Logic for you:
We dropped the first bomb, and asked again for a surrender. The response was, essentially, "Eh, we'll think about it." They didn't respond again for three days. Does that sound like a people who were willing to admit defeat? Does that sound like it would have been possible to invade through conventional means without loss of live far exceeding what the bombs brought? This was a people too proud to admit defeat when it was obvious to them and the rest of the world. They had three days after the first bomb to surrender. They didn't.
So we dropped another. That was enough.
The answer:
We dropped the first one to try to end the war. We dropped the second one because the first one didn't impress the Japanese enough.