Perhaps it is obvious, but I think it was probably negligent of me to assume that the reason for studying mechanics needed no explanation. If an aircraft flies through a hailstorm, then in advance the passengers and crew would like to know that it will survive the event, and after the event the owners and operators would to know whether it can continue to be flown safely. Mechanics is the core discipline or field that underpins such knowledge. It is concerned with the way materials and, or structures (e.g. the aircraft skin) behave when acted upon by a load (impact by hail stones).
Since everything involved in this examples is solid, this type of analysis is usually called solid mechanics. Whereas predicting the lift and drag on the aircraft wings as they are pushed through the air by the engines is classified as fluid mechanics.
Everyday examples of both solid mechanics and fluid mechanics have been collected together to assist in introducing engineering students to these fields and can be found at http://www.EngineeringExamples.org and http://www.EngageEngineering.org
Experimental mechanics is about measuring the behaviour of materials and structures when they are subjected to a load. The picture shows the photoelastic fringe pattern in a plastic model of a crane hook, from which a load has been suspended. The fringes are contours of stress (force per unit area) and where the fringes or contours congregate are sites of likely failure. Using polarised light, photoelastic fringes can be seen in any stressed transparent object, for example make a sandwich of two pairs of polarised sunglasses and a transparent freezer bag then stretch the freezer bag while holding the sandwich to the light. Yes, ok you will need two pairs of hands.
Photoelasticity has fallen out of fashion in experimental mechanics because, except for objects made from glass or transparent plastic, it cannot be used directly on engineering components. However, this photograph is an old favourite that has been used to illustrate several mechanics books and inspired an art installation in the Engineering Library at the University of Sheffield. It was taken in the 1980s by John A Driver, a technician in the Department of Mechanical Engineering at the University of Sheffield.
For more a little more on photoelasticity see http://www.experimentalstress.com/basic_experimental_mechanics/photoelasticity.htm