This is a Sidewinder air-to-air missile, also designated AIM-9E. The blue stripe indicates it was a training model. The Sidewinder has been one of the most successful short-range, air-to-air missiles and was the first heat-seeking guided missile to become operational.
Many models have been produced since the mid-1950s. A variety of aircraft have carried Sidewinders, and variants have been adopted by about 40 countries. They have been used extensively in combat, including the Vietnam and Persian Gulf wars. This object was donated to the Smithsonian in 2003 by the U.S. Air Force Museum.
This object is on display in Mary Baker Engen Restoration Hangar at the Steven F. Udvar-Hazy Center in Chantilly, VA.