The second bomb (imo) was dropped to inform Russia who the biggest dog on the block really was. (I do not think this was Truman's decision all on his own.) He had advisors who had been working with the Manhattan Project. Recall that the US had no mmore bombs left at that time--after Nagasaki that is. Russia was really close to 'the secret'. So, you keep one or gamble for the time to make more.