# 7.6 Conservation of energy  (Page 3/10)

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Another example of energy conversion occurs in a solar cell. Sunlight impinging on a solar cell (see [link] ) produces electricity, which in turn can be used to run an electric motor. Energy is converted from the primary source of solar energy into electrical energy and then into mechanical energy.

Energy of various objects and phenomena
Object/phenomenon Energy in joules
Big Bang ${\text{10}}^{\text{68}}$
Energy released in a supernova ${\text{10}}^{\text{44}}$
Fusion of all the hydrogen in Earth’s oceans ${\text{10}}^{\text{34}}$
Annual world energy use $4×{\text{10}}^{\text{20}}$
Large fusion bomb (9 megaton) $3\text{.}8×{\text{10}}^{\text{16}}$
1 kg hydrogen (fusion to helium) $6\text{.}4×{\text{10}}^{\text{14}}$
1 kg uranium (nuclear fission) $8\text{.}0×{\text{10}}^{\text{13}}$
Hiroshima-size fission bomb (10 kiloton) $4\text{.}2×{\text{10}}^{\text{13}}$
90,000-ton aircraft carrier at 30 knots $1\text{.}1×{\text{10}}^{\text{10}}$
1 barrel crude oil $5\text{.}9×{\text{10}}^{9}$
1 ton TNT $4\text{.}2×{\text{10}}^{9}$
1 gallon of gasoline $1\text{.}2×{\text{10}}^{8}$
Daily home electricity use (developed countries) $7×{\text{10}}^{7}$
Daily adult food intake (recommended) $1\text{.}2×{\text{10}}^{7}$
1000-kg car at 90 km/h $3\text{.}1×{\text{10}}^{5}$
1 g fat (9.3 kcal) $3\text{.}9×{\text{10}}^{4}$
ATP hydrolysis reaction $3\text{.}2×{\text{10}}^{4}$
1 g carbohydrate (4.1 kcal) $1\text{.}7×{\text{10}}^{4}$
1 g protein (4.1 kcal) $1\text{.}7×{\text{10}}^{4}$
Tennis ball at 100 km/h $\text{22}$
Mosquito $\left({10}^{–2}\phantom{\rule{0.25em}{0ex}}g at 0.5 m/s\right)$ $1\text{.}3×{\text{10}}^{-6}$
Single electron in a TV tube beam $4\text{.}0×{\text{10}}^{-\text{15}}$
Energy to break one DNA strand ${\text{10}}^{-\text{19}}$

## Efficiency

Even though energy is conserved in an energy conversion process, the output of useful energy or work will be less than the energy input. The efficiency     $\text{Eff}$ of an energy conversion process is defined as

$\text{Efficiency}\left(\text{Eff}\right)=\frac{\text{useful energy or work output}}{\text{total energy input}}=\frac{{W}_{\text{out}}}{{E}_{\text{in}}}\text{.}$

[link] lists some efficiencies of mechanical devices and human activities. In a coal-fired power plant, for example, about 40% of the chemical energy in the coal becomes useful electrical energy. The other 60% transforms into other (perhaps less useful) energy forms, such as thermal energy, which is then released to the environment through combustion gases and cooling towers.

Efficiency of the human body and mechanical devices
Activity/device Efficiency (%) Representative values
Cycling and climbing 20
Swimming, surface 2
Swimming, submerged 4
Shoveling 3
Weightlifting 9
Steam engine 17
Gasoline engine 30
Diesel engine 35
Nuclear power plant 35
Coal power plant 42
Electric motor 98
Compact fluorescent light 20
Gas heater (residential) 90
Solar cell 10

## Phet explorations: masses and springs

A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energies for each spring.

## Section summary

• The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.
• When all forms of energy are considered, conservation of energy is written in equation form as ${\text{KE}}_{i}+{\text{PE}}_{i}+{W}_{\text{nc}}+{\text{OE}}_{i}={\text{KE}}_{f}+{\text{PE}}_{f}+{\text{OE}}_{f}$ , where $\text{OE}$ is all other forms of energy besides mechanical energy.
• Commonly encountered forms of energy include electric energy, chemical energy, radiant energy, nuclear energy, and thermal energy.
• Energy is often utilized to do work, but it is not possible to convert all the energy of a system to work.
• The efficiency $\text{Eff}$ of a machine or human is defined to be $\text{Eff}=\frac{{W}_{\text{out}}}{{E}_{\text{in}}}$ , where ${W}_{\text{out}}$ is useful work output and ${E}_{\text{in}}$ is the energy consumed.

## Conceptual questions

Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance. The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events. (See [link] .)

Describe the energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.

Do devices with efficiencies of less than one violate the law of conservation of energy? Explain.

List four different forms or types of energy. Give one example of a conversion from each of these forms to another form.

List the energy conversions that occur when riding a bicycle.

## Problems&Exercises

Using values from [link] , how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube? (These electrons were not dangerous in themselves, but they did create dangerous x rays. Later model tube TVs had shielding that absorbed x rays before they escaped and exposed viewers.)

Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

Equating ${\text{ΔPE}}_{g}$ and $\text{ΔKE}$ , we obtain $v=\sqrt{2\text{gh}+{{v}_{0}}^{2}}=\sqrt{2\left(\text{9.80 m}{\text{/s}}^{2}\right)\left(\text{20.0 m}\right)+\left(\text{15.0 m/s}{\right)}^{2}}=\text{24.8 m/s}$

If the energy in fusion bombs were used to supply the energy needs of the world, how many of the 9-megaton variety would be needed for a year’s supply of energy (using data from [link] )? This is not as far-fetched as it may sound—there are thousands of nuclear bombs, and their energy can be trapped in underground explosions and converted to electricity, as natural geothermal energy is.

(a) Use of hydrogen fusion to supply energy is a dream that may be realized in the next century. Fusion would be a relatively clean and almost limitless supply of energy, as can be seen from [link] . To illustrate this, calculate how many years the present energy needs of the world could be supplied by one millionth of the oceans’ hydrogen fusion energy. (b) How does this time compare with historically significant events, such as the duration of stable economic systems?

(a) $\text{25}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{years}$

(b) This is much, much longer than human time scales.

#### Questions & Answers

What is the frictional forc e between two bodies
it is the force which always opposes the motion of the body
ZAMAN
what is a wave
wave means. A field of study
aondohemba
what are Atoms
aondohemba
is the movement back and front or up and down
sani
how ?
aondohemba
wave is a disturbance that transfers energy through matter or space with little or no associated mass.
lots
A wave is a motion of particles in disturbed medium that carry energy from one midium to another
conist
an atom is the smallest unit( particle) of an element that bares it's chemical properties
conist
what is electromagnetic induction?
conist
what's boy's law
mahmud
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
How do you convert 0.0045kgcmÂ³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
list it out I wanna know
Cristal
what the meaning of continuum
What state of matter is fire
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
how can we define vector
mahmud
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
Hanzo
as for me guys u would say time is quantity that measures how long it takes for a specific condition to happen e.g how long it takes for the day to end or how it takes for the travelling car to cover a km.
conist
what is the relativity of physics
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
hello
King
Explain dopplers effect
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
Calculation of kinetic and potential energy
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat