I think it was more to show Russia our raw power (especially the second one). The Russian invasion of Manchuria was much more a source of concern for the emperor than us dropping bombs on civilians en masse, which wasn't a genuine problem for him, per se. Japan was counting on Stalin to negotiate a treaty between the US and Japan where Japan got to retain some of its war-time expanded territories. So, when Stalin gave them the finger and invaded, it was much more of a gut-check moment than the US's taking out civilians. It's also a curious historical note that the surrender terms accepted were the same ones the Japanese agreed to prior to the dropping of the bombs. The emperor wanted to retain his title but we said no. Then, we nuked them twice and agreed to let him keep his title...

This seems to run counter to the standard line that "the nukes prevented a ground war in Japan and saved countless American lives". Japan was already willing to surrender to the terms we eventually gave them and the Russians were already busily claiming territory and would have done our dirty work for us. I think what was unacceptable was not prospective US casualties, but rather Soviet control over all of Asia and Japan.

I think the more interesting question is whether or not flexing our muscle for the Russians might have, in the longer view, saved more lives around the world than it cost. Without witness to the destructive power, who knows if the Soviets and US might have started lobbing nukes at one another, in earnest or by proxy.

Edit: I also think the argument could be made that the dropping of those bombs unambiguously started the run of "US: The Global Superpower"

__________________
"Government big enough to supply everything you need is big enough to take everything you have... The course of history shows that as a government grows, liberty decreases."

-Thomas Jefferson