electricity) and magnetic forces (such as those that affect a compass needle). These two forces were thought to be quite distinct until early in the 19th
century, when scientists began to discover that they are different manifestations of the same force. This discovery is a classical case of the unification
of forces. Similarly, friction, tension, and all of the other classes of forces we experience directly (except gravity, of course) are due to electromagnetic
interactions of atoms and molecules. It is still convenient to consider these forces separately in specific applications, however, because of the ways
they manifest themselves.
Concept Connections: Unifying Forces
Attempts to unify the four basic forces are discussed in relation to elementary particles later in this text. By “unify” we mean finding connections
between the forces that show that they are different manifestations of a single force. Even if such unification is achieved, the forces will retain
their separate characteristics on the macroscopic scale and may be identical only under extreme conditions such as those existing in the early
universe.
Physicists are now exploring whether the four basic forces are in some way related. Attempts to unify all forces into one come under the rubric of
Grand Unified Theories (GUTs), with which there has been some success in recent years. It is now known that under conditions of extremely high
density and temperature, such as existed in the early universe, the electromagnetic and weak nuclear forces are indistinguishable. They can now be
considered to be different manifestations of one force, called the electroweak force. So the list of four has been reduced in a sense to only three.
Further progress in unifying all forces is proving difficult—especially the inclusion of the gravitational force, which has the special characteristics of
affecting the space and time in which the other forces exist.
While the unification of forces will not affect how we discuss forces in this text, it is fascinating that such underlying simplicity exists in the face of the
overt complexity of the universe. There is no reason that nature must be simple—it simply is.
Action at a Distance: Concept of a Field
All forces act at a distance. This is obvious for the gravitational force. Earth and the Moon, for example, interact without coming into contact. It is also
true for all other forces. Friction, for example, is an electromagnetic force between atoms that may not actually touch. What is it that carries forces
between objects? One way to answer this question is to imagine that a force field surrounds whatever object creates the force. A second object
(often called a test object) placed in this field will experience a force that is a function of location and other variables. The field itself is the “thing” that
carries the force from one object to another. The field is defined so as to be a characteristic of the object creating it; the field does not depend on the
test object placed in it. Earth’s gravitational field, for example, is a function of the mass of Earth and the distance from its center, independent of the
1. The graviton is a proposed particle, though it has not yet been observed by scientists. See the discussion of gravitational waves later in this section.
The particles W+ , W− , and Z0 are called vector bosons; these were predicted by theory and first observed in 1983. There are eight types of
gluons proposed by scientists, and their existence is indicated by meson exchange in the nuclei of atoms.
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presence of other masses. The concept of a field is useful because equations can be written for force fields surrounding objects (for gravity, this
yields w = mg at Earth’s surface), and motions can be calculated from these equations. (See Figure 4.26.)
Figure 4.26 The electric force field between a positively charged particle and a negatively charged particle. When a positive test charge is placed in the field, the charge will experience a force in the direction of the force field lines.
Concept Connections: Force Fields
The concept of a force field is also used in connection with electric charge and is presented in Electric Charge and Electric Field. It is also a useful idea for all the basic forces, as will be seen in Particle Physics. Fields help us to visualize forces and how they are transmitted, as well as
to describe them with precision and to link forces with subatomic carrier particles.
The field concept has been applied very successfully; we can calculate motions and describe nature to high precision using field equations. As useful
as the field concept is, however, it leaves unanswered the question of what carries the force. It has been proposed in recent decades, starting in 1935
with Hideki Yukawa’s (1907–1981) work on the strong nuclear force, that all forces are transmitted by the exchange of elementary particles. We can
visualize particle exchange as analogous to macroscopic phenomena such as two people passing a basketball back and forth, thereby exerting a
repulsive force without touching one another. (See Figure 4.27.)
Figure 4.27 The exchange of masses resulting in repulsive forces. (a) The person throwing the basketball exerts a force Fp1 on it toward the other person and feels a
reaction force FB away from the second person. (b) The person catching the basketball exerts a force Fp2 on it to stop the ball and feels a reaction force F′B away from the first person. (c) The analogous exchange of a meson between a proton and a neutron carries the strong nuclear forces Fexch and F′exch between them. An attractive
force can also be exerted by the exchange of a mass—if person 2 pulled the basketball away from the first person as he tried to retain it, then the force between them would
be attractive.
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This idea of particle exchange deepens rather than contradicts field concepts. It is more satisfying philosophically to think of something physical
actually moving between objects acting at a distance. Table 4.1 lists the exchange or carrier particles, both observed and proposed, that carry the four forces. But the real fruit of the particle-exchange proposal is that searches for Yukawa’s proposed particle found it and a number of others that
were completely unexpected, stimulating yet more research. All of this research eventually led to the proposal of quarks as the underlying
substructure of matter, which is a basic tenet of GUTs. If successful, these theories will explain not only forces, but also the structure of matter itself.
Yet physics is an experimental science, so the test of these theories must lie in the domain of the real world. As of this writing, scientists at the CERN
laboratory in Switzerland are starting to test these theories using the world’s largest particle accelerator: the Large Hadron Collider. This accelerator
(27 km in circumference) allows two high-energy proton beams, traveling in opposite directions, to collide. An energy of 14 million electron volts will
be available. It is anticipated that some new particles, possibly force carrier particles, will be found. (See Figure 4.28.) One of the force carriers of
high interest that researchers hope to detect is the Higgs boson. The observation of its properties might tell us why different particles have different
masses.
Figure 4.28 The world’s largest particle accelerator spans the border between Switzerland and France. Two beams, traveling in opposite directions close to the speed of light,
collide in a tube similar to the central tube shown here. External magnets determine the beam’s path. Special detectors will analyze particles created in these collisions.
Questions as broad as what is the origin of mass and what was matter like the first few seconds of our universe will be explored. This accelerator began preliminary operation
in 2008. (credit: Frank Hommes)
Tiny particles also have wave-like behavior, something we will explore more in a later chapter. To better understand force-carrier particles from
another perspective, let us consider gravity. The search for gravitational waves has been going on for a number of years. Almost 100 years ago,
Einstein predicted the existence of these waves as part of his general theory of relativity. Gravitational waves are created during the collision of
massive stars, in black holes, or in supernova explosions—like shock waves. These gravitational waves will travel through space from such sites
much like a pebble dropped into a pond sends out ripples—except these waves move at the speed of light. A detector apparatus has been built in the
U.S., consisting of two large installations nearly 3000 km apart—one in Washington state and one in Louisiana! The facility is called the Laser
Interferometer Gravitational-Wave Observatory (LIGO). Each installation is designed to use optical lasers to examine any slight shift in the relative
positions of two masses due to the effect of gravity waves. The two sites allow simultaneous measurements of these small effects to be separated
from other natural phenomena, such as earthquakes. Initial operation of the detectors began in 2002, and work is proceeding on increasing their
sensitivity. Similar installations have been built in Italy (VIRGO), Germany (GEO600), and Japan (TAMA300) to provide a worldwide network of
gravitational wave detectors.
International collaboration in this area is moving into space with the joint EU/US project LISA (Laser Interferometer Space Antenna). Earthquakes and
other Earthly noises will be no problem for these monitoring spacecraft. LISA will complement LIGO by looking at much more massive black holes
through the observation of gravitational-wave sources emitting much larger wavelengths. Three satellites will be placed in space above Earth in an
equilateral triangle (with 5,000,000-km sides) (Figure 4.29). The system will measure the relative positions of each satellite to detect passing
gravitational waves. Accuracy to within 10% of the size of an atom will be needed to detect any waves. The launch of this project might be as early as
2018.
“I’m sure LIGO will tell us something about the universe that we didn’t know before. The history of science tells us that any time you go where you
haven’t been before, you usually find something that really shakes the scientific paradigms of the day. Whether gravitational wave astrophysics will do
that, only time will tell.” —David Reitze, LIGO Input Optics Manager, University of Florida
Figure 4.29 Space-based future experiments for the measurement of gravitational waves. Shown here is a drawing of LISA’s orbit. Each satellite of LISA will consist of a laser
source and a mass. The lasers will transmit a signal to measure the distance between each satellite’s test mass. The relative motion of these masses will provide information
about passing gravitational waves. (credit: NASA)
The ideas presented in this section are but a glimpse into topics of modern physics that will be covered in much greater depth in later chapters.
152 CHAPTER 4 | DYNAMICS: FORCE AND NEWTON'S LAWS OF MOTION
Glossary
acceleration: the rate at which an object’s velocity changes over a period of time
carrier particle: a fundamental particle of nature that is surrounded by a characteristic force field; photons are carrier particles of the
electromagnetic force
dynamics: the study of how forces affect the motion of objects and systems
external force: a force acting on an object or system that originates outside of the object or system
force field: a region in which a test particle will experience a force
force: a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a
standard force
free-body diagram: a sketch showing all of the external forces acting on an object or system; the system is represented by a dot, and the forces
are represented by vectors extending outward from the dot
free-fall: a situation in which the only force acting on an object is the force due to gravity
friction: a force past each other of objects that are touching; examples include rough surfaces and air resistance
inertia: the tendency of an object to remain at rest or remain in motion
inertial frame of reference: a coordinate system that is not accelerating; all forces acting in an inertial frame of reference are real forces, as
opposed to fictitious forces that are observed due to an accelerating frame of reference
law of inertia: see Newton’s first law of motion
mass: the quantity of matter in a substance; measured in kilograms
Newton’s first law of motion: a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net
external force; also known as the law of inertia
Newton’s second law of motion: the net external force Fnet on an object with mass m is proportional to and in the same direction as the
acceleration of the object, a , and inversely proportional to the mass; defined mathematically as a = Fnet
m
Newton’s third law of motion: whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude
and opposite in direction to the force that the first body exerts
net external force: the vector sum of all external forces acting on an object or system; causes a mass to accelerate
normal force: the force that a surface applies to an object to support the weight of the object; acts perpendicular to the surface on which the
object rests
system: defined by the boundaries of an object or collection of objects being observed; all forces originating from outside of the system are
considered external forces
tension: the pulling force that acts along a medium, especially a stretched flexible connector, such as a rope or cable; when a rope supports the
weight of an object, the force on the object due to the rope is called a tension force
thrust: a reaction force that pushes a body forward in response to a backward force; rockets, airplanes, and cars are pushed forward by a thrust
reaction force
weight: the force w due to gravity acting on an object of mass m ; defined mathematically as: w = mg , where g is the magnitude and direction of the acceleration due to gravity
Section Summary
4.1 Development of Force Concept
• Dynamics is the study of how forces affect the motion of objects.
• Force is a push or pull that can be defined in terms of various standards, and it is a vector having both magnitude and direction.
• External forces are any outside forces that act on a body. A free-body diagram is a drawing of all external forces acting on a body.
4.2 Newton’s First Law of Motion: Inertia
• Newton’s first law of motion states that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on
by a net external force. This is also known as the law of inertia.
• Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object’s mass.
• Mass is the quantity of matter in a substance.
4.3 Newton’s Second Law of Motion: Concept of a System
• Acceleration, a , is defined as a change in velocity, meaning a change in its magnitude or direction, or both.
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• An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the
system.
• Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external
force acting on the system, and inversely proportional to its mass.
• In equation form, Newton’s second law of motion is a = Fnet
m .
• This is often written in the more familiar form: Fnet = ma .
• The weight w of an object is defined as the force of gravity acting on an object of mass m . The object experiences an acceleration due to
gravity g :
w = mg.
• If the only force acting on an object is due to gravity, the object is in free fall.
• Friction is a force that opposes the motion past each other of objects that are touching.
4.4 Newton’s Third Law of Motion: Symmetry in Forces
• Newton’s third law of motion represents a basic symmetry in nature. It states: Whenever one body exerts a force on a second body, the first
body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.
• A thrust is a reaction force that pushes a body forward in response to a backward force. Rockets, airplanes, and cars are pushed forward by a
thrust reaction force.
4.5 Normal, Tension, and Other Examples of Forces
• When objects rest on a surface, the surface applies a force to the object that supports the weight of the object. This supporting force acts
perpendicular to and away from the surface. It is called a normal force, N .
• When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object:
N = mg.
• When objects rest on an inclined plane that makes an angle θ with the horizontal surface, the weight of the object can be resolved into
components that act perpendicular ( w⊥ ) and parallel ( w ∥ ) to the surface of the plane. These components can be calculated using:
w ∥ = w sin ( θ) = mg sin ( θ)
w⊥ = w cos ( θ) = mg cos ( θ).
• The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension, T . When a rope supports the weight
of an object that is at rest, the tension in the rope is equal to the weight of the object:
T = mg.
• In any inertial frame of reference (one that is not accelerated or rotated), Newton’s laws have the simple forms given in this chapter and all
forces are real forces having a physical origin.
4.6 Problem-Solving Strategies
• To solve problems involving Newton’s laws of motion, follow the procedure described:
1. Draw a sketch of the problem.
2. Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the
forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions
from the dot. If vectors act in directions that are not horizontal or vertical, resolve the vectors into horizontal and vertical components and
draw them on the free-body diagram.
3. Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not
accelerate in a particular direction (for example, the x -direction) then F net x = 0 . If the object does accelerate in that direction,
F net x = ma .
4. Check your answer. Is the answer reasonable? Are the units correct?
4.7 Further Applications of Newton’s Laws of Motion
• Newton’s laws of motion can be applied in numerous situations to solve problems of motion.
• Some problems will contain multiple force vectors acting in different directions on an object. Be sure to draw diagrams, resolve all force vectors
into horizontal and vertical components, and draw a free-body diagram. Always analyze the direction in which an object accelerates so that you
can determine whether F net = ma or F net = 0 .
• The normal force on an object is not always equal in magnitude to the weight of the object. If an object is accelerating, the normal force will be
less than or greater than the weight of the object. Also, if the object is on an inclined plane, the normal force will always be less than the full
weight of the object.
• Some problems will contain various physical quantities, such as forces, acceleration, velocity, or position. You can apply concepts from
kinematics and dynamics in order to solve these problems of motion.
4.8 Extended Topic: The Four Basic Forces—An Introduction
• The various types of forces that are categorized for use in many applications are all manifestations of the four basic forces in nature.
• The properties of these forces are summarized in Table 4.1.
• Everything we experience directly without sensitive instruments is due to either electromagnetic forces or gravitational forces. The nuclear
forces are responsible for the submicroscopic structure of matter, but they are not directly sensed because of their short ranges. Attempts are
being made to show all four forces are different manifestations of a single unified force.
• A force field surrounds an object creating a force and is the carrier of that force.
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Conceptual Questions
4.1 Development of Force Concept
1. Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the
same force repeatedly.
2. What properties do forces have that allow us to classify them as vectors?
4.2 Newton’s First Law of Motion: Inertia
3. How are inertia and mass related?
4. What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?
4.3 Newton’s Second Law of Motion: Concept of a System
5. Which statement is correct? (a) Net force causes motion. (b) Net force causes change in motion. Explain your answer and give an example.
6. Why can we neglect forces such as those holding a body together when we apply Newton’s second law of motion?
7. Explain how the choice of the “system of interest” affects which forces must be considered when applying Newton’s second law of motion.
8. Describe a situation in which the net external force on a system is not zero, yet its speed remains constant.
9. A system can have a nonzero velocity while the net external force on it is zero. Describe such a situation.
10. A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory?
11. (a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the
same net external force acting on systems of different masses, producing different accelerations. (c) What law accurately describes both effects?
State it in words and as an equation.
12. If the acceleration of a system is zero, are no external forces acting on it? What about internal forces? Explain your answers.
13. If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration o