The relative densities have no effect on the objects, but the mass (Weight indicates the strength of the gravitationall force on the object ) do. (A little, mostly considering friction and air movements.).
Example, the two balls experiment. One drops two balls, one made from Iron, one from wood. The balls are of equal size, but different mass. Therefore, there densities are also different. Now if you drop these balls, they will hit the ground at the exact same moment.
Therefore, a difference in density does not impact falling speed. Q.E.D
Now seeing as we just conveniently ignored friction in the previous experiment, let's see what happens then. Both objects would get an equal amount of friction, but considering one objects mass(not density, density isn't important) is larger, it's momentum is too. This would mean that that object would slow down a little less, meaning that it would hit the ground faster.
However, this effect is often
neglible. Also, as stated before, it has
nothing to do with the objects densities, only with it's mass. The only way for the density to be relevant is for when it either impacts the mass of the object, or the objects size (and therefore the amount of friction).
Say let's work out a practical example. We have two objects, one having a density of 2 kg/dm³, the other of 4kg/dm³. Both objects are 1dm³ large. Let's also assume that both objects are not hampered by friction, because that is hard to calculate.
Since the energy of the momentum is equal to the energy off the fall, we know:
(m*v²/2)=m*g*h (m=mass, v=speed, g=gravitational force, h=height)
So, when we fill that in:
First object
(v²*2kg/2=2kg*1m*9.81/kg*m)
(v²*
2kg/2=
2kg*1m*9.81/kg*m)
(v²=2*9.81N)
Second object
(v²*4kg/2=4kg*1m*9.81/kg*m)
(v²*
4kg/2=
4kg*1m*9.81/kg*m)
(v²=2*9.81N)
Q.E.D.: Two objects without external influences fall at equal speeds, regardless of their relative mass or density.
Now if an other external force(for example the wind) would want to influence the objects path, this calculation applies
v²*m/2 = Energy required for the speed chance v)
As you can see, m stands for mass, not density. Therefore, density doesn't influence an objects path, not directly through gravitationall force, nor indirectly by using external forces.
Q.E.D.How the hell did you guys go off on a two-page derail? O_o
Someone was being wrong on the internet