To add to the why question: The 1940s were a pretty terrifying time in human history. A few powerful countries were under the total control of people who believed their country was superior and had the right to overrun the world around them. Every major country was trying as hard as possible to make the most effective weapons to win the war. In 1941-42, it looked entirely possible that Germany was going to overrun the Soviet Union, murder or starve most of the people living in Eastern Europe, and be in an invulnerable position controlling Europe with an eye towards the Middle East, while Japan might control much of Asia. The idea of a bomb that could destroy a city looked like the one thing that could defeat Germany and save civilization. The U.S. and U.K. poured a lot of money and top scientists into it because it looked like a war-winner. (Fun fact: The project to develop the B-29 bomber, which dropped the first atomic bomb, was actually more expensive than the bomb project.) In the end, the Soviets fought like hell, the Western allies invaded as well, and Germany lost a conventional war, so Japan got bombed instead.