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

[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 ©)

 

[joejo]

so many answers??!? which one is right guys?!

older dan is that right...because that is easy to understand...

someone please help?!

 

[OlderDan]

so many answers??!? which one is right guys?!

older dan is that right...because that is easy to understand...

someone please help?!

m/s is the correct answer. You can count on it.

Some of the earlier solutions also got the same result. I posted my solution because it is simpler than the approaches posted earlier. Data's is also simple, but it combines two pieces of the given information in one step. Bob's final answer also agrees, but his latest post combines many things in the first substitution. I avoided that in my approach.

There are often many ways to approach a problem, and I'm not claiming mine is the "best", but as a general rule when I have to simplify units I prefer to eliminate as many "derived" units as possible before replacing them with the "fundamental" units of m,kg,s. It usually cuts down on the number of steps and reduces the probability of losing track of something.

 

[Data]

I posted the answer because there are lots of incorrect answers in this thread, which could easily confuse the poster (and apparently have!). m/s is correct.

 

[The Bob]

m/s is correct.

Is 'm/s' standard practise to most people? It was good at GCSE but causes confusion when doing this sort of problem. Making it ms^-1 makes more sense as you can mathematically solve it with letters.

This is only my peronsal opinion and if others find m/s easier then that is fine. Just remember that higher levels of education use ms^-1.

The Bob (2004 ©)