When air resistance is accounted for, why is it that heavier objects fall faster than lighter object

[m25]

When air resistance is accounted for, why is it that heavier objects fall faster than lighter objects?

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[Cawolf]

To determine the terminal velocity one simply sets the force of gravity equal to force of drag.

mg = 0.5C(rho)Av^2

v = sqrt[2mg/c*rh0*A]

This equation hows mathematically how as objects become more massive (with the same cross sectional area in the same medium) their terminal velocity increases.

Conceptually, the force of gravity is stronger in more massive objects so the drag force takes longer (or requires a higher velocity) to completely oppose it.

 

[m25]

To determine the terminal velocity one simply sets the force of gravity equal to force of drag.

mg = 0.5C(rho)Av^2

v = sqrt[2mg/c*rh0*A]

This equation hows mathematically how as objects become more massive (with the same cross sectional area in the same medium) their terminal velocity increases.

Conceptually, the force of gravity is stronger in more massive objects so the drag force takes longer (or requires a higher velocity) to completely oppose it.

So heavier masses fall faster because their terminal velocity is higher? So what about in cases when they hit the ground without reaching their terminal velocity?
And is there an equation that shows acceleration is higher in heavier masses...?

 

[Cawolf]

Heavier things fall faster than lighter things because the force of drag is not effected by the mass of the object. So more massive objects have a greater downward force and therefore greater acceleration towards the earth, meaning they will get to the ground in less time.

The equations are the same. Just sum the net forces and note that a hollow ball will have a net force down that is less than the solid ball of the same shape and material.

 

[TheRhymenocerous]

I bet @Cawolf's explanation is more accurate, but here's how I think about it: It's probably better to ask "why do light objects fall more slowly?" rather than "why do heavy objects fall faster?" Heavy objects fall at the rate all objects would fall if it weren't for air resistance. Air resistance is all about the mass to surface area ratio. The lower the mass:SA ratio, the more air resistance an object will feel. For two objects of the same size (same surface area), the heavier one will experience less air resistance so it'll fall more quickly.

 

[m25]

I bet @Cawolf's explanation is more accurate, but here's how I think about it: It's probably better to ask "why do light objects fall more slowly?" rather than "why do heavy objects fall faster?" Heavy objects fall at the rate all objects would fall if it weren't for air resistance. Air resistance is all about the mass to surface area ratio. The lower the mass:SA ratio, the more air resistance an object will feel. For two objects of the same size (same surface area), the heavier one will experience less air resistance so it'll fall more quickly.

But I thought air resistance is not dependent on mass? Since force of air resistance is proportional to (density of medium)x(velocity^2)x(surface area of object)

 

[Cawolf]

The drag force is anti-parallel to the gravitational force, which is mass dependent.

 

[TheRhymenocerous]

But I thought air resistance is not dependent on mass? Since force of air resistance is proportional to (density of medium)x(velocity^2)x(surface area of object)

I actually have never looked at the equation for air resistance in my life, but for practical purposes, I think what I said should be correct. The mass part comes into play because the force of gravity has to do with the mass, so there'll be a stronger gravitational force. Thinking too hard about formulas gets in the way of intuition, which is super important in physics.

Edit: just like @Cawolf said!

 

[m25]

The drag force is anti-parallel to the gravitational force, which is mass dependent.

But you said drag force is not dependent on mass in your previous post? http://forums.studentdoctor.net/threads/air-resistance-and-acceleration.1096970/#post-15659439

 

[Cawolf]

It is not.

I said the gravitational force (mg) is mass dependent.

 

[TheRhymenocerous]

It's not, but think about it like a force-body diagram. You have your gravitational force pointing down and your drag force pointing up. The bigger the gravitational force (which is mass-dependent), the bigger the net force downward.

 

[m25]

It is not.

I said the gravitational force (mg) is mass dependent.

It's not, but think about it like a force-body diagram. You have your gravitational force pointing down and your drag force pointing up. The bigger the gravitational force (which is mass-dependent), the bigger the net force downward.

Oh I think I got it, thank you!