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There are two forces acting on your piece of paper: 1) the force of gravity, pulling both down with the same force $F_g = m\cdot g$ 2) drag force due to the air. In general, drag force is proportional to the projected area of the object. For regularly shaped objects (like a sphere) the drag is usually expressed as $$F_{drag} = \frac12 \rho v^2 A C_D$$ ...


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While falling, both the sheet of paper and the paper ball experience air resistance. But the surface area of the sheet is much more than that of the spherical ball. And air resistance varies directly with surface area. Hence the sheet experiences more air resistance than the ball and it falls more slowly than the paper ball.


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Yep, air resistance is proportional to surface area and the velocity squared of the object moving through the air https://en.wikipedia.org/wiki/Drag_(physics)


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The short answer is that the hypotheses assumed for the Bernoulli equation are not met for airplanes. (I can't speak for birds since I haven't studied that in detail.) In particular, The air is not incompressible and Energy is not constant - the plane's engines are adding energy to the airflow That said, it's "close enough for the engineers" - ...


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The fastest point of sail depends on the boat (both its hull shape and its sail plan), the wind strength, and the sea state. In general, a beam reach is not the fastest point of sail. For instance, in very light wind some boats will go fastest on a close reach due to the increased apparent wind from going toward the wind. For boats that sail faster than ...


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The main phenomena which limit land vehicle speed are aerodynamic drag, lack of stability, and lack of power. Drag increases (approximately) with the frontal area of the vehicle. Stability increases with the weight, length and width of the vehicle. Finally, power increases (approximately) with the volume of the vehicle. Let's say you keep the shape of the ...


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I'm late to the party here and I think the top vote-getters (Skliwiz, niboz) have adequately answered it, but I'll give my two cents anyway: There are several ways to explain how an airplane flies. Some are more detailed than others, and unfortunately most popular explanation get it wrong. Here are some explanations that are useful, depending on the ...


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Bernoulli's Principle is one very small piece of a large mathematical theory that explains lift. Unfortunately, most attempts to explain lift using Bernoulli's principle without the overall mathematical context (i.e. vector calculus, partial differential equations, boundary conditions, the Navier-Stokes equation, etc.) are either so confusing that few ...


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According to Sighard Hoerner's Fluid Dynamic Drag, this would be the half-sphere with the open side exposed to the wind. Its drag coefficient is 1.42. A rod with a hemispherical cross section will even have a drag coefficient of 2.3 (right column in the graph below). If you restrict the competition to solid objects, still the half sphere wins with a drag ...



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