A 4HP motor capable of continuous operation that is purpose built is a lot larger than an alternator, so getting that kind of power out of a device that size is very attractive.
It sure sounds attractive! But I suspect there's a reason that real 3 kW DC motors are a tad larger than car alternators.... as in, "I have trouble lifting one from the floor without ruining my back". As opposed to a car alternator that fits in the palm of my hand.
If something sounds too good to be true, it probably is?
Anyway, my point: 4hp (3000 W) sounds like a lot to me, especially 3 kW continuously, from something so small as a car alternator.
My 2nd point: at what RPM would the alternator reach its rated 3kW ?.... And would that RPM be practical for a lawnmower?
3rd point: what voltage do you intend to use this lawnmower at?
4th point: how thick would the power cables have to be to deliver the required current from the batteries to your motor at your desired system voltage at the rated power of 3kW?
5th point: how do you intend to power this lawnmower? Batteries, or from the grid, or? If batteries, they would surely have to be big (and probably you'd need to drive the wheels as well, as it'd be near-impossible to push with human strength through a lawn).
I could probably think of a few other things that you might want to think about when continuing with this project, but I figure for the moment the main issues have been mentioned. Am interested in your response and how you would go about tackling those issues.
Personally, I think the easy part of your project will be the modification of the alternator. The pricy part will be the motorcontroller, the batteries (if used) and the cables. I expect that for the money you could buy a brandnew 3.5 hp B&S lawnmower. That would be the practical solution *I* would choose, anyway.
But your project surely makes for an interesting challenge! And I know I would not be up to that challenge....