Solving SI Unit Analysis: Force & Area

[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.

 

[Nickie]

As a scientist, it is important to have a strong understanding of units and their conversions in order to accurately analyze and solve problems. In this case, we are dealing with force and area, which are both fundamental physical quantities and have their own respective units. The first step in solving this problem is to identify the given information and the desired units.

In the first question, we are given the equation Fdrag = CAv2, where Fdrag is the drag force, C is a constant, A is the surface area, and v is the velocity. We are also given the units for force (N) and area (m2). The question asks for the units of the constant C. This means we need to find the units that will cancel out the units of force (N) and area (m2) in the equation Fdrag = CAv2.

The second question gives us the equation F = kA, where F is a force, k is a constant, and A is the area. We are asked to determine the units of k. This means we need to find the units that will cancel out the units of force (N) and area (m2) in the equation F = kA.

To solve these problems, we can use dimensional analysis, which involves converting units to a common system and then canceling out the units to find the desired units. In this case, we will convert all units to the SI system (meters, kilograms, and seconds).

For the first question, we can start by converting the units of velocity (in/s) to the SI unit of meters per second (m/s). We know that 1 in = 0.0254 m, so we can write the conversion as:

1 in/s = (0.0254 m)/s

Next, we can substitute this conversion into the equation Fdrag = CAv2 and cancel out the units of velocity (s) to get:

Fdrag = C(0.0254 m/s)2

Next, we need to cancel out the units of area (m2). We can do this by dividing both sides of the equation by the unit of area (m2):

Fdrag/m2 = C(0.0254 m/s)2/m2

Simplifying this, we get:

Fdrag/m2 = C(0.000645 m2/s2)

Finally, we can cancel out the units of force (N) by