In 1781, george washington forced the surrender of lord cornwallis at?

When General Rochambeau met General Washington in Wethersfield, Connecticut on 22 May 1781 to determine their strategy against the British, they made plans to move against New York City, which was occupied by about 10,000 men under General Sir Henry Clinton, the overall British commander. 

Meanwhile, word had come from General Lafayette in Virginia that Cornwallis had taken up a defensive position at Yorktown, Virginia, next to the York River. Cornwallis had been campaigning in the southern colonies and had cut a wide swath, but his 7,000 troops were now tired and in need of supplies. Cornwallis moved the army to Yorktown in order to link up with the British Royal Navy. 

On 14 August 1781, Washington received news that French Admiral de Grasse, stationed in the West Indies, was sailing with his fleet to the Chesapeake Bay. The New York campaign was quickly abandoned. If they moved quickly, the Americans and French might be able to trap Cornwallis's army at Yorktown. 

Washington started to march towards New York City with his force of 9,000. They stationed approximately 2,500 men at the American forts near the city under Major General William Heath to fool the British into believing that Washington's entire force was still there. 

Rear Admiral de Grasse sailed his French battle fleet of twenty-eight ships north toward Virginia. Simultaneously, on August 21, 1781, Washington began moving his army south. As they marched south, Admiral de Grasse's fleet arrived at the Chesapeake Bay, causing the normally reserved Washington to leap into the air and toss his hat. De Grasse had defeated Admiral Thomas Graves' fleet in the Battle of the Chesapeake and won control of the river. Cornwallis was now stranded. 

On September 28, 1781, Washington and Rochambeau, along with Lafayette's troops and 3,000 of de Grasse's men, arrived at Yorktown. In all, there were approximately 17,000 men converging on Cornwallis's camp. The city was soon surrounded and under heavy fire. 

On October 14, the Franco-American forces captured two major British redoubts at bayonet-point. After a futile counterattack, Cornwallis offered to surrender on October 17. On the 19th of October, the papers were signed and he officially surrendered. About 8,000 British troops became prisoners. 

The British prisoners amounted to about a fourth of all redcoats in the American colonies. It was not clear at the time that Yorktown was the climax of the war, since the British still occupied key ports such as New York City and Charleston, South Carolina. Sporadic fighting continued after the Yorktown surrender, and Washington believed the war might drag on for another year. 

However, British Prime Minister Lord North resigned after receiving news of the surrender at Yorktown. His successors decided that it was no longer in Britain's best interest to continue the war, and negotiations were undertaken. The British signed the Treaty of Paris (1783), recognizing the United States and promising to remove all her troops from the country.