zero!. So to explain this in the context of pulley block system I'll consider bodies \(B_1,B_2,B_3\dots B_N\) which, due to the strings they are attached to, are experiencing a tension of \(\vec{T_1},\vec{T_2}\dots \vec{T_N}\). Also, consider that in a certain time \(t\) these blocks get displaced by \(\vec{S_1},\vec{S_2}\dots \vec{S_N}\). Since thetotal work done by all internal forcesis zero, we can write:\(\boxed{\displaystyle \sum_{i=0}^{N} \vec{T_{i}}.\vec{S_{i}} = 0}\)...\((1)\)

Differentiating the above equation twice we get:

\(\boxed{\displaystyle \sum_{i=0}^{N} \vec{T_{i}}.\vec{a_{i}} = 0}\) (Here \(\vec{a_i}\) denotes the accelleration of the body \(B_i\))

This method is basically used to find the relationship between the accelerations of the various moving bodies of the system.

Hope this will help you!

Log in to reply

This one helped me ;)

Log in to reply

How is virtual tension work method for wedge pulley constraints different from pulleys?

Log in to reply

virtual work is a really a god trick when you get fed up with constrains writing static equilibrium condition . virtual work principle state that when a body in static equilibrium is given a virtual displacement dx then net work done is 0.

Log in to reply

it sounds too boring but its going to be interesting i found it to be useful. try this

a mass tied with a string in vertical plane with horizontal force acting find it if it is at angle theta with the vertical using virtual work method. (it s too easy)

Log in to reply

just give a displacement d(theta) and let net work done =0

mg(-lsin(theta)d(theta)+F(lcos(theta)d(theta)=0

F=mgtan(theta)

{note-this may appear long this time but its time saving trick }

Log in to reply

@Swapnil Das I think this'll help: https://nptel.ac.in/courses/Webcourse-contents/IIT-KANPUR/engg

mechanics/ui/Coursehome_10.htmLog in to reply

Also can anybody please explain in brief about instantaneous axis of rotation.

Log in to reply

It is the point about which the body appers to be in purely rotational motion (no translatory motion).

Log in to reply

How to apply this concept in problem solving?

Log in to reply

Log in to reply

Please reply and enlighten me.

Log in to reply

It basically says \(\displaystyle \sum \vec{T} \cdot \vec{a} = 0\) where \(T\) is the tension of the string and \(a\) is the acceleration of bodies in contact with it.

Log in to reply

Could you add one example? Thanks.

Log in to reply