# 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

This has nothing to do with a falling object. The question does not say anything about falling objects. If they were falling, then you would have an issue because the velocities of the objects would be changing at different rates, and they would reach different terminal velocities. Therefore they would have different drag forces acting on them the entire time.

But this question is not concerned with this scenario. It is more of a general question whose answer it seems like you can already make sense of. The answer is the only one that does not effect the number of collisions with air molecules. The writer of the question should have done a better job specifying the specific movent of the object.

drag force is simply the air resistance which an object experiences during its fall. Its doesn't depend upon the weight of the object because a light object and a heavier object will be falling through the same molecules of air. A lighter object, due to its slow speed will experience less resistance and it continues to fall mainly due to gravity whereas a heavier object due to greater velocity will experience a greater drag force. you cay say (more weight --> more speed --> more drag force)

You're forgetting that all objects have the same acceleration under gravity.

In the absence of the drag forces, any two objects would have the same speed at a given time, so your argument doesn't apply.

Your intuition tells you that weight should matter because the drag force is smaller $$relative$$ to the gravitational force, and will have a less significant effect (even though its value is the same for both objects).

• If the objects were falling then they actually would experience different drag forces due to differences in velocity after release. The problem, however, never specifies falling objects. – Aaron Stevens Oct 7 '18 at 13:00
• I would argue that the word atmosphere implies the presence of gravity. Regardless, the main point is that the velocity and weight are being considered independently so you can't reasonably say weight affects the drag force – bd-ober Oct 7 '18 at 13:10
• I disagree. Movement through the atmosphere is much more general than falling. Cars move through the atmosphere without falling all of the time. I agree with your final conclusion though. – Aaron Stevens Oct 7 '18 at 13:14
• And if you really want to assume a falling object, then the weight will matter. – Aaron Stevens Oct 7 '18 at 13:39