If I throw two objects with the exact same shape and size, but one of them is heavier, will they arrive at the same time? We learn in basic Newtonian physics that mass doesn't influence the speed in which an object fall in vacuum. But if there is air is that still true?

My hypothesis is that the more massive an object is, the faster it will fall through air because then the mass of the air particles become proportionally irrelevant. Am I correct?

  • $\begingroup$ You should modify either your title or the last paragraph, so that a yes or no answer would apply to both. $\endgroup$ – D. Halsey Dec 27 '18 at 0:33
  • $\begingroup$ Search term: "terminal velocity" $\endgroup$ – rob Dec 27 '18 at 0:37
  • $\begingroup$ You have several questions in here which can be addressed. It would be a better question if you would one, or at the most two directly related. What is most important to you? $\endgroup$ – Bill N Dec 27 '18 at 0:39

If the two bodies are exactly the same size and shape, the heavier of the two will reach the ground first. Here is why.

Descending through a gravitational field at a certain velocity releases power in the amount (mass x gravitational acceleration) x velocity in both falling bodies. Since their mass is different, more power is developed by the heavier object, at the same velocity through the air.

That velocity creates air friction on the bodies, which then applies a force to each in the amount (drag coefficient x cross-sectional area x velocity ^2) which opposes their motion through the air. Since their shapes are the same, so will be their drag coefficients, and since they are the same size, their cross-sectional areas will be the same too. This means that the atmospheric drag force on each will be the same, at the same velocity.

The power being released by falling is available to perform work by pushing the bodies through the air. Since the power generation rate of the heavier object is bigger than that of the lighter object, it can perform work against the atmosphere faster, and so it will fall faster- and reach the surface of the earth sooner.

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    $\begingroup$ Interesting. I've never thought of power being a quantity which fundamentally acts by releaseing energy. I've always thought of energy being primary, and power describes the time slope of energy. You're saying, it seems to me, that power is generated so work can be done. Not voting either way. $\endgroup$ – Bill N Dec 27 '18 at 1:52
  • $\begingroup$ power is an effort variable times a flow variable; in this case the effort is a force and the flow is a velocity. By this reasoning, knowing the weight (a force) and sink rate (a velocity) of an airplane in a glide you can solve for the horsepower expended to maintain that glide. I put a sink rate meter from an airplane into my Pontiac Vibe and did the same calculation coasting down a constant 6% slope on the interstate between California and Oregon: 18 HP to maintain 60 MPH. $\endgroup$ – niels nielsen Dec 27 '18 at 2:39

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