I would appreciate some help if poss I am really stuck.
I have an equation t = kpxd^2
I have to find the SI units of K
SI units of t = s
p = kg^-3
x = m
d = m
k is constant
I am really pulling my hair out on this one?
so use the units to give you the answer
s = k * (kg^-3) * (m) * (m)
s = k * (kg^-3) * (m^2)
You have to end up with seconds on the right side
so....
k has to have units to get rid of the (kg^-3) and the (m^2) and you have to end in seconds
so....
to get rid of (kg^-3) you need (kg^3)
to get rid of (m^2) you need (m^-2)
to end up in seconds k needs to have s in it
so....
k ---> s(kg^3)(m^-2)
Oh! I see now, thanks very much.
Sure, I can help you with that!
To find the SI units of K in the equation t = kpxd^2, we can use dimensional analysis.
Step 1: Write down the given SI units:
t = s (seconds)
p = kg^-3 (kilograms per cubic meter)
x = m (meters)
d = m (meters)
Step 2: Substitute the given values into the equation:
s = k * (kg^-3) * m * (m^2)
Step 3: Simplify the equation:
s = k * (kg^-3) * m^3
Step 4: Rearrange the equation to isolate k:
k = s / [(kg^-3) * m^3]
Step 5: Rewrite the denominator using exponent properties:
k = s / (kg^-3 * m^3)
k = s * (kg^3) * m^-3
Step 6: Apply the rules for multiplication and division when dealing with exponents:
k = s * kg^3 / m^3
Finally, we have the SI units of K as:
k = s * kg^3 / m^3
So, the SI units of K in the equation t = kpxd^2 are seconds multiplied by kilograms cubed, and then divided by meters cubed (s * kg^3 / m^3).