How did the federal government get involved in US industry during the war?

Most of the machines and equipment built were used for war purposes. Jeep is a good example of a government company during the war. Also many people received employment in factories (guns, boats, tanks, airplanes), Red Cross employed many nurses during the war and men were either drafted or joined the military willingly. Unemployment was the aftermath of the depression, this was reversed when the war created financial opportunity.