## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

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.

Log in to reply

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

Log in to reply

that is some thing new thanks

Log in to reply

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.

Log in to reply

Log in to reply

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.

Log in to reply

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 ??

Log in to reply

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

Log in to reply

thanks

Log in to reply