Conservation of Mechanical Energy Chapter 6

Conservation of Mechanical Energy Chapter 6

Energy As you know, energy comes in many forms. Kinetic Energy Potential Energy Gravitational Potential Energy (gravity) Elastic Potential Energy (springs, rubber bands) Chemical Energy (chemical bonds) Rest Mass Energy Nuclear (E mc2) Electric Potential Energy (ΔU kq1q2/r) Thermal Energy (heat KE of molecules) Sound (waves) Light (waves/photons) What does it mean to conserve energy?

Conservation of Energy The Law of Conservation of Energy simply states that: 1. 2. 3. The energy of a system is . Energy cannot be nor . Energy can only change (e.g. electrical to kinetic to potential, etc). True for any system with no external forces. ET KE Kinetic Energy PE Potential Energy [kinetic energy due to the motion of molecules (translational, rotational, vibrational)]

Conservation of Energy Energy

Conserved Quantities Other conserved quantities that you may or may not already be familiar with? Conservation of Conservation of . Conservation of . .

ET KE PE Constant The relationship implies that the total mechanical energy of a system is . If the Potential Energy is at a , then the system will have Kinetic Energy. If the Kinetic Energy is at a , then the system will have Potential Energy.

Conservation of Mechanical Energy ET KE PE

Conservation of Mechanical Energy – The Roller Coaster www.howstuffworks.com

Conservation of Mechanical Energy – Skier Critical points to consider PE max Heat (Q) KE max Total Mechanical Energy PE KE

Example 1: A student with a mass of 55 kg goes down a frictionless slide that is 3 meters high. 1. 2. What is the student’s kinetic energy at the bottom of the slide. What is the student’s speed at the bottom of the slide? KEinitial PEinitial KEfinal PEfinal KEinitial PEinitial KEfinal PEfinal

Example 1 (cont.) 1. 2. KEfinal

Example 2: El Toro goes through a vertical drop of 50 meters. Using the conservation of energy, determine the speed at the bottom of the drop. Assume that the initial speed of the coaster is 0 m/s.

The conservation of energy says that the kinetic energy at the bottom of the drop will the gravitational potential energy at the top.

Example 3: A student with a mass of 55 kg goes down a non-frictionless slide that is 3 meters high. Compared to a frictionless slide the student’s speed will be: a. b. c. the same. less than. more than. Why? Because energy is to the in the form of due to .

Example 3 (cont.) Does this example reflect conservation of mechanical energy? , because of . Is the law of conservation of energy violated? : as previously stated, some of the “mechanical” energy is to the environment in the form of .

Conservation of Mechanical Energy Mechanical Energy: If Internal Energy(Q) is ignored: ET KE GPE PEs could be a combination of and energy, or any other form of energy.