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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

Gravitational potential energy

Potential energy for a brick on the table and floor

Potential energy is energy of position. The word “potential” describes the fact that potential energy is not active but has the ability to become active. A good example is to compare the energy of a brick on the table and a brick on the floor. By virtue of its being higher than the floor, the brick has more potential energy on the table compared to when it is on the floor. The brick on the table, however, is not using its energy by moving, heating up, or anything else. It is potential—inactive or stored—energy. Show Many objects store potential energy

Show Many objects store potential energy

How much potential energy does the brick have? If the brick has more mass, the force of gravity gives it more weight and more potential energy. If it has more height, it can fall farther and also has more potential energy. By these arguments we deduce that potential energy depends, at least, on weight and height. Checking the units supports that conjecture—the product of weight times height has units of force times distance, the same as work. The equation for gravitational potential energy is exactly what we surmised. The potential energy of any object of mass, m raised by a height, h is given by equation (3.3). We will see in Chapter 11 that this energy is exactly equal to the minimum work it takes to raise the brick from the floor to the tabletop.

E_{p} = m g h

E_p	=	potential energy (J)
m	=	mass (kg)
g	=	strength of gravity, typ. 9.8 N/kg
h	=	change in height (m)

Gravitational
potential
energy

Potential energy exists because there is a force that we must work against to raise the book from the floor to the table. In this case the force is gravity and we use the gravitational potential energy of equation (3.3). Gravity still acts on the book once it is on the table and therefore the work we do to raise the book is stored as potential energy, which can be recovered by letting the book fall back down again. An important concept is that potential energy represents stored work that may be recovered when the energy becomes active—such as by changing position in height.

If a 14 kg box is raised to a height of 4 m on Earth, what is its gravitational potential energy relative to the ground?

549 J
56 J
3.5 J
0.286 J

Show

Asked: Gravitational potential energy E_p of the box
Given: Box has mass m = 14 kg, box is raised to height h = 4 m, acceleration due to gravity g = 9.8 N/kg
Relationships: E_p = mgh
Solve:

\begin{array}{l} E_{p} & = & m g h \\ = & (14 kg) \times (9.8 N / kg) \times (4 m) \\ = & 549 J \end{array}

Solved Problem 3.1: Potential energy and work done for weightlifting

The current world record weightlifting of 263 kg was set by Hossein Rezazadeh of Iran in 2004. (a) If he held the barbell overhead at a height of 2.0 m above the floor, then how much gravitational potential energy did the barbell have? (b) How much work did he perform to lift the barbell from the ground to the overhead position?

(a) Potential energy of the barbell overhead
(b) Work done by the weightlifter to lift the barbell overhead from the floor

Weightlifter

Mass of the barbell: m=263 kg
Height of the barbell above the floor: h=2.0 m

Gravitational potential energy: E_p=mgh
Gravitational acceleration: g=9.8m/s²

(a) Use the gravitational potential energy equation:

E_{p} = m g h = (263 kg) (9.8 {m/s}^{2}) (2.0 m) = 5, 155 J

(b) The change in potential energy of the barbell from the floor, where E_p=0 J, to its overhead
position, given in part (a), is 5,155 J. The minimum work done by the weightlifter is the same as the change in energy of the barbell, or 5,155 J.

(a) The gravitational potential of the overhead barbell is 5,155 J.
(b) The minimum work done by the weightlifter to lift the barbell overhead is 5,155 J.