Work and Energy Conservation of Energy Chapter 5: Section 3

Learning Targets Identify situations in which conservation of mechanical energy is valid Recognize the forms that conserved energy can take Solve problems using conservation of mechanical energy P4.3A, P4.3B, P4.3e

Kinetic and Potential Energy The motion of many objects often contain a combination of kinetic and potential energy At the highest point of a swinging pendulum there is only gravitational potential energy At other points, the pendulum is in motion, so it has kinetic energy Elastic potential energy is also present in the many springs that are part of the inner working of the clock

Σ represents the sum gravitational and elastic PE Mechanical Energy Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects Mechanical energy is the ability to do work ME = KE + ΣPE Σ represents the sum gravitational and elastic PE All energy, such as nuclear, chemical, internal, and electrical, are classified as non- mechanical energy

Internal vs. External Forces All forces in physics can be classified as either internal or external External forces include the applied force, normal force, tension force, friction force, and air resistance. Internal forces include gravity, magnetic force, electrical force, and spring force.

Conserved Quantities In the absence of external forces, mechanical energy is always conserved When something is conserved, it remains constant This does not mean that the quantity cannot change form during that time, A dollar can be 10 dimes, 100 pennies, or 4 nickels A glass can break, but all of the pieces add up to the same mass of the glass as a whole

Conservation of Mechanical Energy In the absence of friction, including air resistance, the total mechanical energy remains constant The principle is called conservation of mechanical energy ½ mvi2 + mghi = ½ mvf2 + mghf In the case that there is elastic potential energy the term ½ kx2 would be added in

As an egg falls, the potential energy is converted into kinetic energy If the egg were thrown up in the air, the kinetic energy would be converted into gravitational potential energy In situations in which frictional forces are present, mechanical energy conservation no longer holds because kinetic energy is not simply converted to potential energy

Mechanical Energy and Friction In the presence of friction, non-mechanical energy is no longer negligible and mechanical energy is no longer conserved This does not mean that energy is not conserved because the total energy is always conserved When mechanical energy is converted into non-mechanical forms of energy, this energy becomes much more difficult to account for, and the mechanical energy is considered to be lost