Rearranging Formula: Solving for Vw

[XxphysicsxX]

how do i rearrange for Vw??

I just end up canceling the Vw's when I solve it...
Thanks in advance

the formula is:

(Fd)= [(Vw) / (Vw-Vs)] (fs)

 

[Zryn]

Can you write out your working and show how they cancel out? That way someone can help you see if you made a mistake in your algebra.

 

[XxphysicsxX]

Can you write out your working and show how they cancel out? That way someone can help you see if you made a mistake in your algebra.

i get:

Fd (Vw- Vs) = VwFs
Fd( Vw-Vs) - Vw= Fs

and i don't go ant further since the first Vw is a possitive and the second is a negative... meaning they'll cancel each other out..
dont know what I am doing wrong!

 

[Zryn]

When you have two terms multiplied together, such as VwFs, you can not simply split them up like you have done:

Fd (Vw- Vs) = VwFs --> Fd( Vw-Vs) - Vw= Fs ... incorrect
Fd (Vw- Vs) = VwFs --> Fd( Vw-Vs) - VwFs = 0 ... correct

You have to consider them a lumped package when you move them around, essentially you have subtracted VwFs from both sides of the equation. If you only subtracted Vw from both sides of the equation you would get:

Fd( Vw-Vs) - Vw = FsVw - Vw

And this doesn't help you too much.

What you can do is keep in mind the foremost rules of algebra:

a ( b + c ) = ab + ac which is the same as ab + ac = a ( b + c )

Try using this rule to expand and/or factorize the equation and see if you can rearrange it that way.

 

[CellCoree]

To rearrange for Vw, we can use algebraic manipulation to isolate Vw on one side of the equation. First, we can multiply both sides of the equation by (Vw-Vs) to get:

(Fd)(Vw-Vs) = (Vw)(fs)

Next, we can distribute the (Fd) term to get:

(Fd)(Vw) - (Fd)(Vs) = (Vw)(fs)

Then, we can move all terms with Vw to one side of the equation and all other terms to the other side:

(Fd)(Vw) - (Vw)(fs) = (Fd)(Vs)

Factoring out Vw on the left side, we get:

Vw[(Fd) - (fs)] = (Fd)(Vs)

Finally, we can divide both sides by (Fd-fs) to isolate Vw:

Vw = (Fd)(Vs) / [(Fd) - (fs)]

Therefore, the rearranged formula for Vw is:

Vw = (Fd)(Vs) / [(Fd) - (fs)]

I hope this helps you understand how to rearrange the formula to solve for Vw. Remember to always check your work and make sure your units are consistent. Good luck!