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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

Section 1 review

Energy can take many different forms: mechanical; radiant; nuclear; electrical; chemical; thermal; and pressure. Mechanical energy can take several forms, including kinetic energy and potential energy (both gravitational and elastic). Work and energy are closely related, because doing work on an object changes its energy. Potential energy is usually calculated in terms of a reference frame, in which a position of zero energy must be defined. Energy and work are both measured in joules (J).

work, joule (J), kinetic energy, potential energy, gravitational potential energy, elastic potential energy, spring constant, reference frame

W = F d

E_{k} = \frac{1}{2} m v^{2}

E_{p} = m g h

E_{p} = \frac{1}{2} k x^{2}

Review problems and questions

What forms of energy are found in:
1. the Sun?
2. a car's engine?

A 30 kg boy sitting on a 10 kg go-cart wants to travel down a 10 m tall hill starting from rest.
1. What is the initial potential energy of the boy and cart together?
2. What is their initial kinetic energy?

Asked: Initial potential energy E_p,i of boy and cart
Given: Boy and cart have mass m = 40 kg, hill has height h = 10 m, acceleration due to gravity g = 9.8 m/s²
Relationships: E_p = mgh
Solve: $\begin{array}{l} E_{p} & = & m g h \\ = & (40 kg) \times (9.8 m / s^{2}) \times (10 m) = 3, 920 J \end{array}$ Answer: Their initial potential energy is 3,920 J
Their initial velocity is 0, so their initial kinetic energy is also 0.

A 1,000 kg car traveling 15 m/s brakes and comes to a stop after traveling 20 m.
1. What is the car's initial kinetic energy?
2. What is the car's final kinetic energy?
3. How much work did the brakes do to stop the car?
4. How much constant force did the brakes apply in order to bring the car to a stop?

Asked: Initial kinetic energy E_k,i of car
Given: Car has mass m = 1,000 kg, car has initial velocity v_i = 15 m/s
Relationships: E_k = ½mv²
Solve: $\begin{array}{l} E_{k} & = & \frac{1}{2} m v^{2} \\ = & \frac{1}{2} (1, 000 kg) \times {(15 m / s)}^{2} = 112, 500 J \end{array}$ Answer: The car's initial kinetic energy is 112,500 J
At the end, the car is not moving, so its kinetic energy is zero.
The brakes did enough work to reduce the car's kinetic energy to zero. Therefore, they did 112,500 J.
Asked: Force F applied by brakes
Given: Work W = 112,500 J, work done over distance d = 20 m
Relationships: W = Fd
Solve: $W = F d$ Rearrange equation to solve for F: $\begin{array}{l} F & = & \frac{W}{d} \\ = & \frac{112, 500 J}{20 m} = 5, 625 N \end{array}$ Answer: The brakes applied 5,625 N of force.

A baseball outfielder catches a fly ball traveling 25 m/s with his gloved hand. When he catches the 0.14 kg baseball, the outfielder's hand recoils by 10 cm. How much force did the outfielder's hand exert in catching the ball?

Asked: Force F done by hand on ball
Given: Ball has mass m = 0.14 kg, ball has velocity v = 25 m/s, player's hand moves distance d = 10 cm = 0.1 m
Relationships: E_k = ½mv², W = Fd
Solve:

\begin{array}{l} E_{k} = \frac{1}{2} m v^{2} = \frac{1}{2} (0.14 kg) \times {(25 m / s)}^{2} = 43.75 J \\ W = F d \end{array}

Rearrange equation to solve for F:

\begin{array}{l} F & = & \frac{W}{d} \\ = & \frac{43.75 J}{0.1 m} = 437.5 N \end{array}

Answer: The outfielder exerts 437.5 N of force on the ball

A horizontal spring with k = 100 N/m is compressed by 10 cm by a 100 g mass.
1. How much elastic potential energy does the compressed spring store?
2. How much elastic potential energy would the compressed spring store if it were compressed the same distance by a 300 g mass?

Asked: Elastic potential energy E_p stored in spring
Given: Spring constant k = 100 N/m, compression distance x = 10 cm = 0.1 m
Relationships: E_p = ½kx²
Solve: $E_{p} = \frac{1}{2} k x^{2} = \frac{1}{2} (100 N / m) \times {(0.1 m)}^{2} = 0.5 J$ Answer: The spring stores 0.5 J of potential energy.
Potential energy stored in springs does not depend on the mass used to compress the spring. Therefore, in this new case, the stored energy is the same, 0.5 J.

Two pianos are lifted from the ground into a third story window using a crane. If the grand piano has twice the mass of the upright piano, then how much more work will lifting it require?