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*

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## Comments

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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!

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This one helped me ;)

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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.

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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)

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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 }

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

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

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

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How to apply this concept in problem solving?

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Please reply and enlighten me.

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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.

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Could you add one example? Thanks.

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