# Why wouldn't the weight of an object affect the magnitude of the drag force on that object?

I ran into trouble again with a course about drag force on skiing. This is the question, and its explanation:

Which of the following factors would not affect the magnitude of the drag force on an object moving through the atmosphere?

Explanation

Correct answer: Weight of the object

Drag forces in the atmosphere result from air molecules colliding with a moving object. The magnitude of the drag force depends on the speed and shape of the object, and the density of air.

If the speed of the object is larger, the object collides with more molecules each second. More collisions increase the total drag force. For similar reasons, the force increases in denser air. Density measures the total mass, which is related to the number of air molecules, in a volume of air.

The shape of the object also affects the drag force in two ways. First, whether the surface of the object is rounded or has sharp edges, or is smooth or rough, factors into the drag force. Smooth objects with a rounded, gentler shape allow air to flow around them more easily, leading to smaller drag. Second, the forward-facing area of the object perpendicular to the direction of motion also contributes to the force.

The drag force for irregular objects moving at moderate speeds can be calculated with$$F_{drag}=\frac{1}{2} C A \rho v^2$$ where $$C$$ is a drag coefficient that is often determined with experiments, $$A$$ is the forward-facing area, $$\rho$$ is the mass density of the fluid, and $$v$$ is the speed of the object relative to the fluid. Specifically, this model of drag applies only when motion through the fluid causes turbulence — swirling, unpredictable air flow patterns. Both skiers and skydivers meet this criterion.

The question also provided me with four choices:

A) Density of air

B) Weight of the object

C) Shape of the object

D) Speed of the object

Now why wouldn't the weight of an object affect the magnitude of the drag force on the object? The heavier the weight, the faster the speed of the object (due to gravity), which will lead to the object colliding into more air molecules per second and therefore making the magnitude of the drag force on the object slightly bigger.

• Welcome to Physics SE! Please do not post images of texts you want to quote, but type it out instead so it is readable for all users and so that it can be indexed by search engines. For formulae, use MathJax instead. – user191954 Oct 7 '18 at 12:16
• Thanks for your edit! I've fixed up the mathjax here; there's a tutorial linked in my previous comment for future reference. – user191954 Oct 7 '18 at 12:24