Download Chapter 2: Forces and Energy

12/22/12
Chapter 2: Forces and Energy
Goals of Period 2
Section 2.1:
Section 2.2:
Section 2.3:
Section 2.4:
To define the four fundamental forces
To explain the relationship among forces, work, and energy
To describe forms of energy
To understand the law of conservation of energy
2.1 The Four Fundamental Forces of Nature
Why do objects move? Forces can cause objects to move and accelerate. In
this period we examine the origins of forces and find that all known forces can be
classified as one of four fundamental forces.
Based on their properties, all of the currently known forces fall into four types:
the gravitational, electromagnetic, strong nuclear, and weak nuclear forces. All forces
in the universe are due to one or more of these four fundamental forces. Even though
each of these forces has unique properties, at least three of the four forces appear to be
related to one another. Scientists continue to search for a grand unified theory that
would explain all four fundamental forces in terms of a single underlying force law.
The Gravitational Force
Although the gravitational force is the weakest of the four fundamental forces,
it is the most familiar force in our everyday lives. We experience the gravitational force
as the mutual attraction of matter to all other matter. The gravitational force between
the Earth and objects near it causes objects to fall to the surface of the Earth. The
gravitational force is always an attractive force. The greater the distance between two
objects, the smaller the force they exert upon one another. The greater the masses of
the objects, the greater the force.
The Electromagnetic Force
While the electric force and the magnetic force can appear to be distinct and
separate forces, they are, in fact, two different aspects of a single force -- the
electromagnetic force. The electromagnetic force provides the force that bonds
atoms into molecules.
Matter is made up of atoms, which are composed of tiny, dense nuclei
surrounded by clouds of electrons. The positively charged nucleus of an atom consists
of protons and neutrons bound together by the strong nuclear force. The only
significant difference between neutrons and protons is their charge – protons have a
positive electric charge and neutrons have no charge. The nucleus contains more than
99.9% of the atom’s mass. The negatively charged electron cloud surrounding the
nucleus accounts for nearly all of the volume of the atom. Protons and neutrons, called
nucleons, have nearly equal mass, about 2,000 times the mass of an electron.
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The electric charge of protons and electrons is exactly equal in magnitude but
opposite in sign. In a neutral atom, the number of negatively charged electrons in the
atomic cloud is equal to the number of positively charged protons in the atomic nucleus.
There is an attractive electric force between the oppositely charged protons and
electrons that draws protons and electrons to each other.
Particles with the same
electric charge, such as two protons or two electrons, repel each other electrically.
Therefore, unlike the gravitational force, which is always attractive, the electric force can
be an attractive or repulsive force between charged objects. The larger the charge, the
greater the attractive or repulsive force. The greater the distance between charges, the
weaker the force. The electromagnetic force holds matter together by providing the
force that bonds atoms into molecules.
The Strong Nuclear Force
If particles with the same charge repel one another, how can positively charged
protons exist tightly packed in an atomic nucleus? The strong nuclear force is
responsible for holding the neutrons and protons of atomic nuclei together. The strong
nuclear force is the strongest of all the forces, but it is effective only over very short
distances, such as the diameter of a small atomic nucleus.
When the strong nuclear force binds protons and neutrons, the bound object has
less mass than the sum of the masses of the unbound protons and neutrons. The
difference in mass between the unbound and bound neutrons and protons has been
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converted into an amount of energy give by Einstein’s famous equation, E = M c . Here,
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M is the decrease in mass, and c is the speed of light, 3 x 10 meters/second. Since c
is such a huge number (9 x 1016 = 90 quadrillion m2/s2), converting even a tiny amount
of mass will produce a large quantity of energy. The conversion of mass into energy is
the energy source for nuclear power plants, nuclear weapons, and stars such as the
Sun.
While all forces involve an exchange of mass and energy, only the strong nuclear
force is strong enough to produce a measurable change in the amount of mass. For
example, the atoms in a metal spring are bound together by electromagnetic forces
between the positive and negative charges in the atoms. Winding the spring stretches
the electromagnetic bonds and increases the strain potential energy of the spring.
When the spring is stretched, its increased potential energy is reflected in a very slight
increase in the mass of the spring. However, unlike the case of the strong nuclear
force, an increase in mass due to the electromagnetic force is too small to measure.
When we study the strong nuclear force in Physics 1104, we will find that the change in
mass is large enough to be measured by sophisticated scientific equipment.
The Weak Nuclear Force
The weak nuclear force is responsible for the type of radioactive decay that
changes the nucleus of one element into a nucleus of a different element. Like the
strong nuclear force, the weak nuclear force is effective only between particles that are
extremely close together. Physics 1104 explores the strong and weak nuclear forces in
reactions in the sun and in nuclear reactors and the decay of radioactive materials.
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The Frictional Force
The frictional force is NOT one of the four fundamental forces. However, it
results from the fundamental electromagnetic force. In solids, atoms are held together
by atomic forces, which act similarly to springs. Since surfaces are never perfectly
smooth, when two objects rub together, the atoms on their surfaces bump into one
another and move slightly from their equilibrium positions. These movements result in
the frictional force. When the atoms are released, they vibrate back and forth. Their
atomic vibrations represent the conversion of the mechanical energy of motion of
objects into an increase in the thermal energy of those objects. To experience the
frictional force as thermal energy, rub your hands together.
2.2 Forces, Work and Energy
Work is done when a force moves an object over some distance in the
direction of the force applied to the object. We use the force of our muscles to do work
when we push a box across a floor. It takes energy to push the box. Energy is used to
do work.
Fig 2.1 Work is Done When a Force Moves an Object in the Direction
of the Force
The box moves in the
direction of the force.
Force
Pushing a box with a force of 1 newton to move it a distance of 1 meter in the
direction of the force requires 1 joule of work. In English units, pushing the box with a
force of 1 pound to move it 1 foot in the direction of the force requires 1 foot-pound of
work. The larger the force and the farther the box moves, the more work done. No
work is done unless the box moves.
or
Work = Force x Distance
W = F D
where
(Equation 2.1)
W = work (joules or foot-pounds)
F = force applied (newtons or pounds)
D = distance moved in the direction of the force (meters or feet)
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To lift an object, we do work against the downward force of gravity. The force
of gravity acting on an object equals the object’s weight:
Force of gravity = Weight = M g
(Equation 2.2)
M = mass of the object (kilograms)
g = the acceleration of gravity (9.8 m/s2 )
where
To lift an object at a constant velocity, we must exert an upward force equal to
the downward force of gravity. The work done to lift the object is the product of the
amount of the force of gravity acting on the object and the vertical distance it is raised.
The greater the mass of the object and the higher it is lifted, the more work done.
Work = force of gravity x change in height
or
(Equation 2.3)
W = F h
W = work (joules or foot-pounds)
F = force of gravity (newtons or pounds)
h = change in vertical height (meters or feet)
where
Substituting the expression for the force of gravity (Equation 2.2) into the
equation for the work done against the force of gravity (Equation 2.3), we find:
(Equation 2.4)
W = Mg h
Ignoring the energy wasted as friction, the work done against the force of
gravity to lift an object is equal to the weight of the object times the vertical distance it
is lifted. In the case of a falling object, work is done by gravity to make the object fall.
For example, if a 5 newton rock falls 2 meters, the work by the force of gravity on the
rock is 10 joules.
Potential energy is stored energy, which is available to do work. The
gravitational potential energy stored in a raised object is proportional to the height it is
raised and to the mass of the object.
Gravitational potential energy = weight x change in height
E pot
where
= M g h
(Equation 2.5)
M = mass (kilograms)
g = 9.8 m/s2 or 32 ft/s2
h = change in vertical height (meters or feet)
If wasted energy is ignored, the work done to raise an object equals the potential
energy the object gains.
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Concept Check
a)
2.1
How much work is done against the force of gravity to lift a 3.0 kg box
2.0 meters vertically?
________________
b)
If wasted energy is ignored, how much gravitational potential energy does the
box gain by being lifted 2.0 meters?
_________________
2.3
Forms of Energy
Energy is important because it provides the ability to do work. Work is done
when one or more forces move an object over a distance. The objects being moved can
be very small, such as molecules, atoms, electrons, or protons, or they can be much
larger objects. When forces act on objects and do work, energy is converted from one
form to another.
Although there are many ways to classify energy, we will discuss eleven forms of
energy. The first three forms of energy are related to the energy of motion associated
with moving objects, atoms, and molecules.
Kinetic Energy (also called Mechanical Energy of Motion): Moving objects
exhibit kinetic energy. A ball thrown through the air or a car travelling down a
road has kinetic.
Thermal Energy: Energy of motion occurs within an object as its atoms and
molecules vibrate randomly. Thermal energy is the unorganized energy of
motion of vibrating objects too small to see. The faster the atoms and molecules
in a substance vibrate, the more thermal energy the substance has and the
higher its temperature.
Sound Energy: When atoms and molecules vibrate in an organized manner,
their vibrations may travel as a wave. Sound is the transmission of vibrations
through a solid, liquid, or gas by vibrating atoms or molecules. When sound
waves reach our eardrums, the energy in the sound waves causes our eardrums
to vibrate. Our brains interpret the vibrations as sounds.
Matter contains positive and negative electric charges. Forms of energy that
result from the forces between these charges are called electromagnetic energy. We
can distinguish three forms of electromagnetic energy.
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Electrical Energy: Electrical energy results from the forces between charged
particles. These electrical forces exist between charged particles at rest and in
motion.
Magnetic Energy: Charges moving within some types of materials produce
magnetic forces. These magnetic forces are in addition to the electrical forces
between moving charges. Magnetic materials are called magnets and attract or
repel one another due to their magnetic forces. A coil of wire with charges
moving through it acts like a magnet and is called an electromagnet. Electrical
and magnetic energy are closely related.
Radiant Energy: While vibrations of matter produce thermal and sound energy,
radiant energy results from vibrations of electric charges. Radiant energy is
another name for waves of electromagnetic energy. For example, the sun’s
energy is transported to Earth as waves of radiant energy. Radio waves,
microwaves, infrared radiation, light waves, ultraviolet radiation, X-rays and
cosmic rays are all waves of radiant energy. Figure 2.2 illustrates the relative
sizes of these forms of radiant energy.
Figure 2.2: Forms of Radiant Energy
Source: http://spaceplace.nasa.gov
Stored energy, which can be used to do work, is called potential energy. We
consider five types of potential energy.
Gravitational Potential Energy: When an object is raised above the Earth and
released, the gravitational attraction between that object and the Earth causes
the object to fall to the ground. A raised object has gravitational potential
energy.
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Strain Potential Energy: If we stretch or compress a spring and release it, the
spring moves back toward its original length. The stretched or compressed
spring has strain potential energy because it has the potential to move.
Electrical Potential Energy: Electrical potential energy is stored when positive
and negative electric charges are separated. The amount of stored energy
depends on the number of separated charges and the distance they are
separated.
Chemical Potential Energy: Chemical potential energy exists because atoms
and molecules can take in or give off energy when their chemical bonds are
formed or broken.
Nuclear Energy: In nuclear reactions, energy is given off or taken in by atomic
nuclei. Energy is available from the nuclei of atoms that are radioactive and
undergo nuclear changes. Nuclear energy will be discussed in detail later in this
course.
2.4
Energy Conversions and Energy Conservation
Energy can be converted from one form into another form, but during the
conversion process some energy is wasted in undesirable forms. Figure 2.3 shows a box
sliding down a ramp. When the box is at rest at the top of a ramp, all of its energy is
stored as gravitational potential energy. As the box moves down the ramp, much of its
gravitational potential energy is converted into kinetic energy. However, if there is a
force of friction between the box and the ramp, some gravitational potential energy is
converted into thermal and sound energy as the box moves.
Fig. 2.3 A Box Slides down a Ramp
At the bottom,
the box has only
kinetic energy.
As it slides, the box
has some gravitational
potential energy and
some kinetic energy.
At rest at the top,
the box has only
potential energy.
At the bottom of the ramp, the box has no gravitational potential energy. As the
box moves along the floor after it has reached the bottom of the ramp, some of its
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kinetic energy will continue to be converted into sound energy and some into thermal
energy due to friction. Once the box has come to rest, all of its potential energy has
been converted into kinetic, sound, and thermal energy. However, in this process, the
total amount of energy did not change. The joules of gravitational potential energy that
box had at the top of the ramp must equal the sum of its kinetic energy plus the joules
of wasted thermal and sound energy at the bottom of the ramp. Once the box has
stopped moving across the floor, all of its initial gravitational potential energy will have
been converted into the sum of its wasted thermal and sound energy. The initial joules
of energy at the beginning of this energy conversion process must equal the total joules
of energy at the end of the process. This fact illustrates the law of conservation of
energy .
The law of conservation of energy tells us that although energy can be
converted from one form of energy into another form, the total amount of energy
involved in these conversions remains unchanged – energy cannot be created or
destroyed.
The total amount of energy we have now in the Universe is the same
amount of energy that existed at its beginning. Conservation of energy applies not only
to gravitational potential energy from the gravitational force, but to conversions
involving any of the four fundamental forces. In this period, we will apply conservation
of energy to conversions involving gravitational potential, kinetic, electrical, radiant,
thermal, and sound energies. Keep in mind that the law of conservation of energy
requires all of the energy put into a conversion process be accounted for at the end – no
energy can be lost or destroyed.
Fig. 2.4 Conservation of Energy for the Box Sliding Down the Ramp
Gravitational
Potential Energy
In
Useful Kinetic
Energy Out
Wasted Thermal
& Sound Energy
Out
Grav. Potential Energy In = Kinetic Energy Out + Thermal and Sound Energy Out
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From the law of conservation of energy, we know that the total energy input to
an energy conversion process must equal the total energy output. However, not all of
the energy out is useful. In all energy conversions, some energy is wasted. The
amount of the total energy in that is converted into useful energy out is the efficiency of
the conversion process.
Efficiency

Useful Energy Out
Total Energy In
(Equation 2.6)
When a series of energy conversions are required to produce the desired form of
energy, energy is wasted in each step of the process. The overall efficiency of a series
of energy conversion processes can be quite low. The overall efficiency is the product of
the efficiencies of each step in the process.
Overall Efficiency = (Efficiency of step 1) x (Efficiency of step 2) x (Efficiency of step 3) x …
or
Overall Efficiency = Efficiency1 x Efficiency2 x Efficiency3 x …..
(Equation 2.7)
Often the form of energy most readily available is not the most useful form.
Coal can be burned to provide heat, but converting the chemical energy stored in coal
into electrical energy requires a series of intermediate steps. In each step of the
conversion process, some energy is wasted. In the process of using electricity, such as
to light bulb, also wastes energy. The series of energy conversions from the chemical
energy in coal to radiant energy from a light bulb can have a low efficiency.
Concept Check 2.2
a)
A series of two energy conversions has efficiencies of 25% and 60%. What is
the overall efficiency of this series of two conversions?
________________
b)
A third energy conversion is added to the process described in part a). The
efficiencies of the three conversions are 25%, 60%, and 50%. What is the
overall efficiency of this series of three conversions?
________________
c)
Explain why the overall efficiency decreased when a third energy conversion was
added.
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Period 2 Summary
2.1:
All forces currently known can be classified into four fundamental forces:
1)
the Gravitational force, an attractive force between all objects.
2)
the Electromagnetic force, electric and magnetic forces that arise from
charged particles.
3)
the Strong Nuclear Force that holds atomic nuclei together.
4)
the Weak Nuclear Force, responsible for some nuclear decays
2.2:
Work is done when a force moves an object over a distance in the direction of
the force. Work = Force x Distance, or W = F D
One joule of work is done when a force of 1 newton moves an object a distance
of 1 meter in the direction of the force.
The work needed to raise an object vertically against the force of gravity is
W = M g h
One joule is the amount of work done against the force of gravity when a
1 newton weight is lifted a vertical distance of 1 meter.
Potential energy is stored energy, which is available to do work.
The gravitational potential energy stored in a raised object is proportional to the
height it is raised and to the mass of the object.
E pot = M g h
If wasted energy is ignored, the work done to raise an object equals the
potential energy the object gains.
2.3:
Energy provides the ability to do work. Energy takes many different forms.
Eleven forms of energy are defined on pages 17 – 19.
2.4:
The law of conservation of energy states that energy can be converted
from one form into another, but energy cannot be created nor destroyed.
The total amount of energy put into a conversion process must equal the total
amount of energy out in all forms.
When a raised object slides down a ramp, some of its stored gravitational
potential energy is converted into the kinetic energy of the moving object
and some energy is wasted as sound energy and as thermal energy from
the friction between the object and the ramp.
Conservation of energy requires that all of the original gravitational
potential energy be accounted for:
Potential energy in = kinetic energy out + sound and thermal energy out.
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Period 2 Summary, Continued
The efficiency of an energy conversion process is the ratio of the useful energy
that results from the process to the total energy put into the process.
Efficiency of an energy conversion =
Useful Energy Out
Total Energy In
In many situations, producing the desirable form of energy requires a series of
energy conversion processes. For a series of energy conversions, the overall
efficiency is the produce of the efficiencies of the individual steps.
Overall Efficiency = Efficiency1 x Efficiency2 x Efficiency3 …
Solutions to Chapter 2 Concept Checks
2.1
a)
W = M g h = 3.0 kg x 9.8 m/s2 x 2.0 m = 58.8 joules
b)
If we assume no energy is wasted, the gravitational potential energy
gained by the lifted box equals the work done to lift it: 58.8 joules
a)
Overall Efficiency = Eff1 x Eff2 = 0.25 x 0.60 = 0.15 = 15%
b)
Overall Efficiency = Eff1 x Eff2 x Eff3 = 0.25 x 0.60 x 0.50 = 0.75 =7.5%
c)
In every energy conversion process, some energy is wasted so the
efficiency of the process is less than 100%. Multiplying a value by a
number less than 1 results in a product smaller than the original value.
2.2
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