Converting W²/NJHz to MKS: Step-by-Step Guide

[joejo]

Given: W = J/s, J = Nm, N = kgm/s2, Hz = 1/s
Convert W²/NJHz to mks and simplify. Make sure to list every step.

can someone please guide me...this is what I have so far...im not sure if I am doing it right though...


J/s² underline meaning over...
kgm/s² * Nm* 1/s



is this right...

 

[The Bob]

Given: W = J/s, J = Nm, N = kgm/s2, Hz = 1/s
Convert W²/NJHz to mks and simplify. Make sure to list every step.

What is an mks?

can someone please guide me...this is what I have so far...im not sure if I am doing it right though...

I can but I need a little help from you.

Also try this thread.

The Bob (2004 ©)

 

[joejo]

thx bob...i don't know but I will email my teacher and ask him...

 

[The Bob]

PM me when you have found out.

The Bob (2004 ©)

 

[Werg22]

MKS it a measure system. You are already working with MKS.

 

[Werg22]

Maybe you need to convert to cgs...

 

[jtbell]

No, I think he's just supposed to reduce it to the simplest possible combination of meters, kilograms, and seconds, after substituting for watts, joules, etc.

 

[The Bob]

MKS it a measure system. You are already working with MKS.

In that case it is fairly simple.

Given: W = J/s, J = Nm, N = kgm/s2, Hz = 1/s
Convert W²/NJHz to mks and simplify. Make sure to list every step.

Write W as Js^-1, J as Nm, N as kg ms^-2 and Hz as s^-1.

$$\frac{W^2}{N \times J \times Hz} = \frac{(Js^{-1})^2}{kg \ ms^{-2} \ \times \ Nm \ \times \ s^{-1}}$$

Now it is time to start using your basic knowledge of maths to multiply and divide this out.

$$\frac{J^2s^{-2}}{\frac{kg \m}{s^2} \ \times \ Nm \ \times \ \frac{1}{s}} = \frac{J^2}{s^2} \div (\frac{kg \m}{s^2} \ \times \ Nm \ \times \ \frac{1}{s}}) = \frac{J^2}{s^2} \div \frac{kg \m \times Nm}{s^2 \times s}$$

$$= \frac{J^2}{s^2} \times \frac{s^3}{kg \m \times Nm} = \frac{J ^2 \ s^3}{kg \m \times Nm \times s^2} = \frac{J ^2 \ s}{kg \m \times Nm} = J^2 \ s \ kg^{-1} \ Nm^{-1}$$

This is what I get however I feel that the (Js^-1)² = J²s^-2 might be said to be wrong by someone more in the know than I am on units. However this is what I think until I am told otherwise.

If this does not make too much sense then look at the thread I mentioned in the second post. It will explain things more clearly.

The Bob (2004 ©)

 

[KingNothing]

First convert all your 'givens' to MKS, starting with the most basic (Hz).

MKS means everything is meters, kilograms, and seconds. If something is on the 'bottom' of a fraction, rewrite it as being multiplied times the top, only make the exponent negative. Example: $$\frac{4}{x^2} = 4x^{-2}$$

$$Hz=(s^{-1})$$
$$N=(kg)(m)(s^{-2})$$
$$J=(kg)(m^2)(s^{-2})$$
$$W=(kg)(m^{2})(s^{-3})$$

Now just plug them into your big equation:

$$(W^2)(N^{-1})(J^{-1})(Hz^{-1})$$

For $$(W^2)$$, all you have to do is double all the exponents of that part once you substitute, so $$(W^2)=(kg^2)(m^4)(s^{-2})$$.

Now, that's one part that I've done for you. I'd like to see you substitute the rest in on your own. Just remember, that when you've determined, for example, $$J=(kg)(m^2)(s^{-2})$$, then $$J^{-1}=(kg^{-1})(m^{-2})(s^{2})$$...all the exponents switch signs. When multiplying like terms, add their exponents. For example, $$(m^4)(m^{-3})=(m^{-1})$$. I put parentheses around everything so I don't get confused by two-letter variables.

 

[joejo]

lol...still kinda confused..but this seems righter then me (oops is righter a word)...

so this is right...

 

[joejo]

oh thanks kingnothing i just saw ur reply...i will work it out now...and post my answer...thanks to all that replied

 

[The Bob]

I see what you have done. My method, in my eyes, is fine but I simply need to learn the conversions (as N and J are the same as you have written and I would not have expected).

Cheers.

The Bob (2004 ©)

 

[joejo]

so is ur way right too the bob?! u guys r losing me

 

[joejo]

hey guys i did all the work on paper...my final answer is

(kg4)(m7)(s-11)

please tell me that's right??

 

[joejo]

$$=(kg^{4})(m^{7})(s^{-11})$$

i hope this latex stuff works...

 

[The Bob]

$$=(kg^{4})(m^{7})(s^{-11})$$

i hope this latex stuff works...

Personally I got m kg^-1 s^-1.

The Bob (2004 ©)

 

[KingNothing]

I got $$m^1 * s^{-1}$$ in other words, meters per second.

Bob, how did you get an extra kg on the bottom?

Watts squared yields kg^2, then on the bottom Joules and Newtons both have kg^1 so there is no kg on top or bottom.

 

[The Bob]

Here is my workings:

$$N = kg \ ms^{-2}$$

$$J = Nm = kg \ ms^{-2} \times m = kg \ m^2 s^{-2}$$

$$W = Js^{-1} = kg \ m^2 s^{-2} \times s^{-1} = kg \ m^2 s^{-3}$$

$$\frac{W^2}{J \times N \times Hz}$$ $$= \frac{(kg \ m^2 s^{-3})^2}{kg \ m^2 s^{-2} \times kg \ ms^{-2} \times s^{-1}}$$

$$= \frac{kg^2 \ m^4 s^{-6}}{kg \ m^2 s^{-2} \times kg \ ms^{-2} \times s^{-1}}$$

$$= \frac{kg^2 \ m^4 s^{-6}}{kg^2 \ m^3 s^{-5}} = m s^{-1}$$

So I agree with KingNothing and I realized my mistake was a missing squared on my kilograms.

Stupid me.

The Bob (2004 ©)

 

[KingNothing]

Alright, it's time to check my answer to prove to you villains that I'm right. :P
meters=5
kg=8
seconds=3

Watt=(8)(5^2)(3^-3)
Watt^2 = 54.87 (about)
Newton = (8)(5)(3^-2)
Newton = 4.44
Joule = (8)(5^2)(3^-2)
Joule = 22.22
Hz = (3^-1)
Hz = .33

Newton * Joule * Hz = 32.56
Watt^2 = 54.87

So, Watt^2 over Newton * Joule * Hz = 1.69


And with my simplification, 5/3 = 1.6666666

Tada!

 

[The Bob]

Alright, it's time to check my answer to prove to you villains that I'm right. :P

All credit to you. I said you were right and I was simply checking my method for joejo as I got the impression it made sense to him/her.

The Bob (2004 ©)

 

[joejo]

hey kingnothing...ur totally losing me...can you please show me how you got that answer...im so lost...and i have a quiz 2mr?!

thanks...i have my work if you want to see...so don't think I am asking for the answer...ive been stuck on it since friday...

thanks

 

[KingNothing]

Yes, show your work. Just break your 'givens' down into MKS, then substitute them in and use algebra.

As crazy as this may sound, I looked at your numbers and you have 90% of it right! So don't worry. I think a simpler example will clear things up.

Convert $$\frac{N}{Hz}$$ to MKS.
$$N = \frac{Kg * m}{s^2}$$
Now, this is where it might get tricky. Dividing by $$s^2$$ is the same as multiplying by $$s^{-2}$$!
Therefore, we can rewrite $$\frac{Kg * m}{s^2}$$ as $$Kg * m * s^{-2}$$

So now we're half done. Rewrite the other part, Hz.
$$Hz = \frac{1}{s}$$ or $$Hz = s^{-1}$$.

So now it's converted to MKS, it's just not simplified.
$$\frac{N}{Hz} = \frac {Kg * m * s^{-2}}{s^{-1}}$$
Which is just substitution.

Now just think about that part on the bottom. Remember how moving something to the top made the exponent's sign change? You can do the same thing here.

$$\frac {Kg * m * s^{-2}}{s^{-1}} = Kg * m * s^{-2} * s^1$$

It's really close, but we have two like terms, the $$s$$. When you multiply two like terms with different exponents, you add the exponents. Therefore, $$s^{-2} * s^1 = s^{-1}$$.

According to my numbers, switching the negative signs and exponents is the only part you are doing wrong. But the rest you are doing fine.

 

[joejo]

i didddddd...it didn't work...i have it scanned...but it won't fit...please don't make me do the latex stuff again...

 

[KingNothing]

No, don't bother with Latex. We can probably understand what you mean. The reason I say you are close is this:

for my exponents on the Kg unit, they were +2, -1, and -1, meaning they summed to zero and that's why there is no Kg in the final answer. Yours summed to 4.

for my exponents on the meters unit, they were +4, -1, and -2, meaning they summed to +1. Yours summed to 7.

It seems to me like when you are multiplying like terms like y^2 * y^-1, you are adding the exponents like this: 2+1=3, so it is y^3. No. It is y^1.

 

[joejo]

$$W=(kg)(m^{2})(s^{-3})$$


$$(W^2)(N^{-1})(J^{-1})(Hz^{-1})$$

For $$(W^2)$$, all you have to do is double all the exponents of that part once you substitute, so $$(W^2)=(kg^2)(m^4)(s^{-2})$$.

well i added the like terms...but i think you/I made a mistake earlier ...for W2 u said that is was quote above...should it become -6 because you squared it...thats where are answers differ... because s is orginally -3*2= -6

thanks

 

[joejo]

so wen i got my answer I used -3*2= s-6

and u used s-2?? why is that...isn't it W2

thanks

 

[KingNothing]

Yes, it was a typo. It's $$s^{-6}$$

 

[joejo]

therefore making my answer right...right??...because that affects your answer...

 

[Werg22]

I get m/s

W=kg*m^2/s^3
N=kg*m/s^2
J= kg*m^2/s^2
Hz=1/s

(kg*m^2/s^3)^2/ (Kg*m/s^2* Kg*m^2/s^2*1/s)

So

(kgm^2/s^3)^2/(kg^2*m^3/s^5)

(kg^2*m^4/s^6)(s^5/ kg^2*m^3)

kg^2*m^4*s^5/s^6*kg^2*m^3

m/s

 

[learningphysics]

therefore making my answer right...right??...because that affects your answer...

The answer is $$ms^{-1}$$

$$(W^2)(N^{-1})(J^{-1})(Hz^{-1})$$

leads to... $$kg^2m^4s^{-6}*kg^{-1}m^{-1}s^{2}*kg^{-1}m^{-2}s^{2}*s^{1} = ms^{-1}$$

Watch out for the sign of your exponents.

 

[Data]

$$\frac{\mbox{W}^2}{\mbox{NJHz}} = \frac{\left(\frac{\mbox{Nm}}{\mbox{s}}\right)^2}{\left(\frac{\mbox{N}^2\mbox{m}}{\mbox{s}}\right)} = \frac{\mbox{m}}{\mbox{s}}$$

 

[OlderDan]

Aw Data, you beat me to it. A nice concise simplification. I'm going to post mine anyway since its still in the buffer

Given: W = J/s, J = Nm, N = kgm/s2, Hz = 1/s
Convert W²/NJHz to mks and simplify. Make sure to list every step.

can someone please guide me...this is what I have so far...im not sure if I am doing it right though...


J/s² underline meaning over...
kgm/s² * Nm* 1/s



is this right...

So many posts for such a small problem

$$\frac{W^2}{NJHz}$$

$$W=\frac{J}{s}$$

$$J=Nm$$

$$N = \frac{kgm}{s^2}$$

$$Hz = \frac{1}{s}$$

$$\frac{W^2}{NJHz} = \frac{(\frac{J}{s})^2}{NJ\frac{1}{s}} = \frac{\frac{J}{s}}{N} = \frac{Nm}{Ns} = \frac{m}{s}$$

 

[KingNothing]

So many posts for such a small problem

Precisely the reason why. Because some people feel they need to re-post the right answer for seemingly no reason ;).

Joejo, answer these problems. Simplify these so there is no fractions, only exponents:

$$x^2 *x^{-5} = ??$$


$$\frac{x^7}{y^4} = ??$$

Answer those and we will be able to see your problem.

 

[OlderDan]

Precisely the reason why. Because some people feel they need to re-post the right answer for seemingly no reason ;).

Well no doubt mine was more than needed, but at the time I started working on all the laborious tex stuff, somebody needed to post a solution that was concise and to the point eliminating the derived units as much as possible before sustituting in all the m, kg, and s all over the place. Most of the incorrect solutions posted were needlessly complex, and that's probably why they were wrong.

 

[The Bob]

Here is my workings:

$$\frac{W^2}{J \times N \times Hz}$$

$$= \frac{kg^2 \ m^4 s^{-6}}{kg^2 \ m^3 s^{-5}} = m s^{-1}$$

So I agree with KingNothing and I realized my mistake was a missing squared on my kilograms.

The Bob (2004 ©)

I have already shown how to do the simplification. It is a full example.

The Bob (2004 ©)