I was wondering if this formula is dimensionally correct:
v = Square root FX/m divided by mass
v= m/s F= kgm/s^2 X = meters divided by mass (kg)
v = root kgm * m
s^2
------
kg
My half solution:
m/s = root kgm^2
s^2
------
root kg
m/s = m/s root kg
--- the kg cancels
root kg
which leaves me with: m/s = m/s
thus the equation is dimensionally correct(?). I am unsure however if I violated any square root rules. Please help.
It is correct.
You did not violate any square root rules. The square root of a product is the product of the square roots, and the square root of a quotient is the quotient of the square roots.
Yes, the formula you provided is dimensionally correct. You have correctly analyzed the dimensions of each term in the formula and showed that they cancel out to give the dimension of velocity, which is meters per second (m/s). The equation is dimensionally consistent.
To determine if a formula is dimensionally correct, you need to check that the units on both sides of the equation are consistent.
Let's break down the formula:
v = sqrt(F * X / m)
Where:
v = velocity (m/s)
F = force (kg * m/s^2)
X = distance (m)
m = mass (kg)
Now, let's substitute the units into the formula:
v = sqrt((kg * m/s^2) * (m) / (kg))
The units cancel out in the following way:
v = sqrt((kg * m * m) / (s^2 * kg))
Now, we simplify:
v = sqrt(m^2 / s^2)
Taking the square root of m^2 gives us |m|, and since we are dealing with positive values, we can write it as:
v = m / s
This shows that the dimension on the left side (m/s) matches the dimension on the right side (m/s), so the formula is dimensionally correct.
You have correctly identified that the equation is dimensionally correct. You did not violate any square root rules in your approach.