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Or would the piano dent the titanium and kill you?

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    $\begingroup$ Suppose the titanium suit is 15 cm thick and the piano falls 1 mm, then clearly you'd be fine. Suppose instead the suit's 1 atom thick and the piano falls 10 m, then clearly you'd be dead. So this is a very poorly constrained problem. $\endgroup$ – Kyle Kanos Sep 26 '15 at 21:20
  • $\begingroup$ Depends on whether you're holding an umbrella. $\endgroup$ – Reinstate Monica -- notmaynard Jan 9 '17 at 21:03
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You would have a few issues to contend with here. Most importantly, Newton's laws of motion tell us that "for every action, there is an equal but opposite reaction." So, when you push against a door, for example, you feel the door give you a push back. Likewise, when the piano hits your titanium suit the suit is going to react to that incredible force. It could dent - especially if the piano falls from a large height. The mass of a piano is 280 kg, or about 620 pounds according to a quick google search. According to another site, a strong titanium tube can withstand about 4000 lbs of force, or 17700 Newtons. So if the piano were simply sitting on such pipes, it would be OK.

However, gravity accelerates the piano at about 10 m/s^2. Some quick calculations show that if the piano fell for 4 seconds, but was stopped by your suit very quickly in 0.1 s...

v = a*t = 10*4 = 40 m/s

a stopping = delta v / delta t = 40 / 0.1 = 400 m/s^2

Force for stopping = 280 * 400 = 112,000 N, easily enough to dent the titanium.

You might also get knocked over, jostling you around quite violently inside the suit, where you head might smash into the helmet, etc. So, long story short, if the piano fell from any significant height such a suit probably wouldn't save you.

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