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CHAPTER 3 - WORK AND ENERGY
Definition of Work
Work is defined as a force exerted through a distance.
Whenever work is done, energy is transferred from one object to
another or transformed from one form to another.
To calculate the work done, we multiply the applied force times
the distance moved in the same direction as the force.
The equation used to calculate the amount of work done is:
W=F·D
where W is the work done, F is the force applied, and D is the
distance moved in the direction of the force.
Example
A worker pushes horizontally on a crate with a force of 300 N and
the crate moves 5.0 m. How much work was done?
In the metric system, the unit of force is the Newton and the unit of
distance is the meter. A force of one Newton exerted through a
distance of one meter is called a Joule which is the metric unit of
work. In the English system, a force of one pound exerted through
a distance of one foot is known as a foot pound and is the basic
unit of work.
1 joule = 1 newton X 1 meter
When we use the phrase that work is being done against something
we mean that the applied force is equal but opposite to the force
being opposed. Work done against gravity means a force equal to
the weight of the object being lifted is applied over a vertical
distance. Work done against friction means the applied force is
equal to the frictional force but moves in the direction opposite to
the frictional force.
Example
How much work is needed to lift a 5.0 kg block to a shelf 3.0 m
above the floor?
Power
Power is defined as the time rate of doing work or using energy.
The equations for power are:
Power = Work / time
P = W/t
P = Fd/t = FV
where P is power, W is work, t is time, F is force, d is distance, and
V is speed.
The basic unit of power is the J/s which is called a watt(w).
Example
A person with a mass of 100 Kg climbs a vertical height of 4.0 m
in 25 seconds. Find (a) the work done and (b) the power output of
the person.
Be careful not to confuse the symbol for watt(w) with the letter
variable used for work(W).
In the British system the unit of power is the foot pound per
second. We use a larger unit, the horsepower(hp) for engines.
1 horsepower(hp) = 550 lb X 1 ft /1 s = 550 ftlb/s = 746 watts
1 watt = 1n X 1m / 1 s
Energy consumed can be calculated using the power equation if we
know the power consumption of the device and the time it is in
use. The equation is:
E=P·t
where E is the energy used, P is the power used and t is the time
over which it is used. The resulting unit is a Joule. If we express
power in kilowatts(1000 watts) and time in hours, we get a unit
used in calculating power company bills, the kilowatthour(kwhr).
Example
A household uses 2.0 kw of power 24 hours a day for 30 days. If
electricity costs $.08 per kwhr, what is the electric bill for the
month?
Kinetic Energy and Potential Energy
Energy is defined as the ability to do work. Another way to look at
the concept of energy is that it has the ability to cause a change in
the motion, condition or position of an object. The metric unit of
energy is the Joule.
In this section we will consider mechanical energy which is
composed of kinetic energy and certain types of potential energy.
Potential energy is the energy an object has because of its position,
location, or condition. If work must be done to change one of
these, we say there is a change in the potential energy.
Lifting an object to a higher position requires that work be done.
This work is stored in the lifted object as gravitational potential
energy. The equation used to calculate work done against gravity
is:
Work = Force X Distance
Force = Weight = Mass X Acceleration Due to Gravity
W = mgh
GPE = mgh
where W is the work done, m is the mass of the object lifted, g is
the acceleration due to gravity, h is the distance the object is lifted,
and GPE is the gravitational potential energy. The unit of potential
energy is also the Joule.
Example
How much potential energy is given to a 2.04 kg book that is lifted
a distance of 0.5 m?
Gravitational potential energy is often considered to be zero on the
surface of the earth. In this case, the surface of the earth is called
our reference point. It is chosen because it is the most convenient
zero point in many cases. An object in a hole in the ground would
have a negative gravitational potential energy since some work
would be done in bringing it up to the surface. Remember that the
reference point is arbitrary and can be chosen so that it simplifies
the situation.
Kinetic energy is energy associated with motion. The kinetic
energy of an object is equal to the work done increasing the speed
of the object from zero or decreasing the speed of an object to zero.
It is calculated using the formula:
Ek = ½mv2
where Ek is the kinetic energy, m is the mass of the object and v is
the speed of the object. In the classical sense, the object must have
a mass and speed to have kinetic energy. The unit of kinetic energy
is the Joule.
Example
Find the kinetic energy of a 7.0 kg cannon ball moving at 5.0 m/s.
The work done on an object is equal to its change in kinetic
energy.
Example
A 6.0 kg bowling ball is rolled down the lane. What is the change
in kinetic energy of the ball if a force of 30 newtons is applied for
a distance of 1.5 meters?
If the ball does 30 joules of work on the pins, what is its speed
when it hits the back wall?
An application of this concept involves stopping a car. To bring a
car to a stop, the brakes must convert the kinetic energy of the car
into heat energy. The force of friction must be applied over a
distance.
If we double the speed of a car from 20mph to 40 mph, the fact
that the speed is squared in the kinetic energy formula means the
kinetic energy of the car is now four times as much. This means
the brakes must do 4 times the work. If the braking force is
constant, the stopping distance now is 4 times as great. That is why
any speeding in a school zone is dangerous.
Forms and Sources of Energy
The forms of energy that we will consider are briefly defined here.
Mechanical Energy is kinetic energy and energy associated with
motion or position such as Gravitational Potential Energy.Thermal
or Heat energy is energy associated with motion of the individual
molecules of a substance or object. It is generally considered to be
a type of mechanical energy.
Electrical Energy is associated with the motions of electric charges
as in electric currents.
Chemical Energy is energy associated with the formation and
breaking of chemical bonds in fuels and other applications.
Radiant Energy is energy associated with electromagnetic radiation
such as light from the sun or microwaves.
Nuclear Energy is released during fission and fusion reactions
when small amounts of matter are converted into relatively large
amounts of energy.
Conservation of Energy
The Law of Conservation of Energy states that energy can be
neither created or destroyed. When energy is changed from one
form to another it is conserved.
The total energy of an isolated system remains constant.
An isolated system is something that is not affected by anything
that is not part of it.
When we consider conservation of mechanical energy, we only
include kinetic energy and the appropriate form(s) of potential
energy. If we consider a situation where gravity is the only force
involved, we can use the equation:
Initial Energy = Final Energy
(Ek + Ep)1 = (Ek + Ep)2
(½mv2 +mgh)1 = (½mv2 +mgh)2
where the subscript 1 indicates the initial energy conditions and the
subscript 2 indicates the final energy conditions.
Example
An object is dropped from a height of 12 m. What is its speed
when it has fallen half the distance?
The exception to the above discussion occurs during nuclear
reactions when a significant amount of matter is changed to energy
or energy to matter. Since matter and energy are different forms of
the same thing, it is more accurate to describe conservation of
matter and energy together.
The source of energy for our bodies is the food we eat. We actually
give off heat energy at the rate of a 100 w light bulb.
The main commercial sources of energy are coal, oil, and natural
gas(fossil fuels). The use of nuclear, hydroelectric, and other
renewable energy sources has increased over the last several
decades.
Energy Sources Today
The U.S. accounts for 5% of the world's population, but consumes
25% of the world's energy. Since the use of fossil fuels and nuclear
energy sources gives rise to pollution and environmental concerns,
nonpolluting fuels and energy sources are being developed.
The three major sources of energy in the U. S. are petroleum,
natural gas and coal. Together they account for about 84% of the
energy produced and used in the U. S.
Petroleum and natural gas results from the decomposition, over
millions of years, of plankton that has accumulated at the bottom
of freshwater lakes or shallow seas. Petroleum is measured in units
called barrels which consist of 42 U. S. gallons. An actual drum of
oil contains 55 gallons.
Imported petroleum accounts for more than half of the oil
consumed. Most of it comes from Mexico, Canada, Venezuela, and
Saudi Arabia.
Coal is formed from the remains of ancient plant material found in
swamps and bogs. Coal, like gas and oil, contains energy from the
Sun captured millions of years ago.
The first stage in the coal making process is the formation of
peat(not peat moss). Peat is a relatively high carbon fibrous
material which can be burned as a fuel and still is in some parts of
the world.
The next stage in coal formation is called lignite. This material is
called brown coal and has a higher carbon content than lignite.
Lignite will eventually turn into bituminous coal also known as
soft coal. This type of coal is very abundant in the U. S. and is
easily mined. A technique called strip mining is sometimes used
since this type of coal is often found relatively near the surface of
the Earth.
The last stage in coal formation is called anthracite or hard coal.
This type of coal has the highest carbon content and is the most
rock-like of the forms of coal. Anthracite is mined from deep
underground shafts which makes it more expensive in terms of
money and lives.
All of the forms of coal contain impurities such as silt, iron oxide
and sulfur. The sulfur combines with oxygen to produce sulfur
oxides and acid rain when the coal is burned. The carbon combines
with oxygen to produce carbon oxides which contribute to the
greenhouse effect.
Coal burning utility plants are now required to use scrubbers and
other exhaust cleaning devices to reduce harmful emissions. Some
power plants have converted to fuel oil or natural gas as fuel
sources to reduce pollution.
Alternative Fuels and Sources of Energy
Hydropower produces electricity with practically no pollution.
Problems are most of the best dam sites have been developed.
Flooding behind the dam ruins agricultural land and ecosystems.
Nuclear power uses energy produced when a uranium or plutonium
atom undergoes fission(splits apart) in the place of energy from a
fossil fuel to produce heat and steam to turn turbines connected to
generators. At the present time, energy generated from nuclear
reactions is expensive. If the reactions and the materials involved
are not properly controlled they can be very dangerous. We get
about 8% of our energy from nuclear reactors.
Gasohol, a mixture of ethanol and gasoline can be used in properly
equipped vehicles. Problems are its use does not reduce production
of pollution and twice as much energy is used in its manufacture
than it produces.
Wind Power is nonpolluting and has been used for centuries.
Problems are lack of land appropriate for wind energy farms and
the inconsistency of the wind.
Solar Power uses energy directly from the sun to supply heat or
light. This energy can also be stored in thermal masses to be
released later. Photovotaic cells can convert sunlight into
electricity which can be used immediately or stored in batteries or
capacitors for later use. Problems are efficiency(only about 25% to
30%) and cost of the electricity. Solar generated electricity costs
about $.30 per kwhr compared to that generated by fossil fuels at
$.08 per kwhr.
Geothermal energy is produced wherever water is heated by
magma or hot rocks beneath the Earth’s surface and makes its way
to the surface to be utilized as a heat source. Geothermal sources in
Oregon, Idaho, and California are in use today.
Hydrogen gas can be used to store energy for later use since it
must be produced by the electrolysis of water. It is not actually a
source of energy but it can be used as a method of storing solar
energy. There are actually a few cars in production that can use
hydrogen gas as a fuel.
A newly discovered low polluting fuel that is being researched is
methane hydrate which is described as ice that burns. It is
estimated that the energy available in all the methane hydrate is
equal to twice the energy stored in all of the world's fossil fuel
reserves. Research on extraction and use is underway.
Study
1. Key Terms p 86
2. Applying the Concepts 1 – 35 p 87
3. Questions for Thought 1, 5, 7, 8, 12 p 89