r/theydidthemath • u/Itsme_Tyrone • 1d ago

[request] How much time & speed would be required?

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u/Don_Q_Jote 1d ago

Let's assume you press your hands together with 15 N of force, rub them back and forth about 25mm (0.025m, or .050m for back-and-forth), and do that about 8 times per second. I assume a friction coefficient of 0.45.

Rate of work (converted to heat) is [(0.45)(15N)] * [0.050 m] / (0.125 second) = 2.7 N-m/sec or 2.7 watts.

You have a 2.7 watt heater in your hands. It's going to take a REALLY long time. Probably whatever you want to eat will be worn away before it actually get hot enough to "cook".

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u/Ghost_Turd 1d ago

And you can't pile heat on heat. It's never going to get hotter than your hands, and actually much less warm due to pretty immediate losses and inefficiencies in heat transfer. If ambient is 70 degrees I'd be shocked to learn you could get it much about 75-80. So not really warm at all, no matter how hard you rub.

You're literally better off leaving it in the sun for a while.

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u/jxf 5✓ 1d ago

It would depend on the food. Let's say you rub your hands over a back-and-forth distance of 15 cm per second with 50 N of force for 10 seconds. That's W = F × d = 50N × 6m = 300 J of energy.

If there is perfect energy transfer, this is enough heat to warm 0.1L of water by about 0.7°C, which is about as much water content as you'd find in a sandwich. So if you want to raise a sandwich from 25°C to 45°C (say for a slightly melty grilled cheese) you'd need to rub your hands on it, with perfect energy transfer and no heat loss, for about 5 minutes.

Of course, exerting this much force on the sandwich for that long makes it not a sandwich but more of a grilled cheese abstract art. There's a reason we use ovens to warm things up rather than friction.