In 1783, the young United States had won independence from Great Britain, but it still found itself faced with a weak government, social problems, and difficulties in foreign affairs. Identify at least one problem from each category and explain how the Constitution and its provisions helped solve the problem.

In 1783 the United States of America had many political and social problems, including a weak central government, fraying social fabric, and no coherent foreign policy. The ratification of the Constitution in 1789 eventually solved these and other dysfunctions by centralizing power.
The Articles of Confederation were a series of treaties between the newly independent states that attempted to replace some of the governmental functions which were lost when they ceased to be British colonies. The internal state governments continued much as before, but there was no central government. That's why the Articles of Confederation were drawn up. The powers given to the government under the Articles were very weak. The federal government couldn't raise taxes without the consent of the states. It wasn't permitted a strong army, and it couldn't make agreements with foreign countries without the agreement of the states.
Social capital in the new United States, the relationships and norms of behavior that hold a society together, was severely damaged at the end of the War of Independence. At least half the population hadn't supported the war, the Continental Army was being stripped of soldiers and hadn't been paid, and the economic dislocation caused by the war had created hardship and distrust among the parts of the colonies most affected by the fighting.
During the war, the Continental Congress sent diplomatic and trade representatives to Europe to get and keep support for the rebellious colonies and to help create relationships which would help integrate the new country into the family of nations and the global trading system. But that's not the same as having a foreign policy. European governments were wary of making commitments to people who they thought would lose their war, who had no recognized currency and limited gold, and who were preaching ideas they themselves considered dangerous.
The ratification of the Constitution solved these three problems by centralizing power in the new federal government. The Constitution itself is basically a delineation of that government's power. A significant increase in power for the federal government over that of the Articles of Confederation was the power to compel taxation. This meant the new government could generate its own revenue, instead of relying on loans or disbursements of gold from the states.
The Constitution didn't create social capital by itself, but it did create receptacles for it. It created the idea of the United States. It created a flag and a seal and other symbols which all the states of the Union were bound to recognize. It's hard to overstate how important this was in repairing the fabric of American society. It gave people a way to relate to each other which was independent, literally, of their history. Rebels and Tories were forced to live together under a new set of laws, and this meant that, if they chose, they could put aside their former animosity and forge new relationships.
Perhaps the quickest improvement in the government of the United States after the Constitution was ratified was the centralization of authority for foreign policy in one place. According to Article II, the President has the sole authority to make foreign policy. Congress, of course, tries to affect policy and take some power for itself, but even in that tug-of-war, making foreign policy is still contained within the federal government instead of the states. This, combined with the other powers given to the federal government in the Constitution, made it much easier for the United States to make or break agreements with other nations. The fact we won the War of Independence forced other countries to deal with the federal government as the sole legitimate American authority in international affairs.