# Differing Mass, Same Size, In Atmosphere- gravitational acceleration

In a vacuum, gravity acts on different mass exactly the same. However, what about on earth.....what is the relationship between two identical sized objects, in the exact same atmosphere.....but of different mass? For example, dropping two identical sized bowling balls from height of 10 meters, one ball is 10kg, the other is 20 kg. Is there a formula for speed or acceleration? Or, would the formula be impossibly complex because it is different for every set of object, due to differing coefficients of drag?

Real World example- I'm about 245 pounds. My friend is about 175 pounds. When we go mountain biking, on the downhill sections....we both coast. Well, I've noticed that I end up passing him very quickly, or must stay on my brakes if I wish to stay behind him. Clearly, assuming everything other than our mass is the same (my drag should actually be slightly more than his, just due to my size..but let's pretend it's not), yet I'm accelerating faster than he is. Or.....maybe something else is at work?

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PhysicoRaj
Gold Member
On earth and in vacuum, gravity acts the same. In the case of light objects, they are stopped by air on earth. Talking into consideration you and your friend's example, it would have been better if you both did this experiment by diving from a height. Then the formula to find the velocity is, v^2=u^2 + 2gh. When it comes to mountain biking, do both of you start at the same time with initial velocity 0 ? If yes, then the drag is compensated by your momentum(since you weigh more). The wind blowing uphill pushes your friend and he ends up behind you, since he is lighter than you. You weigh more. Hence you have more momentum. Your body withstands the drag of air or ground as the momentum is more.
Hence you move faster than him.
If you want the equations, here:
*)v^2=u^2 + 2gh
*)h=ut+1/2gt^2
*)v= u+gt
v=final velocity; u=initial velocity; g=gravitational acceleration; t=time; h=height.

Drakkith
Staff Emeritus
The difference between two identically sized object having different masses is that drag affects the lighter one more than it does the heavier one. Otherwise the acceleration due to gravity is equal. An object twice as massive feels a force twice as much but requires twice the force to accelerate the same amount, so it all equals out to be the same.

Thanks, yes acceleration due to gravity is always the same...but resistance isn't. Since I'm heavier, I'll go faster downhill (especially if there is a head-wind)....but I'll fall way behind climbing.

Got it. So, the bottom line is that more weight has you: fighting harder against inertia when changing speed....more resistance to gravity when climbing....more friction from the tires on the road (this can be reduced with higher pressure and a "highway" tread pattern)....and wind resistance (assuming the heavier vehicle is also larger....if not, this isn't a factor).

To minimize the energy consumed when driving any vehicle, you want to try not to change speed any more than absolutely necessary, avoid hills, coast down the other side of hills (let inertia work for you), and reduce highway speed (to try to minimize wind resistance, which increases exponentially with velocity).

Thanks guys.

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