Finding units of constants using dimensional analysis

[Nirupt]

Homework Statement

When an object falls through air, there is a drag force that depends on the product of the surface area, A (m2), and the square of the velocity, in (m/s). The equation is Fdrag = CAv2. The metric unit of force is the Newton, or (N). 1 N = 1 kg*m/s2. What are the units of the constant C?

and

Given the equation F =kA, where F is a force, k is a constant, and A is area, use unit analysis to determine the units of k.

Homework Equations

The Attempt at a Solution

Answer choices for the first:

m*s2/N

m*s2/N4

N*s2/m4

N*s/m2

Answer choices for the second:

N*m2, or kg*m3/s2

N/m2, or kg/(m*s2)

m2/N, or m*s2/kg

N*m, or kg*m2/s2

I'm just having trouble starting this class out, and I'm sure this stuff is simple but I'm being thrown off by the steps and my teacher is pretty disorganized but his explanations are confusing me. I would love information and steps on how to solve this.

 

[CAF123]

First step would be to rearrange each of your equations for the quantity you want the units for. What exactly is it you find difficult? Dimensional analysis is used so that the units on both sides of an eqn check out. (I.e think of it like 'you can only equate a vector with a vector'. Similarly, a force can only equal a force, etc.. so units on left = units on right)

 

[haruspex]

Just rearrange the equation: F = CAv²; C = F/(Av²).
Then substitute for F etc. using the units as though they were algebraic variables:
C = (kg m s^-2)/(m² (m/s)²)
and simplify.

 

[Nirupt]

Wow.. for some reason I was forgetting to rearrange the equation which is the first step.. lol sorry I was just over thinking it.