3.2

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Videos: Conservation of energy Elastic potential energy Elastic potential energy in your bicep and tricep muscles Energy and work Gravitational potential energy Kinetic energy Physics of wind power Solar flare is a plasma in motion Steam rising out of cooling tower at a nuclear power plant

Investigations: 3A: Work and the force vs. distance graph (p. 113) 3B: Inclined plane and the conservation of energy (p. 118) 3C: Work and energy for launching a paper airplane (p. 122) 3D: Springs and the conservation of energy (p. 124) 3E: Conservation of momentum (p. 128) 3F: Collisions (p. 132) 3G: Shock absorbers and dampers (p. 139) 3H: Specific heat of water and steel (p. 144)

Science: Algebra derivation using the conservation of energy Brownian motion Choosing origin for potential energy reference frame Difference between heat and temperature Einstein's theory of relativity Elastic potential energy Elastic potential energy in your muscles Elastic potential energy in your muscles Energy and power for light bulb Energy and work Energy content of phases of matter Energy flow in open and closed systems Faster than light travel? Forms of energy Friction Galileo and the Leaning Tower of Pisa Gravitational potential energy Hooke's Law for springs Intensity of sunlight at Earth's surface Kelvin temperature scale and absolute zero Kinetic energy Law of conservation of energy Loose springs and stiff springs (BLM) Ordered and random kinetic energy Other conservation laws in physics Plasma in motion during a solar flare Plasma is a phase of matter Potential energy Power and radiant energy Power is the rate of doing work Radiant energy Relationship between momentum conservation and Newton's third law Symmetry in the physics of collisions Units of work and energy van der Waals forces

Technology: Batteries and electrical power Calories on food labels Conserving energy in everyday life Converting units and understanding energy content from food Efficiency in technology Energy content of everyday goods Energy flow in clothing manufacture Energy transformations in an internal combustion (piston) engine Energy transformations in technology usually produce heat Everyday objects that store energy Everyday technology in our age of energy Friction from brake pads in a car's wheel Hydroelectric dam Objects with elastic potential energy Power in everyday technology Power, wattage, and the light bulb Radiant power and the light bulb Technology and agriculture over the last century

Engineering: Calculating energy production for the Hoover Dam Design a wind turbine power plant Efficiency Electric current Electromagnetic spectrum Open and closed systems Siting constraint for power plants Specific heat Springs Volts, amps, and power

Mathematics: Algebra derivation using the conservation of energy Calculating energy production for the Hoover Dam Changes in a quantity represented by Greek symbol Δ Choosing origin for potential energy reference frame Converting units and understanding energy content from food Deducing a physical equation Different rates of change Hooke's Law for springs Non-linear relationships Proportional relationships Using algebra to derive temperature conversion formula Using algebra to solve for a variable

Interactive Simulations Interactive simulation of motion down an inclined plane Motion down an inclined plane Interactive simulation of an oscillating spring Spring-loaded carts simulation Elastic collisions between two balls Inelastic collisions between two balls Interactive simulation of an oscillating spring Interactive simulation of an oscillating spring Wind power design simulation Interactive Calculators Work equation calculator Kinetic energy equation Potential energy equation Elastic potential energy equation Efficiency equation Conservation of momentum in collisions equation Power equation calculator
Electric power equation Temperature conversion equation Specific heat equation

1 - Science of Physics
2 - Forces and Motion 3 - Energy Transformations Chapter 3 at a glance 3.1 - Energy 3.2 - Conservation of energy 3.3 - Flow of energy 3.4 - Temperature and the kinetic theory of matter 3.5 - Chapter review4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy

3.2 - Conservation of energy

Energy is all around us in many different forms. But the amount of energy in any one given form might change over time. The electrical energy passing through the filament of an incandescent light bulb is converted to light and thermal energy that radiate away from the bulb. An important principle of physics is that the total amount of energy in a system does not change, even if the energy changes from one form to another. This section addresses how changes in one form of energy go hand-in-hand with changes in other forms of energy.
Systems and interactions
The system	The goal of physics is to deduce the rules for how the universe works. Thinking about the whole complex universe at once, however, is both impossible and also unnecessary. A group of interacting objects and influences is called a system. We choose a system to include only the objects and influences—such as forces—that are important to what we are investigating. If we want to understand the speed of a falling ball, we might include the height of the ball, its mass, speed, and the force of gravity. The color of the sky or exact materials inside the ball are information we exclude from the system because these details do not matter to the motion we are studying.
Open and closed systems	Think about a system as an imaginary shell, or boundary, that completely encloses the behavior you want to understand. If we allow matter or energy to cross the boundary then we say the system is open. A cup of hot coffee on a table is an open system. In a few hours the thermal energy leaks out into the room and in a few days the water evaporates away leaving only the coffee residue in the bottom of the cup. Both matter and energy have left the system. If no matter or energy or force can cross the boundary then we say the system is closed. Closed systems are useful to think about because in a closed system the total energy remains constant. The total energy at one time will be the same as the total energy at a later time. In an open system, however, the energy can change because the surroundings can add or remove energy from it.

Approximating a closed system	While there is no such thing as a truly closed system, it is often a very good approximation to assume a closed system as a starting point for investigating how something works. In many experimental situations, such as a car rolling down a ramp, the leakage of energy into forms not counted—such as thermal energy (or heat)—is small compared to the matter and energy that are included in the system. In these cases it may be a very good approximation to treat the system as if it were perfectly closed. The analysis is much easier and we get the “big picture” of what happens. Even if the energy leakage is substantial, the closed-system approximation provides a necessary reference for identifying important missing details such as friction. Scientists almost always start with a simplified model then add details based on comparing the predictions of the model with the actual reality of experiments or observations.
Test your knowledge	Is the Earth a closed system?
	No. Lots of energy enters the Earth from the Sun and some mass can enter when asteroids hit the Earth.