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Physics Reading
Objective B1
Sir Isaac Newton developed his Three Laws of Motion from centuries of thought and observation. In a letter to Robert Hook, Newton
wrote “If I have seen further, it is by standing on the shoulders of giants.” In particular two “giants” that helped Newton develop his work
were the famous scientists Aristotle and Galileo. To understand these two scientists, is to understand Newton and his laws of motion.
For more information about the physics of Aristotle versus Galileo, go to
http://csep10.phys.utk.edu/astr161/lect/history/aristotle_dynamics.html
Newton’s First Law of Motion (Law of Inertia)
Newton’s First Law states that an object at rest remains at rest, and an object in motion continues in motion at a constant velocity in a
straight line, unless acted upon by an external force or unbalanced force. An external force or unbalanced force is crucial for students to
comprehend. Below are two illustrations of forces acting on a book in a balanced and unbalanced state.
Figure 1: Forces
(from
http://www.physicsclassroom.com/Class/newtlaws/U2L1d.html)
For example, Marks’s car is stuck in a snowdrift, so he asks Bob sitting in the passenger seat to push him out of the snow. He agrees
and starts pushing as hard as he can on the dashboard; yet the car doesn’t move. Bob, in this example, is considered the internal force.
In order for the car to move, he should have stepped out of the car and pushed from there; thus becoming the external force needed to
cause the car to move.
Figure 2: Newton’s 1st Law
(from
http://www.physicsclassroom.com/Class/newtlaws/U2L1a.html)
An object resisting a change in its “natural state of motion” (stopped or moving in a straight line) is what Newton referred to as inertia.
This is why Newton’s First Law of Motion may as well be coined the Law of Inertia; the resistance an object has to a change in its state
of motion.
To learn more about Newton’s First Law, go to
http://www.astronomynotes.com/gravappl/s2.htm#A1.1
Newton’s Second Law of Motion
Sir Isaac Newton wrote his three laws of motion in his book in a specific order being that each one builds upon the each other.
Newton’s First Law stated that an object at rest will remain at rest, and an object in motion will continue in motion at a constant velocity
in a straight line, unless acted upon by an external force or unbalanced force. Thus, the First Law describes what will occur if there is no
force. However, Newton’s Second Law describes what will happen if there is an external and unbalanced force.
Newton’s Second Law states when an external, unbalanced force acts on an object,
the object will accelerate in the same direction as the force. The acceleration varies directly as the force, and inversely as the mass.
This in itself may be a bit confusing for the students. So, present it to them using an equation.
When an external, unbalanced for acts on an object, the object will accelerate in the same direction as the force. For example, the
object might be moving to the right, while a force is pushing it to the left causing the object to slow down. Its acceleration is in the
direction of the force, which is to the left, but it is still moving to the right. The acceleration varies directly as the force, which means that
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if the force increases, the acceleration will also increase and vice versa if the force decreases, the acceleration will also decrease. For
example, push something harder and it will accelerate more. They are directly dependent on each other. Though acceleration and force
may vary directly; acceleration inversely varies with mass. This means that if the mass is larger, the acceleration is less and vice versa
if the mass if less, the acceleration is more. In other words, if something has less mass, it is easier to make it move faster. They depend
inversely on each other. This may be written mathematically as shown below:
a@F
Figure 3: Newton’s 2nd Law
(from
http://www.astronomynotes.com/gravappl/s2.htm#A1.2)
Figure 4: Newton’s 2nd Law
(from http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#nt3)
To learn more about Newton’s Second Law, go to
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3a.html
Newton’s Third Law of Motion (Action-Reaction)
To review, Newton’s First Law describes what happens when there is no force. His Second Law describes what happens when there is
a force. And lastly, his Third Law describes what happens when objects interacting.
Newton’s Third Law states that for every action force, there is an equal and opposite reaction force. This law is also known as the Law
of Action-Reaction Pair. A force is a push or pull upon an object, which results from its interaction with another object. According to
Newton, whenever object A and object B interact with each other; they exert forces upon each other both equal in magnitude and
opposite in direction. For example, when sitting in a chair, your body exerts a downward force on the chair and the chair exerts an
upward force on your body. These two forces are called action-reaction pair because they always come in pairs.
Figure 5: Action-Reaction Pair Forces
(from
http://www.physicsclassroom.com/Class/newtlaws/U2L4a.html)
An important concept to illustrate when looking at action-reaction pairs is that the two forces are acting on different objects, not on the
same object. For example, have the students stand on the ground and identify the action-reaction pair forces. The students are pushing
on the ground with a force due to gravity (Fg down) and the ground is pushing upon them (FN up). The FN is the normal force that
balances out the force due to gravity down. It is always perpendicular to the surface the object is on.
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Lastly, action-reaction pair forces may either be in direct contact or action-at-a-distance force. Here are some examples of actionreaction forces that depend on the objects being in direct contact, meaning that the two objects involved are touching each other to
exert forces in equal magnitudes and opposite directions.
1. The baseball forces the bat to the right (an action); the bat forces the ball to the left (the reaction).
2. Athlete pushes bar upward (an action); the bar pushes athlete downwards (the reaction).
Figure 6: Contact Forces
(from
http://www.physicsclassroom.com/Class/newtlaws/U2L4b.html)
Here are some examples of action-reaction pairs occurring without friction, or even without direct contact, known as action-at-adistance force.
1. A rocket pushes out exhaust (an action); the exhaust pushes the rocket forward (the reaction).
2. The earth pulls down on a ball (an action); the ball pulls up on the earth (the reaction).
3. If I push on a lawn mower, it pushes back on me with an equal, but opposite force. Explain why we don’t both just stay still.
 The forces are acting on different bodies (and there are other forces to consider).
 It doesn’t matter to the lawn mower that there is a force on me… all that matters to the lawn mower is that there is a force on it,
so it starts to move!
 Another action-reaction pair you need to consider is that I am pushing backwards on the ground, and it pushes forwards on
me.
Figure 7: Action-Reaction Pair (from
http://www.studyphysics.ca/newnotes/20/
unit01_kinematicsdynamics/chp05_forces/lesson17.htm)
To learn more about Newton’s Third Law, go to
http://theory.uwinnipeg.ca/mod_tech/node24.html
Objective B2
Electromagnetic force is one of the four fundamental forces of the universe. It is a force that involves the interactions between
electrically charged particles that occur due to their charge and for the emission and absorption of photons. An electromagnetic force
generates an electromagnetic field, which exerts on electrically charged particles. Electricity and magnetism are two aspects of a single
electromagnetic force. On the macroscopic scale, both electric and magnetic forces behave differently, even though they are identical
at the subatomic scale, where moving charges create both electrical and magnetic fields.
Scottish physicist James Clerk Maxwell was able to deduce that electricity and magnetism are mutual manifestations of the same force
involving the exchange of photons. By means of his mathematical equations, he was able to integrate light and wave phenomena into
electromagnetism; illustrating how electric and magnetic fields travel together through space as waves of electromagnetism with
changing fields reciprocally sustaining one another.
To learn more about James Clerk Maxwell, go to http://www.clerkmaxwellfoundation.org/
Excluding gravity, electromagnetic forces are responsible for nearly all the phenomena encountered in daily life. It is a force that acts on
electrically charged particles, such as protons and electrons. Electrically charged particles are influenced by and create electromagnetic
fields. Consequently, electric and magnetic forces may be acknowledged in regions called electric and magnetic fields. The interaction
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between a moving charge and the electromagnetic field is the primary source of the electromagnetic force. Thus electricity and
magnetism are ultimately inextricably linked. However, in many cases, one aspect may dominate, and the separation is meaningful.
To learn more about the physics of electromagnetic forces and fields, go to
http://www.chemistrydaily.com/chemistry/Electromagnetism
Electric Force
The heart of the electric force lies with charge, which like mass, is an intrinsic property of matter. However, unlike mass, there are two
kinds of charges, commonly referred to as positive and negative. In the 1900s, Ernest Rutherford and Niels Bohr proposed a simple
model of the atom illustrating that ordinary matter is made up of atoms, which have positively charged nuclei and negatively charged
electrons surrounding them.
An electron has a fundamental negative charge and a proton has a fundamental positive charge. The unit of electric charge is the
Coulomb, which is 6.24 x 1018 natural units of electric charge (i.e., 6.24 x 1018 times greater than the charge on an electron or proton).
Therefore, charges on an electron are negative and very small (-1.6 x 10-19 Coulombs) and charges on a proton are positive and very
small (+1.6 x 10-19 Coulombs). A positive charge can join with a negative charge and result in a net charge of zero. Most importantly,
charge is always conserved in a system. In other words, charge cannot be created or destroyed, and the net charge in an isolated
system will not change.
Figure 1. Charge Interactions (from
http://www.glenbrook.k12.il.us/gbssci/phys
/Class/estatics/u8l1c.html)
The ancient Greeks discovered that by rubbing amber together, it attracted small, light objects. Greek philosopher, Thales of Miletus,
believed that amber had a soul as well as another Greek philosopher three centuries later, Theoprastus. Though little progress in the
study of electricity occurred within the 2,000 year period after Theoprastus; however, an English physician, William Gillbert published in
which declared many other substances other than amber could be charged by rubbing as well. He coined these substances with a Latin
name electrica, which is derived from the Greek word elektron, which means “amber”. In 1646, English writer and physician Sir Thomas
Browne, first used the word electricity. A common day example of electric charge being transferred between two objects would be by
rubbing them together plastic and fur. This would result in electrons from the fur being rubbed off onto the plastic and leaving the fur
positively charged, meanwhile the plastic negatively charged.
Figure 2. Electric Charge (from
http://www.physics.sjsu.edu/becker/physics51/elec_charge.htm)
The fundamental rule at the base of all electrical phenomena is that “like charges repel and unlike charges attract.”
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Figure 3. Charge Interactions (from
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l1c.html)
The law that describes how strongly charges push and pull each other is called Coulomb’s Law. The equation consists of two charges
Q1 and Q2 separated by a distance r with the magnitude of the force proportional to the charges, and, as with gravitation, inversely
proportional to the square of the distance between them. Between any two charged particles, electric force is infinitely greater than the
gravitational force. Most observable forces such as those exerted by a coiled spring or friction may be directed to electric forces acting
between atoms and molecules. The electric force, in particular, is responsible for most of the physical and chemical properties of atoms
and molecules.
Figure 4. Illustration of Coulomb’s Law
(from
http://www.sciencemadesimple.
com/static.html)
To learn more about electric forces, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html
Electric Field
Fields of electric forces are a common way to depict the effects that charges have on one another. Instead of looking at the force
between two charges, we look at how a charge creates a force "field" in the empty space around it. For example, an electric field will
surround an isolated positive change and a negative charge placed anywhere in this force field is attracted toward the positive charge.
Similarly, a positive charge placed in identical location will be repelled. Furthermore, the motion of an individual charge may be affected
by its interaction with the electric field and, for a moving charge, the magnetic field. Hence, a moving electric charge will produce a
magnetic field and a charge moving in a magnetic field will experience an electric force.
Figure 5. Electric Field: Positive and Negative Fields
(from http://www2.glenbrook.k12.il.us/gbssci/phys/
Class/estatics/u8l4c.html)
The strength of an electric field E at any point is defined as the electric force F exerted per unit positive electric charge q at that point, or
E = F/q. An electric field collectively has direction and magnitude and can be characterized by lines of forces, or field lines, that start on
positive charges and expire on negative charges. The electric field is stronger where the field lines are close together than where they
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are farther apart. The value of the electric field has dimensions of force per unit charge and is measured in units of Newton’s per
Coulomb (N/C).
Figure 6. Electric Field: Field lines near equal but opposite charges Z
(from http://www.iop.org/Our_Activities/Schools_
and_ Colleges/Teaching_Resources/Teaching%20Advanced
%20Physics/Fields/ Electrical%20Fields/page_4802.html)
To learn more about electric fields, go to
http://www.colorado.edu/physics/2000/waves_particles/wavpart3.html
Magnetism and Electromagnetism
Magnetism is another aspect of an electromagnetic force. Recall that an electric field acting on a charge occurs from the presence of
other charges and from a varying magnetic field. Reversely, the magnetic field acting on a moving charge arises from the motion of
other charges and from an alternating electric field. Though they may be interrelated, they behave quite differently.
Magnetic Force
A magnetic force is an attraction or repulsion that occurs between electrically charged particles that are in motion. Whilst only electric
forces exist among stationary electric charges, both electric and magnetic forces reside among moving electric charges. The magnetic
force between two moving charges is the force exerted on one charge by a magnetic field created by the other. This force is zero if the
second charge is traveling in the direction of the magnetic field due to the first and is greatest if it travels at right angles to the magnetic
field. Magnetic force is responsible for the action of electric motors and the attraction between magnets and iron.
Figure 7. Magnetic Force: force between small permanent bar magnets (from
http://www.swe.org/iac/images/NewMagnet.jpg)
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Figure 8. Magnetic force acting on a charged particle that is moving
perpendicular to a magnetic field. (from http://www.windows.
ucar.edu/physical_science/magnetism/images/
force_charge_vel_mag_field_vectors.jpg)
The magnetic field is the resultant of moving electrically charged particles or intrinsic within magnetic objects such as a magnet. In a
magnet, the atomic structure is such that the magnetic fields around individual atoms (due to moving electrons) are aligned together to
create an overall additive effect. Because of this additive effect, a magnet is an object that demonstrates a strong magnetic field and will
attract materials like iron. Magnets are dipoles, having two poles called the north seeking pole (N) and south seeking pole (S). Two
magnets will be attracted by their opposite poles, and each will repel the like pole of the other magnet. The north and south magnetic
poles of a magnetic object are related to the Earth's north and south magnetic poles. The magnetic flux is defined as moving from North
to South. Magnetism has countless uses in modern life such as: a can opener, a navigational compass, refrigerator magnets, motors,
computer diskettes, speakers, VCR/VHS tape, refrigerator, clothes dryer, etc.
Figure 9. Magnetic Flux
(from http://www-
spof.gsfc.nasa.gov/Education/wmfield.html)
To learn more about magnetism, go to
http://www-spof.gsfc.nasa.gov/Education/Imagnet.html
Magnetic Field
Magnetic forces can be detected in regions called magnetic fields. A changing electric field may produce a magnetic field and vice
versa, independent of exterior change. A magnetic field is part of an electromagnetic field that exerts a force on a moving charge. A
magnetic field is a region around a magnet, moving charge such as an electric current or by a changing electric field. The effects of
such forces are unmistakable in the deflection of an electron beam in a cathode-ray tube and the motor force on a current-carrying
conductor. In addition, magnetic fields such as that of Earth can cause magnetic compass needles and other permanent magnets to
line up in the direction of the field.
Figure 10. Magnetic field or lines of flux of a moving charged particle.
(from http://www.school-for-
7
champions.com/science/magnetism.htm)
Electromagnetic Waves
The basis of electromagnetism lies with Maxwell’s equations, stating that “an electric field is created when a magnetic field changes,” “a
magnetic field is created when an electric field changes,” and “the direction of the created magnetic field is perpendicular to the
changing electric field.” Anytime an electron is accelerated, an electric field is created, thus beginning the process of creating sustained
electromagnetic fields which propagate energy even in the vacuum of deep space. For convenience, we call these electromagnetic
waves or simply light. Visible light represents only a small part of the electromagnetic spectrum, but is most common to use because
we observe visible light with our eyes. Other portions of electromagnetic spectrum include radio waves, microwaves, infrared radiation,
ultraviolet radiation, X-rays, and gamma rays.
To learn more about electromagnetic waves, go to
http://www.colorado.edu/physics/2000/waves_particles/index.html
Objective B3
In physics, a charge may also be known as an electric charge, electrical charge, or electrostatic charge and symbolized with either
letters e or q, which represents the quantity of a charge of a single particle possessing more or fewer electrons than protons. Electric
charge is a fundamental property which determines the electromagnetic interaction between subatomic particles. Electrically charged
particles are affected by and produce electromagnetic fields. This interaction that occurs between a moving charge and the
electromagnetic field is the foundation of the electromagnetic force, which is one of the four fundamental forces.
An electric charge is a trait of a subatomic particle, which becomes quantized when expressed as a multiple of an elementary charge
(e). In atoms, an electron carries a negative elementary or unit charge; whereas the proton carries a positive elementary or unit charge.
Both charges are equal and opposite of one another. This is an elemental physical constant and units of an electric charge are in
atomic units. Charged particles with identical sign repel one another, whilst opposite sign charged particles attract. This is illustrated
quantitatively in Coulomb’s Law, which states the quantity of the repelling force is proportional to the product of the two charges, and
decreases proportionality to the square of the distance.
Elementary Charge
When two objects possessing an electric charge are brought near each other, an electrostatic force is created between them. An
electrostatic force is the resultant of an electrostatic field which surrounds any object that is charged. Thus, the electric field strength at
any given distance from an object is directly proportional to the amount of charge on the object. Yet, in close proximity to any object
having a fixed electric charge, the electric field strength dwindles in proportion to the square of the distance from the object; also known
as the inverse square law.
To get some general information about the inverse square law, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html
An electrical charge occurs whenever the number of protons in the nucleus of an atom differs from the number of electrons surrounding
that nucleus. If there are more electrons than protons, the atom will have a negative charge. If there are fewer electrons than protons,
the atom will have a positive charge. For example, charging something can be compared to removing bricks from a road and putting
them on a sidewalk: There are exactly as many “holes” in the road as there are bricks on the sidewalk.
This is alike, but opposite in polarity to the electrical charge carried by the proton. A particle, atom, or object with a negative charge
encompasses a negative electric polarity; a particle, atom, or object with a positive charge encompasses a positive electric polarity.
Fundamentally, if electrical charges are of identical polarity, the electrostatic force is repulsive. If the electrical charges are of opposite
polarity, the electrostatic force is attractive. A positive net force equals a repulsive force, and a negative net force is attractive. This
relation is known as Coulomb's law.
Figure 1: Electric charges (from
http://www.studyphysics.ca/30/charging.pdf)
For more information about electrical charges, go to
http://library.thinkquest.org/10796/ch11/ch11.htm
The Law of Conservation of Charge says that charge is neither created nor destroyed. In every event, whether macro to microscopic,
the principle of conservation of charge applies. Any object that is electrically charged has an excess or deficiency of some whole
number of electrons - electrons cannot be fractioned. Therefore, the charge of an object is a whole-number multiple of the charge of the
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single electron. In essence, the quantity of charge accepted by an atom is always a multiple of the elementary charge; an electrical
charge carried by a single electron or a single proton.
Coulomb of Charge
The net charge of an object consisting of atoms is equivalent to the arithmetic summation, with the consideration of polarity, of the
charges of all the atoms combined. The unit of an electrical charge quantity in the International System of Units is the Coulomb. One
Coulomb (1 C) is equal to approximately 6.24 x 1018 elementary charges. Therefore, an elementary charge is approximately 1.60 x 10 19 C. One Coulomb is roughly equal to the amount of charge that passes through a 100-W light bulb in one second. In the real world, it
is not uncommon for objects to hold charges of many Coulombs.
Electrical Forces
The interaction between charged objects is a non-contact force, which diminishes rapidly with distance. Every electrical force involves
at least two charged objects and a distance between these objects. For example, two-like charged balloons repel each other and the
strength of their repulsive force can be altered by changing three variables. The first measure of charge on one of the balloons will
affect the strength of the repulsive force. The greater the charge is on a balloon, the greater its repulsive force. The second measure of
charge on the second balloon will also affect the strength of repulsive force. Gently rub the two balloons with animal fur, students
should notice that they will repel a bit. Now, rub the two balloons together energetically, increasing the charge and the repulsive force.
Lastly, the distance between the two balloons will have momentous and apparent effect upon the repulsive force. The electrical force is
noticeably strongest when the balloons are closest together. Simply stated, decreasing the distance between the two balloons, greatly
increases the electrical force. The magnitude of the electrical force and the distance between the two balloons is understood to be
inversely related.
Figure 2: Example Problem
(from http://www.studyphysics.ca/30/coulomb.pdf)
To learn more about electrical forces, go to
http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html
Coulomb’s Law
Recall from Newton’s law of gravitation that gravitational force between two objects of mass m1 and mass m2 is proportional to the
product of the masses and inversely proportional to the square of the distance d between them where G is the universal gravitational
constant. The electrical force between any two objects obeys a similar inverse-square relationship with distance.
This relationship was discovered by eighteenth century French physicist Charles Coulomb (1736 – 1806). Coulomb demonstrated that
a force is also proportional to the product of the charges. His work, the unit of electrical charge is named after him and interestingly one
of the first people to begin designing the metric system.
To learn more about Charles Coulomb, go to
http://www-history.mcs.st-and.ac.uk/Biographies/Coulomb.html
Coulomb being familiar with how like charges repel, he observed using the torsion balance, the spheres on the torsion balance twist
away from the other balls.
Figure 3: Torsion Balance
(from http://www.studyphysics.ca/30/coulomb.pdf)
By identifying the following: distance between the balls, the force needed to twist them or torque, and the charges on the balls, he was
able to construct a formula. In equation form, Coulomb's law can be stated as
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Figure 4: Coulomb’s Law (from
http://library.thinkquest.org/10796/ch11/ch11.htm)
which means the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the
objects and inversely proportional to the square of the separation distance between the two objects. It provides an accurate portrayal of
the force between two objects when the objects act as point charges.
For example, a charged conducting sphere interacts with other charged objects in a behavior that eludes its charge to be located at its
center. While the charge is uniformly broadened across the surface of the sphere, the center of charge can be deemed as the center of
the sphere. The sphere acts as a point charge with its excess charge located at its center. Since Coulomb's law applies to point
charges, the distance d in the equation is the distance between the centers of charge for both objects; not the distance between their
nearest surfaces (http://www.glenbrook.k12.il.us/gbssci/Phys/Class/estatics/u8l3b.html).
Coulomb’s Law Constant (k) and Newton’s Gravitational Force (G)
The proportionality constant k in Coulomb’s Law is analogous to G in Newton’s Law of Universal Gravitation. However, instead of being
a minute number like G, the electrical proportionality constant k is a very large number; k = 9.0 x 109 N*m2/C2. Here is a comparison of
Newton’s Law of Universal Gravitation and Coulomb’s Law.
Figure 5: Comparison (from
http://www.studyphysics.ca/30/coulomb.pdf)
Contrast this with the gravitational force of attraction between two masses of 1 kg, each a distance of 1 m apart: 6.67 x 10 -11 N. This is
an exceptionally small force. For the force to be 1 N, two masses 1 m apart would have to be about 122,000 kilograms each.
Gravitational forces between ordinary objects are significantly too small to be exposed except in experiments. Electrical forces between
ordinary objects are large enough to be commonly experienced.
Example Problem #1:
Calculate the electrostatic force exerted on an electron by a proton at a distance of 10 -10m. Compare this with the gravitational force
between the two. In the light of your comparison, discuss why gravity, and not electromagnetism, is the fundamental force most
apparent to us on a macroscopic scale.
G: Identify known values in variable form.
O: Identify the unknown value
A: Substitute and solve
From Coulomb’s law, the force between an electron and a proton at a distance of 10 -10 m has a magnitude of
For comparison, the magnitude of the gravitational force between the same two particles is
Inverse Square Law
The relationship between electrostatic force and distance can be further portrayed as an inverse square relationship. By means of
careful observations, an electrostatic force between two point charges may vary inversely with the square of the distance between two
charges. Understanding this inverse proportionality will allow the students to develop a better awareness about how to use the equation
in terms of as a guide; a guide towards thinking about how variation in one quantity may affect another quantity. The inverse square law
is a simple recipe for many algebraic problem-solving.
The inverse square relationship between electrostatic force and separation distance is illustrated in the table below.
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Row
Separation Distance
Electrostatic Force
1
20.0 cm
0.1280 N
2
40.0 cm
0.0320 N
3
60.0 cm
0.0142 N
4
80.0 cm
0.0080 N
5
100.0 cm
0.0051 N
Figure 5: Inverse Square Law
(from
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l3c.html)
Example Problem #2:
Two charged objects have a repulsive force of .080 N. If the distance separating the objects is doubled, then what is the new force?
Answer: 0.020 N
Explanation: The electrostatic force is inversely related to the square of the separation distance. So if d is two times larger, then F is
four times smaller - that is, one-fourth the original value. One-fourth of 0.080 N is 0.020 N.
To learn more about the Inverse Square Law, go to
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/estatics/u8l3c.html
Objective B4
Most students will be able to say that gravity is the force that pulls things down. Though known prior to his birth, Newton is credited with
the discovery that gravity is universal (i.e., any object with mass has a gravitational field). The force that causes objects to “fall” (all
objects are PULLED to the CENTER of a mass) on Earth is the (1) same force that causes the Earth to continuously orbit the Sun, and
in turn, (2) the Sun to revolve around the center of the Milky Way Galaxy.
Figure 1. Shows the effect of an increasing mass and an
increase in distance between the masses
(from http://www.physicsclassroom.com/
Class/circles/U6L3c.html)
Gravity, the name referring to the attractive forces between objects, is a theory explaining the cause of these attractions. Through
observations of its affect on objects and the use of Newton’s laws of motion, gravitational force is measurable. Gravitational force is a
field force that is infinite in distance and therefore extends throughout the universe. However, gravitational force diminishes greatly with
separation between the masses (the inverse square law). Newton’s Law of Universal Gravitation states that every object attracts every
other object and that the force of attraction is directly proportional to the masses of the objects; and, as stated above, inversely
proportional to the square of the distances between the two masses. This law is represented symbolically as:
F~
m1m2
d2
m1 = mass of the first object (kg)
m2 = mass of the second object (kg)
d2 = the square of the distances between the centers of the masses (m)
To learn more about Newton’s Law of Universal Gravitation go to
http://www.physicsclassroom.com/Class/circles/U6L3c.html.
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Thanks to experiments by Henry Cavendish, Newton’s Law of Universal Gravitation can be written as an exact equation when including
the Universal Gravitational Constant (G). Cavendish, in the eighteenth century, measured the torsion force in a bar as two large lead
spheres were brought close to the masses at the end of the bar. By carefully measuring all the masses, the force of torsion, and the
distance the balance was twisted, Cavendish could calculate G. Due to Cavendish’s discovery of the gravitational constant, G = 6.67 x
10-11 N m2/kg2 the universal gravitational law can be written as the exact equation:
F=
G m1m2
d2
F = force (N)
G = gravitational force constant (6.67 x 10-11 N m2/kg2)
m1 = mass of the first object (kg)
m2 = mass of the second object (kg)
d2 = the square of the distances between the centers of the masses (m)
Gravity is one of the four fundamental forces (the others are the strong nuclear, electromagnetic, and weak nuclear). With G being so
small, gravity is the weakest of the four fundamental forces.
To learn more about the four fundamental forces, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html#c1
Figure 3. This is a quantitative graph that shows the acceleration on an
object, due to the force of gravity, decreasing as the distance between the
masses increases. (from http://www.physicsclassroom.com/
Class/circles/U6L3e.html)
Though the force of gravity decreases as distance increases, gravitational forces do not cease. It must be understood that Earth’s
gravitational force on an object will diminishes with distance, but it will NEVER reach zero. Even if an object were placed at the farthest
reaches of space Earth’s gravitational force will still be present. The measurable amount of force from Earth may be very small at this
point, when compared to the gravitational forces of other bodies closer to the object, but it will never be zero. This rapid reduction of the
gravitational forces between two objects as the distance between the objects increases follows the inverse square law.
For more information about the inverse square law and gravity go to http://hyperphysics.phy-
astr.gsu.edu/hbase/forces/isq.html#isqg.
Einstein furthered Newton’s work on gravitation with General Relativity, where the cause of the gravitational force is described. In
General Relativity, gravitation is a geometric property caused when masses deform space and time. We perceive this geometric
property as a force of attraction between masses as defined by Newton’s Law of Universal Gravitation. To learn more about General
Relativity, go to http://archive.ncsa.uiuc.edu/Cyberia/NumRel/GenRelativity.html
Other concepts associated with gravity include weight, centripetal force, tides, and escape velocity. To learn more about the connection
to gravity, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grvcon.
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