# Homework Help: Math Problem No Numbers ?

1. Apr 24, 2005

### 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 im doing it right though....

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

is this right.....

2. Apr 24, 2005

### The Bob

What is an mks???

I can but I need a little help from you.

3. Apr 24, 2005

### joejo

thx bob...i dont know but I will email my teacher and ask him...

4. Apr 24, 2005

### The Bob

PM me when you have found out.

5. Apr 24, 2005

### Werg22

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

Last edited: Apr 24, 2005
6. Apr 24, 2005

### Werg22

Maybe you need to convert to cgs...

7. Apr 24, 2005

### Staff: Mentor

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.

8. Apr 24, 2005

### The Bob

In that case it is fairly simple.

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.

9. Apr 24, 2005

### 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.

10. Apr 24, 2005

### joejo

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

so this is right...

11. Apr 24, 2005

### joejo

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

12. Apr 24, 2005

### 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.

13. Apr 24, 2005

### joejo

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

14. Apr 24, 2005

### joejo

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

(kg4)(m7)(s-11)

15. Apr 24, 2005

### joejo

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

i hope this latex stuff works....

16. Apr 24, 2005

### The Bob

Personally I got m kg-1 s-1.

17. Apr 24, 2005

### 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.

Last edited: Apr 24, 2005
18. Apr 24, 2005

### 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 realised my mistake was a missing squared on my kilograms.

Stupid me.

Last edited: Apr 24, 2005
19. Apr 24, 2005

### 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)
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

20. Apr 24, 2005

### The Bob

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.

21. Apr 24, 2005

### 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 wanna see...so dont think im asking for the answer...ive been stuck on it since friday....

thanks

22. Apr 24, 2005

### 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.

Last edited: Apr 24, 2005
23. Apr 24, 2005

### joejo

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

24. Apr 24, 2005

### 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.

25. Apr 24, 2005

### joejo

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