Experiment M-9 CONSERVATION OF ENERGY AND MOMENTUM Purpose The purpose of this experiment is to study the laws of conservation of energy and conservation of momentum as applied to the collision of two collision cars on a linear air track. It is also desired to become familiar with the concepts of impulse and of coefficient of restitution. Theory A moving body possesses a quality which causes it to exert a force upon anything which tries to stop it. The faster an object is traveling, or the more massive it is, the more difficult it is to stop. Sir Isaac Newton called this quality of a moving body the "quantity of motion" of the body. Today, it is termed the momentum of the body and is defined by the relation: Momentum = mv (1) where v is the velocity of the mass m. Momentum is a vector quantity, having the same direction as the velocity vector. The momentum of any body is, naturally, the result of forces which accelerated the body from rest to velocity v. In order to alter the velocity of a body -- that is, to cause it to change momentum -- an unbalanced force must be applied. The larger this force is, or the longer that it is applied, the greater will be this change in momentum. In mathematical terms, this would be stated: Ft mv2 - mv 1 ( 2 ) where (mv2 - mv1) represents the change in momentum and Ft represents the product of the unbalanced force and the time for which it is applied -- a quantity which is commonly known as impulse. This quantity is also a vector quantity. In an isolated system of bodies, the total momentum is constant. This is a general law of nature, commonly known as the law of conservation of momentum. For example, in a collision of two particles along a straight line, if the momentum of one particle decreases by a certain value, the momentum of the other particle increases by an equal amount. If the two particles a and b collide and then rebound with no loss in kinetic energy, the collision is said to be perfectly elastic. On the other hand, if the particles collide and stick together, the collision is termed perfectly inelastic. If the collision is not perfectly elastic, the relative velocity of the colliding particles after the collision is smaller than before the collision. The negative ratio of the relative velocity after collision to the relative velocity before collision, known as the coefficient of restitution (e), is a measure of the elasticity of a collision. e = Vaz - Vb2 (3 ) Val - vbi J If the collision is perfectly elastic, the coefficient of restitution is unity. A perfectly inelastic collision has a value of zero. Generally, the coefficient of restitution has a value somewhere between these two extremes