# 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