How Do W/m² and kg·s⁻³ Compare in Physics Units?

[Maya Erikson]

Homework Statement

trying to show that the units W m-2 are equivalent to kg s-3

Homework Equations

1 W = 1 J s-1 ?

The Attempt at a Solution

energy per unit time?

p.s. I am very new to physics, a beginner in understanding the whole concept of units, any advice?

 

[Rick88]

1W= 1J s^-1, yes.

Now you need to know what 1J is.
Just think about a formula to find energy, and you should get to your answer.R.

 

[Maya Erikson]

1 J = 1 kg x m^-2 / s^-2

and, E = P x t
1 J = 1 W x 1 s

so, 1 kg x m^-2 / s^-2 = 1 kg x m^-2 / s^-3 x s ??

and now i don't have any idea where I am going with this.

 

[Rick88]

you know that
E = 1/2 m v², right?

so, in terms of units
J = kg m² s^-2

But W = Js^-1 = kg m² s^-3.

But you were asked to find the units of Wm^-2, so..

 

[gneill]

1 J = 1 kg x m^-2 / s^-2

and, E = P x t
1 J = 1 W x 1 s

so, 1 kg x m^-2 / s^-2 = 1 kg x m^-2 / s^-3 x s ??

and now i don't have any idea where I am going with this.

Watch your notation! It'll derail you if you're not careful.

J = kg m^2/s^2

A negative exponent "moves" the value between the numerator and denominator. That is,

a^-1 = 1/a

and

1/a^-2 = a^2

What you've written for the units of the Joule would then be:

1 kg x m^-2 / s^-2 = kg*s^2/m^2

Which I'm sure is not what you intended.

Perhaps you meant:

kg*m^2*s^-2