T^2=k R^3

[airkyd]

can soem one resolve his equation for me, find the units for k .... T is measured in seconds.... R is measured in meters .

 

thnx

[BigMoosie]

[math]T^2 = k R^3[/math]

 

[math]k = \frac{T^2}{R^3}[/math]

 

It looks like k is measured in [math]s^2m^{-3}[/math] (seconds squared per cubic meter). I cannot imagine its use though.

[5614]

err, k is a constant, it is unit-less.

 

If I had a value for T and a unit for R you could resolve k quite simply.

[Dave]

err, k is a constant, it is unit-less.

 

Just because k is a constant doesn't mean it's unitless. For example, take Newton's law of universal gravitation: [math]F = -\frac{G m_1 m_2}{r^2}[/math]. G is certainly a constant (the gravitation constant) and it also has units N m² kg^-2 (you can work this out).

[5614]

So do all constants have a unit? I'd say yes, if they didn't then they wouldn't be homogeneous (as in the same units on both sides of the equation) and I only just thought of that.

 

I suppose in y=kx the constant may not have a unit, as y and x don't really have units, or does 1 unit on the x axis count as a unit?

 

Going back to the OP, [math]T^2 = k R^3[/math] I'm guessing that k does have a unit.

[airkyd]

thansk guys

 

i posted is question in the pysics section and did get much infor on it ..... but still does any one knwo what the contstant represents????

 

its only gce physics..... :/ or is my teacher pushing me too hard

[ecoli]

So do all constants have a unit? I'd say yes' date=' if they didn't then they wouldn't be homogeneous (as in the same units on both sides of the equation) and I only just thought of that.

 

I suppose in y=kx the constant may not have a unit, as y and x don't really have units, or does 1 unit on the x axis count as a unit?

 

Going back to the OP, [math']T^2 = k R^3[/math] I'm guessing that k does have a unit.

 

When the proportionality constant is involved with things with the same units on both sides of the equation, then it doesn't have a unit.

 

Only example I can think of is the coeficient of friction. Ff = uFn

[Sisyphus]

Actually, it seems like the constant has no unit whenever it's being used to equate different units. For example, in the equation "force equals mass times acceleration," the only reason we can say "equals" is because we have arbitrarily selected units such that the constant is one. The force, for example, could be measured in dynes, which is equal to one gram cm/sec^2. However, if we were to use a different unit of force, mass, distance, or time, the constant would be something other than one. So really, we can say one of three things:

 

"The numerical value of net force measured in dynes is equal to the numerical value of mass in grams of the body multiplied by its acceleration measured in centimeters per second squared."

 

OR

 

"The numerical value of force is equal to some constant (no unit) times mass times acceleration."

 

OR

 

"The numerical value of force varies as mass times acceleration."

 

It's this last one one that's the least clumsy, since it gets to the substance of what's being said without having to mess around with units or constants.