A ship travelling at say 10% of c has a significant chance of hitting matter in space. What would the chance be of a collision, and how large would the force be?

If there are no efforts taken to avoid it, the ship is certain to hit matter. It would look something like this, but much much worse.

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btw at what fraction of c would hydrogen atoms start to have an ionising effect on the crew of such a ship?

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the solar system

The energy produced in the collision would depend on the mass of the particle hitting the ship.

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Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

Formula for kinetic energy:

KE = 1/2mv^2, where

KE = kinetic energy (joules)
m = mass (kg)
v = velocity (m/s)

Assume 1 gram object hitting ship

KE = 450 giga Joules [edited prev. math error]

TNT is 2.7E6 Joules/kg

TNT equivalent = 183 tons

The bombload from five B-52s just landed on your windshield! Better call dent wizard fast!!

Our page on shielding;
http://www.orionsarm.com/ships/shielding.html
impacts with dust grains are like bombs going off; impact with interstellar hydtrogen however, is like a constant drizzle of radiation.

and a images of few early interstellar colony ships with large ice shields (later replaced by more active shielding as speeds and technology improved)
http://www.orionsarm.com/ships/Dyaush_Colony_Ship.jpg
http://www.orionsarm.com/worlds/Dante_and_Lumiere.jpg
http://tinypic.com/y0as5

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This assumes that the relativistic effects are negligible. At .1c, is this a reasonable assumption?

Depends on what you mean as "negligible". If you are talking about setting your atomic clock, then no.

For ballpark figures at 0.1c the relativstic correction isn't relevant . You'll still get the same answer to two sig figs in this case.