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Is it possible to imagine a virtual displacement for a simple pendulum?

Physics Asked by Arnab Maiti MAS on January 24, 2021

Because I could not understand the term "virtual displacement" properly I have too much questions with it. I will be helpful with your answer. My question:

Can we imagine a virtual displacement for a simple pendulum? Is it possible to have virtual displacement for the system?

If yes: then what will be its virtual displacement?

If No: Give an example where virtual displacement is possible.

One Answer

Yes. If the pendulum is at an angle $theta$ to the vertical, imagine changing $theta$ to $theta+delta theta$.

Here is an example of how to use a virtual displacement: Consider a bubble of radius $R$ with an excess pressure $P$ compared to outside, and with surface tension $T$. In equilibrium there are no unbalanced forces, so if some small change $dR$ in the radius occurs there will be be no work done. But the work done will be $$ delta W=Td(Area)-Pd(Volume) =T d(4pi R^2)-P d(4/3pi R^3) =8pi T RdR -4pi P R^2 dR = 4pi(2TR- P R^2)dR =4pi R(2T-PR)dR $$ This has to be zero, so $P= 2T/R$ ---- the well-known formula for the excess pressure in a bubble.

Answered by mike stone on January 24, 2021

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