If you attach a step-up circuit (like a boost converter) to a battery, and then run a brushed DC motor off of that higher voltage, will that motor have a higher mechanical power output than if you just hooked up the motor to the battery (without the circuit)?
In this post about how voltage and current relate to the torque and speed of a motor, the top answer states that:
For the same motor, ideally if you apply double the voltage you'll double the no-load speed, double the torque, and quadruple the power. This is assuming of course the DC motor doesn't burn up, reach a state which violates this simplistic ideal motor model, etc.
If this method would not work, is there any way to force a motor to pull more current from the battery, increasing power draw (and the energy in the battery would just run out faster) but increasing the mechanical power output of that motor?
I have heard of electric cars using boost converters to power higher voltage motors with lower voltage battery packs. If the answer to the above question is no, then why do these car manufacturers not just use motors that are the same voltage as their battery packs?
Finally, would stepping up the voltage of a battery to run a motor that would be rated for a higher voltage achieve more mechanical power? This was touched on in the post I linked to but not fully explained. Could this same increase in power be achieved with a different motor at the same lower voltage rating (the referenced user mentions stall current as another factor that affects motor electrical power draw and mechanical output)? In short, would stepping up voltage from a battery to run a higher voltage motor ever be useful to increase mechanical power output (ignoring efficiency or battery life)?