Differing Mass, Same Size, In Atmosphere- gravitational acceleration

[maximiliano]

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?

 

[PhysicoRaj]

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]

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.

 

[maximiliano]

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.

 

[PJC01]

I would like to clarify that the statement "in a vacuum, gravity acts on different mass exactly the same" is not entirely accurate. In a vacuum, all objects fall at the same rate regardless of their mass, but this is due to the absence of air resistance. In an atmosphere, gravity does act on different masses differently due to the presence of air resistance or drag.

To answer the question about the relationship between two identical sized objects with different masses in the same atmosphere, we need to consider Newton's Second Law of Motion, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), or F=ma. This means that the heavier object will experience a greater force due to gravity and therefore will accelerate faster than the lighter object.

There is a formula for calculating the speed or acceleration of an object in a given gravitational field and in the presence of air resistance, but it can be complex and will depend on various factors such as the shape and surface area of the object, the density of the atmosphere, and the coefficient of drag. This is why it may seem that the formula is different for every set of objects, as there are many variables at play.

In the real world example of mountain biking, the difference in mass between you and your friend does play a role in your acceleration, but there may be other factors at play as well. For example, if your friend is in a more aerodynamic position or has a bike with lower air resistance, he may experience less drag and therefore accelerate faster. Additionally, the type and condition of the trail, as well as the skill and technique of the rider, can also affect acceleration. Overall, it is a combination of factors that determine the speed and acceleration of an object in a given situation.