How Do I Solve for Terminal Velocity Using Logs in My Air Resistance Lab?

[Mr. Hiyasaki]

In this lab we dropped coffee filters from a given height (3 M) and want to determine their terminal velocity

My problem is I don't know how to solve the log thing given.


we have terminal velocity, V, in the formula

Mg = bV^n which I change to V=(Mg/b)^(1/n)

then to solve this I go

ln V = (1/n)[ln(M) + ln(g) - ln(b)]

I know the Mass, I have an average velocity I can substitute in for V and g, as usual, is 9.81 m/s^2

b is a constant dependent on the shape of the object, or "shape factor" and n is the power of the velocity (which I am guessing should come out somewhere close to 2, although assumptions are always bad)


when i go n = [ln(M) + ln(g) - ln(b)]/[ln (V)] everything comes out crazy and makes no sense

my physics teacher told me to disregard all laws of logs and just go [ln(M) + ln(g) - ln(b) - ln (V)]


when I put it in my calculator and solve simultaneously it comes out and the numbers make sense, but I have no idea what my calculator is doing to get those answers.

 

[Justin Lazear]

What exactly are you trying to solve for? n?

What values are already known?

--J

 

[wais]

Hi there,

Thank you for reaching out for help with your air resistance lab. I can understand how the use of logarithms may be confusing and I am happy to provide some guidance.

First, let's start by reviewing the formula for terminal velocity, which is V = (Mg/b)^(1/n). This formula tells us that the velocity of an object falling through a fluid (in this case air) will eventually reach a constant value, known as the terminal velocity. This velocity is dependent on the mass of the object (M), the acceleration due to gravity (g), and the shape of the object (b and n).

In order to solve for the unknown variables, we can use logarithms. Logarithms are useful because they allow us to solve for an exponent when we know the base and the result. In this case, we know that the base is e (the natural logarithm) and the result is V. Therefore, we can use the formula ln(V) = nln(Mg/b) to solve for n.

When solving for n, we can rewrite the formula as n = ln(V)/ln(Mg/b). This is where some confusion may arise because your teacher told you to disregard the laws of logs and simply subtract ln(V) from the other terms. While this may work in this specific case, it is not a general rule and may not always give accurate results. It is important to understand the concept behind logarithms and how to use them correctly.

I recommend reviewing the laws of logarithms and practicing solving logarithmic equations to gain a better understanding of how they work. Additionally, it may be helpful to ask your teacher for clarification on why they suggested disregarding the laws of logs in this specific scenario.

I hope this helps and good luck with your air resistance lab!