Dimensionalysis and Conversions

[honphysics12]

Homework Statement

Use the units given in the table below to determine whether the formulas are dimensionally consistent.

/ this symbol (to the left) means divided by

Length= distance= m

mass= Kg

time= s

area= m squared

speed= m/s

acceleration= m/s squared (only the s is squared)

force= Kg m/s squared (only the s is squared)

energy= Kg m squared /s squared

power= Kg m squared /s cubed

Homework Equations

How do you solve these and how do you multiply the units?

Does energy= (mass) (acceleration) (length)

Does speed= acceleration/time

Does area= (length) (length)

Does energy= (mass) (speed squared)

Does energy= (mass) (acceleration)/length

The Attempt at a Solution

I tried the first one.

energy= (mass) (acceleration) (length)
= [Kg] [m/s squared] [m]
= [Kg m squared /s]

Is that right?

 

[neutrino]

The Attempt at a Solution

I tried the first one.

energy= (mass) (acceleration) (length)
= [Kg] [m/s squared] [m]
= [Kg m squared /s]

Is that right?

Does that answer match with the unit for energy, which you wrote earlier?

Treat the units as you would ordinary numbers.

 

[honphysics12]

So when I multiply the 2 m's and the 2 s's, they become squared right?

The answer would then be Kg m squared /s squared.

 

[neutrino]

Correct.

 

[Avodyne]

So when I multiply the 2 m's and the 2 s's, they become squared right?

Right! That's really all there is to it.