I love Peaker's answer. To elaborate with a sort of concrete example of how haskell can help you avoid logic bugs as in your physics simulation example:

In code where the types start to to tell you less, e.g. when doing a bunch of number crunching, and you have a signature that looks like:

    func :: Int -> Int -> Int -> Int

It's common for the programmer to use a "newtype wrapper" to bring some of the logic into the type system like:

    newtype Velocity = Velocity Int
    newtype Force = Force Int
    newtype Iteration = Iteration Int

Then the type system will catch if you accidentally use the Velocity when what you want is Force, etc.