Conservation of Energy

Conservation of Energy

Conservation of energy,principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant.When objects interact

energy can change form (energy transduction)

energy can be transferred (energy transfer)

Conservation of Energy

A decrease in one form of energy will result in an increase in another form of energy of equal magnitude.

E1=E2

So, we can prove what we stated earlier that the energy is transformed, not destroyed.

Conservation of Energy FormulaThe Basic formula of conservation of energy is simple:

Energy spent in one act = Energy gained in the related act

An object when dropped from a height transforms its potential energy into kinetic energy.

Mathematically it can be expressed as a Conservation of Energy Equation as follows:

mgh = 1/2 mv2

where, m is the mass of the object, v is its final velocity after falling from a height of h and g is the acceleration due to gravity.Sample ProblemA skier glides down a frictionless hill of 100 meters, the ascends another hill, of height 90 meters, as shown in the figure below. What is the speed of the skier when it reaches the top of the second hill?

SolutionThe skier is in a conservative system, as the only force acting upon him is gravity. Instead of calculating the work done over the curved hills, we can construct an alternate path, because of the principle of path independence:

We construct a path of two segments: one is horizontal, going between the two hills, and one is vertical, accounting for the vertical drop between the two hills. What is the work done over each of these two segments? Since the gravitational force is perpendicular to the displacement in the horizontal segment, no work is done. For the second segment, the gravitational force is constant and parallel to the displacement. Thus the work done is: W = Fx = mgh = 10mg . By the Work-Energy Theorem, this net work causes an increase in velocity. If the skier started with no initial velocity, then we can relate the final velocity to the work done: mv f 2 = 10mg We can cancel the mass and solve for v f : v f =Vf = (20) (9.8m/s)Thus the final velocity of the skier is 14 m/s.

What is conservation of momentum?In any collision, the total momentum before the collision is equal to the total momentum after collision, provided that there is no external force acting.