3.3

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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

Power

Different amounts of power used to do the same amount of work

In everyday conversation the words energy and power are often used interchangeably but the true meanings are different. Energy is the ability to do physical work and is measured in joules. However, the same amount of work can be done slowly or quickly. For example, lifting a 1 kilogram ball one meter takes a minimum of 9.8 joules of work. But, suppose you do it very slowly, taking a whole minute. How is that different from doing it quickly, say in one second? Clearly there is a difference. The total work done, however, is the same in both cases.

The difference is the rate at which the work is done. The rate at which work is done, or the rate at which energy is transferred, is called power. Power is an indication of the level of “effort” required to perform a given amount of work. If you want to move a boulder a few meters, then one person can do it in a few minutes using only a modest amount of power. If you want to move the boulder the same distance but more quickly (in a few seconds!), then you will need much more power—that can only be delivered by a team of horses or a front loader machine.

P = \frac{E}{t}

P	=	power (watts, W)
E	=	energy or work (J)
t	=	time (s)

Whereas work and energy are measured in joules, power is measured in joules per second. A power of one joule per second (J/s) is one watt (W). The watt is named in honor of James Watt, a Scottish engineer who developed the first practical steam engine and thereby provided the power for the industrial revolution. Doing 9.8 joules of work in 60 seconds requires 0.16 watts—approximately the power output of a small mouse. Doing the same 9.8 joules of work in 1 second requires 9.8 watts of power, which is 60 times greater.

If an engine can produce 670 J of energy in 1 minute, how many watts can it output?

11 W
670 W
40,200 W
Not enough information

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Solved Problem 3.8: Energy used by a light bulb

How much energy does an incandescent light bulb rated at 100 watts use in one hour?

Energy E used by the light bulb

Power of the light bulb P = 100 W; time that bulb is burning t = 1 hr

Power:

P = \frac{E}{t}

Time is usually expressed in seconds, but we are given the time in hours. So the first step is to convert the time to seconds:

t = (1 hr) (\frac{60 min}{1 hr}) (\frac{60 s}{1 min}) = 3, 600 s

We are asked for the energy, not the power, so we must use algebra to rearrange the power equation to solve for energy. Multiply both sides by time t and cancel terms:

\begin{matrix} P \times t = \frac{E}{t} \times t & \to & P \times t = \frac{E}{t} \times t & \to & E = P t \end{matrix}

Now insert the values to calculate the answer:

E = P t = (100 W)(3,600 s) = 360, 000 J

Energy used in one hour by the light bulb is 360,000 J.