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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

Efficiency

Beach ball dropped off the roof of a building. How fast will it fall?

Imagine dropping a beach ball from the top of a building. At first, its measured speed would agree very well with the theoretical formula

v = \sqrt{2 g h}

we derived from energy conservation, but at some point it cannot fall any faster. It's not that energy conservation is wrong; it's that we neglected to account for air friction slowing down the beach ball's descent. The real speed of the beach ball is slower than the theoretical speed because of friction.

Friction slows down a falling ball

The efficiency of a process describes how well the process transforms input energy into output energy. If you drop a wood ball, the input energy is the ball's potential energy, while the output energy is its kinetic energy. At speeds up to 10 m/s, the process of falling is close to 100% efficient—all of the potential energy lost by dropping in height is converted into kinetic energy. At speeds above 10 m/s, the efficiency gradually diminishes as more and more of the potential energy is spent overcoming air friction, and less is left to become kinetic energy. At the terminal velocity of 33 m/s, the efficiency becomes zero, because all of the potential energy is lost overcoming friction, rather than converting into kinetic energy.

η = \frac{E_{o u t}}{E_{i n}}

η	=	efficiency
E_out	=	output energy of a system (J)
E_in	=	input emergy of a system (J)

Efficiency is the ratio of the output energy of a system to its input energy. Since work and energy are directly related to each other, the definition of efficiency can also be expressed as the ratio of the work performed by a system to the work input to the system. In the solved problem, we calculated that the swimmer's work was 60% efficient in moving across the pool, while spending 40% of his work in overcoming viscous friction.

Efficiency is a very important parameter in technology. The best solar cells commercially available convert only 15% of the power in sunlight into electrical power. Typical rechargeable batteries are 20% efficient, which means that you get only 20 joules of output energy for every 100 joules of input energy you spend charging the battery. A solar power system that can provide electricity overnight requires both solar cells and batteries. Together, the system efficiency is 15% × 20% or only 3%! That means as much as 97% of the original solar energy ends up as waste heat. Many scientists and engineers are working to improve the efficiency of both solar cells and batteries.

If Max does 500 J of work spinning a 10% efficient generator, how much electrical energy will he produce? Show

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