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So I want to calculate the impact speed of a wrecking ball. I know that I can do that using potential and kinetic energy and the height it was swung from... but that does not account for the air resistance. I found some tutorials for how to calculate speed of free falling object, but the ball is moving on a curve held by the rope...

Can anybody help me with this please? (And I'm sorry for my english)

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    $\begingroup$ In the case of a wracking ball, its weight will be much higher than its air resistance, because it has a huge mass (think feather vs. anvil). So the effect of drag I suspect would be extremely (!) small. $\endgroup$
    – zh1
    Commented Jun 11, 2018 at 21:34

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@zhutchens is correct. The drag force experienced by a wrecking ball traveling at a speed of ~tens of meters a second through air will be negligible compared to the force of gravity, and can safely be ignored in the analysis you describe. Equating the potential and kinetic energies is indeed a quick and convenient way to solve for the velocity of the ball at the bottom of its swing.

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  • $\begingroup$ How would one calculate it tho? I get that it has almost no effect on the wrecking ball, but let's say it's made of polystyrene. What would happen then? How fast would the ball be in the lowest point of the curve? (Just curious now...) $\endgroup$
    – Jakub Rádl
    Commented Jun 11, 2018 at 21:54
  • $\begingroup$ @JakubRádl, that's a much different question. Drag forces are non-linear, so require a lot more work to incorporate into a solution. $\endgroup$
    – BowlOfRed
    Commented Jun 11, 2018 at 21:58
  • $\begingroup$ Could someone at least point me to some article/video about this please? I found nothing... $\endgroup$
    – Jakub Rádl
    Commented Jun 11, 2018 at 22:04
  • $\begingroup$ search on "aerodynamic drag on sphere" $\endgroup$
    – niels nielsen
    Commented Jun 12, 2018 at 1:11
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As mentioned before by two people, if you want to for practical applications you can assume that the drag force is negligible. Should you really want to calculate the drag force then you can do so. The thing is you would calculate it the same way as a free-falling object. Why?

Well (air)-drag is not direction dependent, it depends on the speed (along the curvature of the circle described by the chain and pivot); it depends on the shape of the face of the object (luckily a sphere makes this easy as it's the same shape in every direction); the viscosity and the density of the fluid (air in this case); and the surface area of the face (for a sphere this is the cross-section, so the area of a circle).

Meaning that if you could calculate drag force if it was free-falling than you could also do so if it's on a pendulum.

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