How does mass and velocity affect the amount of damage?

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I’m not a science-y person, but I love sci-fi. In a novel I read near a decade ago (Larry Niven’s Known Space series), he mentions occasionally kinetic weapons. I’ve seen this online as well with tungsten-based projectiles being discussed. So my question is how does mass and velocity affect the amount of damage? If I had a nickel-sized object, how fast would it need to go to cause city-wide devastation (would it be possible or would the damage output be capped based on either size or velocity)? Conversely, If I launched something at the speed of sound, would the damage output be the same if it were different-sized objects?

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Anonymous 0 Comments

KE = MV^2

(kinetic energy is equal to the mass of the object times the square of the speed of the object)

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>The atomic bomb exploded over Hiroshima released about 1.5×10^13 joules of energy. ([https://serc.carleton.edu/quantskills/activities/botec_earthquake.html](https://serc.carleton.edu/quantskills/activities/botec_earthquake.html))

A nickel weighs about 5 grams. So doing some basic algebra I come up with V = sqrt(KE/M), and when I plug in the values I get V = 1,732,050 (m/s)

The speed of light is about 300,000,000 (m/s) and that’s as fast as anything can go. The nickel would have to be traveling at a little more than half the speed of light to take out a city.

Anonymous 0 Comments

Wolfram Alpha can be a good tool get get an intuitive feel for things, using the formulas mentioned in this thread.

A nickel weighs about 5 grams. Here’s the calculation for that mass at the speed of sound (340m/s).

[https://www.wolframalpha.com/input?i=1%2F2+*+5g+*+%28340m%2Fs%29%5E2](https://www.wolframalpha.com/input?i=1%2F2+*+5g+*+%28340m%2Fs%29%5E2)

289 J (joules) How much is that? It’s in the neighborhood of a bullet.

How about an aerodynamic telephone pole of tungsten, about 10000kg, at about Earth escape velocity (11km/sec)?

[https://www.wolframalpha.com/input?i=1%2F2+*+10000kg+*+%2811km%2Fs%29%5E2](https://www.wolframalpha.com/input?i=1%2F2+*+4000kg+*+%2811km%2Fs%29%5E2)

We’re up to gigajoules (1 billion times more than the first example). You can play around with other numbers.
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