There are a number of elements in the system that may produce problems.
1) The alternator will not be able to change the output current quickly. Look up "load dump"
2) The drill will take a lot of current when starting, and may do strange things when powered up when already spinning
3) The drill will take current at a poor power factor, either with a lagging current or with a current that is very non-sinusoidal or both
4) The inverter will take more current if the DC voltage drops.
5) The surge current taken by the drill will be more than the rating of the inverter.
6) A non-sinusoidal current waveform may mean that the inverter is effectively overloaded during part of the cycle even when the drill is a t full speed
7) If the current waveform taken by the drill is lagging, that means that power will be put back into the inverter for a short time during each half-cycle of the supply, which the inverter may not handle well.
8) There may be much of the power amplifier circuitry which is in use even when the sound is off.
9) Many power amplifiers have inverters in them to boost the voltage. The on-off-on operation may result in a surge current, and the circuitry that reduces surge on turn on will not have had time to reset if the voltage drop is brief.
My suggestion would be get a vehicle that has more electrical power and is designed for powering large AC loads.
Ford F-150: Power dispenser with V2L function
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