Rearranging Formula: Solving for Vw

  • Context: High School 
  • Thread starter Thread starter XxphysicsxX
  • Start date Start date
  • Tags Tags
    Formula
Click For Summary

Discussion Overview

The discussion centers around the rearrangement of a formula to solve for the variable Vw. Participants are exploring algebraic manipulation techniques and addressing issues related to canceling terms in the equation. The context appears to be homework-related, focusing on mathematical reasoning.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant asks how to rearrange the formula (Fd) = [(Vw) / (Vw-Vs)] (fs) to solve for Vw, expressing frustration over canceling Vw's during the process.
  • Another participant requests the first poster to show their working steps to identify potential mistakes in their algebra.
  • A participant shares their working steps, indicating they reached a point where they believe the Vw terms cancel each other out, but they are unsure why this happens.
  • Another participant challenges the algebraic manipulation presented, stating that the approach taken is incorrect and emphasizes the need to treat terms multiplied together as a single entity when rearranging the equation.
  • Suggestions are made to apply algebraic rules for expansion and factorization to aid in rearranging the equation correctly.

Areas of Agreement / Disagreement

There is no consensus on the correct method to rearrange the formula, as participants express differing views on the algebraic steps and the treatment of terms in the equation.

Contextual Notes

Participants have not fully resolved the algebraic steps involved in rearranging the formula, and there are indications of missing assumptions regarding the manipulation of terms.

XxphysicsxX
Messages
21
Reaction score
0
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)
 
Mathematics news on Phys.org
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.
 
Zryn said:
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!
 
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.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 42 ·
2
Replies
42
Views
6K
  • · Replies 41 ·
2
Replies
41
Views
6K
  • · Replies 9 ·
Replies
9
Views
3K
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
5K
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K