Practically this should work OK, however there may be small obscure bits that don't get overwritten - it really depends on how paranoid you are about people possibly getting a tiny snippit of information from you if they are really dedicated.
If you are worried about people grabbing your photos or personal documents it should not be a big deal - provided the entire partition is used. If you are worried that someone might know that once upon this time that drive was used in a particular machine, something like that, then no.
Realistically though, 99999/100000 it would be easier to get the information they want another way (social engineering, beating it out of you, bribery, dumpster-diving, key logging).
I would point out that 40 gig drives would be very old, and likely to start failing, so you may have bigger concerns on your hands soon. (And remember that if a drive starts failing, data can be hidden in the failing parts of the drive which can't easily be overwritten, but might be recovered with enough effort sometimes)