Japan was unwilling to surrender for a long time even though Japanese cities got bombed on a near daily basis near the end of the war. The US gambled on, for a lack of a better word, the wow-factor of the atomic bomb. They guessed correctly that Japan’s leaders would assume that there’s no way in hell the US could produce another one of these “special” bombs. They dropped the second one to basically say: “Hey, we got a huge stockpile of these things so we can do this as long as you like”. Or to put it simply: It was a show of force. When Nagasaki got hit Japanese leaders were in a council meeting about the Hiroshima bombing and the Soviet’s declaration of war on Japan and even after the news arrived in Tokyo half the cabinet was still insistent on their own terms of surrender. They didn’t know how many more bombs America had and that fear played a huge part in Hirohito’s decision to end the war after more than 14 hours of debate that day.

The first one to prove that it exists, the second to prove that America had the resources, manufacturing, and still had the balls to do it again even after seeing what it did. America dropped one to get the world's attention and respect, and again to establish horrifying dominance. "I can do this all day" energy.

Unconditional surrender was not assured the first time. It was the second time. The Japanese do not give up easily.

The conventional ordinance dropped on Tokyo killed many more people than Little Boy killed in Hiroshima. The Japanese barely surrendered after the nuclear attacks. I would suggest listening to Dan Carlin's Hardcore History miniseries Countdown to Armageddon if you want to know more.