Sorry But This Latex is Poor.... Here Arrow means vector and Yes it is Dot product. I wonder How This arrow is shifted down side while In Latex Coding it seems to be correct.

will Any Body Tell what is Exact Latex Code For representing an vector dot product ??

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## Comments

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TopNewestSuppose you are asked to find relation between acceleration of \(m_{1}\) and \(m_{2}\).

Figure

I like to do this with the help of calculus.Let \(l\) be tha length of the string.

Then

\(x+y+2z=l\)

On differentiating this wrt time (two times) we will get

\(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +2\frac { { d }^{ 2 }z }{ { d{ t }^{ 2 } } } =0\)

Let the acceleration of \(m_{1}\) and \(m_{2}\) be \(a_{1}\) and \(a_{2}\) respectively

then \({ a }_{ 1 }=-2{ a }_{ 2 }\)

Here (-)sign with \(a_{2}\) just denotes direction.

If we want to find relation between magnitudes of accelerations then the relation will be

\({ a }_{ 1 }=2{ a }_{ 2 }\)

Search for 'string constraint' on utube. You will get some similar types of example there.

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Well I always Prefer

Virtual work Method:That is Net work done By Internal Forces ( Like here it is Tension in Strings) on a system will be

zero\(\sum { \xrightarrow { T } \xrightarrow { x } } \quad =\quad 0\\ \\ or\\ \\ \sum { \xrightarrow { T } \xrightarrow { v } } \quad =\quad 0\\ \\ or\\ \\ \sum { \xrightarrow { T } \xrightarrow { a } } \quad =\quad 0\\ \).

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that is some thing new thanks

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Nice method.

Image

But \(2T_{1}=T_{2}\)

So \(T_{1}a_{1}=2T_{1}a_{2}\)

So \(a_{1}=2a_{2}\)

By using calculus or virtual work method ultimately we will reach the same answer.

Thank you Deepanshu for sharing this method. :D

This method is very good for finding relation between accelerations of different masses.

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So \( \vec { T } \cdot \vec { x }=0\)

If you differentiate this equation w.r.t time (two times) you will get

\( \vec { T } \cdot \vec { a }=0\).

By using this equation you can easily find relation between accelerations of masses.

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Sorry But This Latex is Poor.... Here Arrow means vector and Yes it is Dot product. I wonder How This arrow is shifted down side while In Latex Coding it seems to be correct.

will Any Body Tell what is Exact Latex Code For representing an vector dot product ??

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\vec { A } \cdot \vec { B }and enclosed it within brackets then you will see it's output as --\(\vec { A } \cdot \vec { B } \)

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thanks

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