Could the Articles of Confederation have worked? Why or why not?
The Articles of Confederation could not succeed and were bound to fail because they did not give Congress and the national government enough power. The new United States just fought a war to end what they considered tyrannical rule of a strong government that overpowered local government and the leaders of the U.S. feared a powerful central government. Because of this, they did not give the central government the power it needed to rule effectively. It did not give Congress the power to tax, so the government ended up printing money which caused inflation. It did not give Congress the power to draft troops, so the U.S. military was small leaving the U.S. weak. Congress did not have the power to control interstate commerce or stop states from printing their own money, causing economic chaos within the U.S. The Articles did not give Congress the power to place tariffs on foreign goods, hurting American businesses that could not compete with cheaper British goods. The U.S. government had no chief executive so there was no one to enforce the laws that were passed. The list can go on. With the rebellion led by Daniel Shays in Massachusetts, the leaders of the U.S. realized the Articles were not working which led to the Constitutional Convention where the Articles were abandoned and the new U.S. Constitution was written.
Only under the new Constitution could the country succeed. The Constitution addressed many of the problems created by the Articles by creating a federal system of government with a much more powerful national government. It gave the national government the power to tax, draft troops, control interstate commerce, etc. It also created an executive branch and a federal court system, both of which were lacking under the Articles of Confederation. The greatest argument against the new Constitution was that it gave the national government too much power. This argument was addressed by the framers by creating a system of checks and balances, creating a system with three branches, each with its own separate powers (separation of powers), and creating a federal system where powers were divided between the federal government and state governments, with some powers delegated to the federal government, some reserved to the states and some shared by both.
This depends on what you mean by "work." The Articles could have allowed for a country to exist, but it would likely have been a very economically weak country and it would also have been very vulnerable to being conquered militarily.
The Articles could have kept the country together. After all, they did "work" for about 10 years. However, the US would not have become rich or powerful under them. It would not have become rich because there would have been little trade between the states and each state would have had an isolated and fairly small economy. It would not have become powerful because the states would have been unlikely to give enough money for a strong military.
So, the US could have stayed together, but it would have been a much poorer country and might have been conquered by some foreign power.