A potential reason that Truman might have decided to drop the bomb on Japan: Shock and awe. When you win a fight in a small way, the people you beat might be tempted to plot to take over when you're not paying attention anymore. A good example is how WW1 led to WW2. Germans were upset about a lot of the consequences of WW1, but the sanctions and punishments directed at them were not powerful enough to completely destroy them, so they ended up being involved in the start of WW2. 

By dropping the bomb, Truman essentially permanently broke the spirit of the Japanese in a fatal manner.
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