FWIW this is an old sci-fi idea / plot device called a Bussard ramjet:
http://en.wikipedia.org/wiki/Bussard_ramjet
But this isn't meant to dispute your calculations. The linked article comes to the same conclusion: it's not feasible, too little interstellar hydrogen.
Naturally, a very large force field ramjet will deplete interstellar hydrogen along the main routes between stars, leading to a situation known as "peak hydrogen", and possibly prompting the invasion of developing hydrogen-rich planets on some sort of flimsy pretext.
Most scientists working on imaginary spacecraft projects therefore eschew the Bussard, correctly anticipating the moment when, shortly after the leader gives a speech on the deck of a starship in front of a huge "Hydrogen Accomplished" banner, the price of hydrogen rises to over $5 a gallon and starships are all left to rust in the front yard.
... and yet that 0.01g of stuff would produce lots of friction and heat if spaceship flies with 10%+ of light speed...
ETA: Yup, I was considering the Ramjet design. Scale of the scoop overwhelmed itself trying to acquire enough to function. I was just startled at how little interstellar hydrogen there is; I knew it wouldn't be much, but 0.01g in ten million cubic kilometers was even less than I'd assumed.