# CONSERVATION OF ENERGY Conserved quantities Mechanical energy Conservation of mechanical energy Progetto “Physics in English” Work and energy Prof.ssa.

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CONSERVATION OF ENERGY Conserved quantities Mechanical energy Conservation of mechanical energy Progetto “Physics in English” Work and energy Prof.ssa A. Martorana

CONSERVATION OF MASS When we say that something is conserved, we mean that it remains constant An example of a conserved quantity is Mass

CONSERVATION OF MASS For instance, imagine that a light bulb is dropped on the floor and shatters into many pieces.

CONSERVATION OF MASS No matter how the bulb shatters, the total mass of all the pieces together is the same as the mass of the intact light bulb because mass is conserved

MECHANICAL ENERGY Objects can have either kinetic or potential energy The description of the motion of many objects, however, often involves a combination of kinetic and potential energy as well as different kinds of potential energy! We call the sum of these energies at work on an object: mechanical energy

KINETIC ENERGY Energy associated with motion

POTENTIAL ENERGY An object has the potential to move because of its position Gravitational potential Elastic potential

MECHANICAL ENERGY A pendulum clock swinging is an example to describe the changes in Mechanical energy

MECHANICAL ENERGY The pendulum swings back and forth At the highest point, there is only GRAVITATIONAL POTENTIAL ENERGY associated with its position At other points, it is in motion – so it has KINETIC ENERGY as well! But, it also has ELASTIC POTENTIAL ENERGY because this is present in the many springs that are part of its inner workings

MECHANICAL ENERGY How do we analyze situations that include KINETIC, GRAVITATIONAL POTENTIAL AND ELASTIC POTENTIAL ENERGY? We apply the principle of mechanical energy only to objects that contain kinetic energy, Gravitational potential energy and elastic potential energy.

NONMECHANICAL ENERGY All energy that is not mechanical energy is classified as Nonmechanical energy : Nuclear Chemical Internal Electric

MECHANICAL ENERGY Mechanical energy = the sum of kinetic energy and all forms of potential energy associated with an object or group of objects

ENERGY ENERGY MECHANICAL NON-MECHANICAL KINETIC POTENTIAL GRAVITATIONAL ELASTIC

CONSERVATION OF MECHANICAL ENERGY The principle in which the total mechanical energy remains the same in the absence of friction Initial mechanical energy = final mechanical energy (in the absence of friction)

CONSERVATION OF MECHANICAL ENERGY The mathematical expression for the conservation of mechanical energy depends on the forms of potential energy in a given problem If the only force acting on an object is the force of gravity, the conservation law can be written as follows: 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 gravityfinal velocityacceleration due to gravity

CONSERVATION OF MECHANICAL ENERGY If other forces are present, simply add the appropriate potential energy terms associated with each force Energy conservation occurs even when acceleration varies We simply equate the initial mechanical energy to the final mechanical energy and ignore all the details in the middle

NONMECHANICAL ENERGY In situations in which frictional forces are present, the principle of mechanical energy conservation no longer holds because kinetic energy is not simply converted to a form of potential energy The principle becomes: As in the previous law, we just add the work done by frictional forces

NONMECHANICAL ENERGY Mechanical energy is not conserved in the presence of friction In the cases of kinetic friction, nonmechanical energy becomes relevant This does not mean that energy in general is not conserved – total energy is always conserved

NONMECHANICAL ENERGY However, the mechanical energy is converted into forms of energy that are much more difficult to account for, and the mechanical energy is considered to be lost

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