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BHS PHYSICS-UNIT04: DYNAMICS
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UNIT04: Dynamics
This unit, Newton's Laws of Motion, will discuss the ways in which motion can be
explained. Isaac Newton (a 17th century scientist) put forth three laws which explain why
objects move (or don't move) as they do and these three laws have become known as
Newton's three laws of motion.
A. Definitions


Dynamics: The study of why the state of motion for an object changes … using
Newton’s Laws of Motion
Kinematics: The study of how the motion of an object can be described … using
words, graphs, diagrams, and equations.
Newton’s Laws of Motion:



Newton's First Law of Motion: An object at rest tends to stay at rest and an object
in motion tends to stay in motion with the same speed and in the same direction
unless acted upon by an unbalanced force.
Newton's Second Law of Motion: The acceleration of an object as produced by a
net force is directly proportional to the magnitude of the net force, in the same
direction as the net force, and inversely proportional to the mass of the object.
Newton's Third Law of Motion: For every action, there is an equal and opposite
reaction.
By the end of this unit, you will be able to analyze scenarios like the Turkish Twist at
Canobie Lake Park, where riders are *stuck* to a neoprene wall inside of a horizontal
cylinder spinning at a high rate of speed (see illustration below):
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B. What are Forces?
A force is a push or pull upon an object resulting from the object's interaction with another
object. Whenever there is an interaction between two objects, there is a force acting on
each of the objects. When the interaction ceases, the two objects no longer experience a
force.
All forces (interactions) between objects can be placed into two broad categories:


Contact forces are types of forces in which the two interacting objects are
physically in contact with each other. Examples of contact forces include frictional
forces, tensional forces, normal forces, air resistance forces, and applied forces.
Action-at-a-distance forces are types of forces in which the two interacting
objects are not in physical contact with each other, but are able to exert a push or
pull despite the physical separation. Examples of action-at-a-distance forces
include gravitational forces, electric forces, and magnetic forces.
Force is a quantity which is measured using a standard metric unit known as the Newton.
One Newton is the amount of force required to give a 1-kg mass an acceleration of 1 m/s2.
A Newton is abbreviated by an "N." If you say "10.0 N," you mean 10.0 Newtons of force.
Thus, the following unit equivalency can be stated:
Force is a vector quantity. A vector quantity is a quantity which has both magnitude and
direction. To fully describe the force acting upon an object, you must describe both its
magnitude (size) and its direction. Thus, 10 Newtons is not a full description of the force
acting upon an object. In contrast, 10 Newtons, downwards is a complete description of
the force acting upon an object; both the magnitude (10 Newtons) and the direction
(downwards) are given.
Because force is a vector and has direction, it is common to represent forces using
diagrams in which the force is represented by an arrow. Such diagrams are called Free
Body Diagrams. The size of the arrow is reflective of the magnitude
of the force and the direction of the arrow reveals the direction in
which the force is acting. Because forces are vectors, the influence
of one individual force upon an object is often canceled by the
influence of another force acting on the same object. For example,
the influence of a 20-Newton upward force acting upon a book is
canceled by the influence of a 20-Newton downward force acting
upon the book. In such instances, the two individual forces are said
to "balance each other"; there would be no unbalanced force acting
upon this book.
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Forces that will be considered in this Unit:
Name of Force
Symbol
Gravitational Force
(also known as
Weight)
Force at a Distance Forces
The gravitational force is the force with which the earth, moon, or other massive body
attracts an object towards itself. By definition, this is the weight of the object. All
objects upon earth experience a gravitational force which is directed "downward"
towards the center of the earth. The gravitational force on an object on earth is always
equal to the weight of the object as given by the equation:
Fgrav = m g
Fgrav
where:
m = mass (in kg)
g = acceleration of gravity = 9.81 m/s2 (on Earth)
Name of Force
Symbol
Applied Force
Fapp
Normal Force
Fnorm
Friction Force
Ffrict
Contact Forces
An applied force is a force which is applied to an object by another object or by a
person. If a person is pushing a desk across the room, then there is an applied force
acting upon the desk. The applied force is the force exerted on the desk by the person.
The normal force is the support force exerted upon an object which is in contact with
another stable object. For example, if a book is resting upon a surface, then the
surface is exerting an upward force upon the book in order to support the weight of
the book. On occasion, a normal force is exerted horizontally between two objects
which are in contact with each other.
The friction force is the force exerted by a surface as an object moves across it or
makes an effort to move across it. The friction force opposes the motion of the object.
For example, if a book moves across the surface of a desk, the desk exerts a friction
force in the direction opposite to the motion of the book. Friction results when two
surfaces are pressed together closely, causing attractive intermolecular forces
between the molecules of the two different surfaces. As such, friction depends upon
the nature of the two surfaces and upon the degree to which they are pressed together.
The friction force can be calculated using the equation:
Ffrict = µ Fnorm
where:
µ = coefficient of friction (unitless)
Drag Force
Fdrag
Tension Force
Ftension
Spring Force
Fspring
The drag force is a special type of frictional force which acts upon objects as they
travel through a fluid. Like all frictional forces, the drag force always opposes the
relative motion of the object. This force will frequently be ignored due to its
negligible magnitude. It is most noticeable for objects which travel at high speeds
(e.g., a skydiver or a downhill skier) or for objects with large surface areas.
Tension is the force which is transmitted through a string, rope, or wire when it is
pulled tight by forces acting at each end. The tensional force is directed along the
wire and pulls equally on the objects on either end of the wire.
The spring force is the force exerted by a compressed or stretched spring upon any
object which is attached to it. This force acts to restores the object, which compresses
or stretches a spring, to its rest or equilibrium position. For most springs (specifically,
for those said to obey "Hooke's Law"), the magnitude of the force is directly
proportional to the amount of stretch or compression.
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Free-Body Diagrams: Free-body diagrams are diagrams used to show the relative
magnitude and direction of all forces acting upon an object in a given situation.
The size of the arrow in a free-body diagram is reflective of the magnitude of the force.
The direction of the arrow reveals the direction in which the force acts. Each force arrow
in the diagram is labeled to indicate the type of force. It is customary in a free-body
diagram to represent the object by a box and to draw the force arrow from the center of the
box outward in the direction in which the force is acting. Two examples of free-body
diagrams are shown below.
Object Resting on a Desk
Physical
Situation
Free-Body
Diagram
Box on a String
Physical
Situation
Free-Body
Diagram
BHS PHYSICS-UNIT04: DYNAMICS
Even though the cartoon below does not make sense from a physics standpoint (why?), it
provides an opportunity to practice making Free-Body Diagrams. Sketch free body
diagrams for the elephant, the monkey, and the second pulley in from the right. Illustrate
all influences on these objects from other objects by showing arrows that point in the
appropriate directions and label them consistent with the table on the previous page.
Neglect all friction.
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Select an object from each of the images below. In the corresponding box to the right,
identify and sketch a free body diagram for the object selected. In each case, represent the
object by a dot and replace all of the external influences on that object by appropriately
labeled arrows that represent each of the external forces.
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C. Newton's First Law of Motion
Newton's First Law of Motion: An object at rest tends to stay at rest and an
object in motion tends to stay in motion with the same speed and in the
same direction unless acted upon by an unbalanced force.
There are two parts to this statement – one which predicts the behavior of stationary
objects and the other which predicts the behavior of moving objects. These two parts are
summarized in the following diagram.
Newton's first law of motion is sometimes referred to as the "law of inertia." The behavior
of all objects can be described by saying that objects tend to "keep on doing what they're
doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this
same state of rest. If in motion with an eastward velocity of 5 m/sec, they will continue in
this same state of motion (5 m/sec, East). If in motion with a westward velocity of 2 m/s,
they will continue in this same state of motion (2 m/sec, West). The state of motion of an
object is maintained as long as the object is not acted upon by an unbalanced force. All
objects resist changes in their state of motion – they tend to "keep on doing what they're
doing."
The Big Misconception: The idea which dominated the thinking for nearly 2000 years
prior to Newton was that it was the natural tendency of all objects to assume a rest
position. This misconception rears its ugly head in a number of different ways (and at a
number of different times).
Newton's laws declare loudly that a net force (an unbalanced force) causes an acceleration
and the acceleration is in the same direction as the net force.
Newton’s laws also declare that no force is required for an object to just keep moving at
constant speed in a straight line. Conversely, if an object is moving at constant speed in a
straight line, then there is no net force acting on an object
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D. Newton’s Second Law
Newton's Second Law of Motion: The acceleration of an object as
produced by a net force is directly proportional to the magnitude of the
net force, in the same direction as the net force, and inversely proportional
to the mass of the object.
Newton's second law of motion pertains to the behavior of objects for which all existing
forces are not balanced. The second law states that the acceleration of an object is
dependent upon two variables – the net force acting upon the object and the mass of the
object. The acceleration of an object depends directly upon the net force acting upon the
object, and inversely upon the mass of the object. As the net force increases, so will the
object's acceleration. However, as the mass of the object increases, its acceleration will
decrease.
In terms of an equation, the net force is equal to the product of the object's mass and its
acceleration.
Fnet = m a
Throughout this lesson, the emphasis has been on the "net force." The acceleration is
directly proportional to the "net force;" the "net force" equals mass times acceleration; the
acceleration is in the same direction as the "net force;" an acceleration is produced by a
"net force." The NET FORCE. It is important to remember this distinction. If all the
individual forces acting upon an object are known, then the net force can be determined.
By substituting standard metric units for force, mass, and acceleration into the above
equation, the following unit equivalency can be written:
One Newton is defined as the amount of force required to give a 1-kg mass an acceleration
of 1 m/s2.
BHS PHYSICS-UNIT04: DYNAMICS
Check Your Understanding (perform all calculations to two significant digits)
1. What acceleration will result when a 12-N net force is applied to a 3.0 kg object?
A 6.0 kg object?
2. A net force of 16 N causes a mass to accelerate at the rate of 5.0 m/s2. Determine
the mass.
3. An object is accelerating at 2.0 m/s2. If the net force is tripled and the mass of the
object is doubled, what is the new acceleration?
4. An object is accelerating at 2.0 m/s2. If the net force is tripled and the mass of the
object is halved, what is the new acceleration?
5. Free-body diagrams for four situations are shown below. The net force is known
for each situation. However, the magnitudes of several of the individual forces are
not known. Analyze each situation individually to determine the magnitude of the
unknown forces.
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6. An applied force of 50 N is used to accelerate an object to the right across a
frictional surface. The object encounters 10 N of friction. Use the diagram to
determine the normal force, the net force, the mass, and the acceleration of the
object. (Neglect air resistance.)
7. An applied force of 20 N is used to accelerate an object to the right across a
frictional surface. The object encounters 10 N of friction. Use the diagram to
determine the normal force, the net force, the coefficient of friction (µ) between
the object and the surface, the mass, and the acceleration of the object. (Neglect air
resistance.)
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8. A rightward force is applied to a 6-kg object to move it across a rough surface at
constant velocity. The object encounters 15 N of frictional force. Use the diagram
to determine the gravitational force, normal force, net force, and applied force.
(Neglect air resistance.)
9. A rightward force is applied to a 10-kg object to move it across a rough surface at
constant velocity. The coefficient of friction, µ, between the object and the surface
is 0.2. Use the diagram to determine the gravitational force, normal force, applied
force, frictional force, and net force. (Neglect air resistance.)
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E. Newton's Third Law
Newton's Third Law of Motion: For every action, there is an equal and
opposite reaction.
The statement means that in every interaction, there is a pair of
forces acting on the two interacting objects. The size of the
force on the first object equals the size of the force on the
second object. The direction of the force on the first object is
opposite to the direction of the force on the second object. Forces always come in pairs –
equal and opposite action-reaction force pairs.
A variety of action-reaction force pairs are evident in nature. Consider the propulsion of a
fish through the water. A fish uses its fins to push water backwards. But a push on the
water will only serve to accelerate the water. In turn, the water reacts by pushing the fish
forwards, propelling the fish through the water. The size of the force on the water equals
the size of the force on the fish; the direction of the force on the water (backwards) is
opposite to the direction of the force on the fish (forwards). For every action, there is an
equal (in size) and opposite (in direction) reaction force. Action-reaction force pairs make
it possible for fishes to swim.
Check Your Understanding
1. While driving, suppose a bug strikes the windshield of your car. Obviously, a case of
Newton's third law of motion. The bug hit the windshield and the windshield hit the bug.
Which of the two forces is greater: the force on the bug or the force on the windshield?
2. A gun recoils when it is fired. The recoil is the result of Newton’s Third Law. As the gases
from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet
pushes the gun backwards. How do the accelerations of the bullet and the gun compare?
F. Free Fall and Drag
Free fall is a special type of motion. Objects which are
said to be undergoing free fall, are not encountering a
significant force of air resistance; they are falling solely
under the influence of gravity. During free fall, all objects
will experience the same acceleration, regardless of their
mass. But why? Consider the free-falling motion of a
1000-kg baby elephant and a 1-kg overgrown mouse.
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From a free-body diagram, it can be seen that the 1000-kg baby elephant
experiences a greater force of gravity. According to Newton’s Second Law,
his greater force of gravity would have a direct affect upon the elephant's
acceleration; thus, based on force alone, it might be thought that the baby
elephant would accelerate faster. But acceleration depends upon two factors:
force and mass. The 1000-kg baby elephant obviously has more mass (or
inertia). This increased mass has an inverse affect upon the elephant's
acceleration. And thus, the direct affect of greater force on the 1000-kg
elephant is offset by the inverse affect of the greater mass of the 1000-kg
elephant; and so each object accelerates at the same rate - approximately 10
m/s/s. The ratio of force to mass (Fnet/m) is the same for the elephant and the
mouse under situations involving free fall.
Falling with Air Resistance (Drag): As an object falls through air, it usually encounters
some degree of air resistance. The drag force is the result of collisions of the object's
leading surface with air molecules. The actual amount of drag encountered by the object is
dependent upon a variety of factors. The two most common factors which have a direct
affect upon the amount of drag are the speed of the object and the cross-sectional area of
the object. Increased speeds result in an increased amount of air resistance. Increased
cross-sectional areas result in an increased amount of air resistance. Below are four freebody diagrams showing the forces acting upon an 85-kg skydiver falling at various speeds.
For each case, find the net force and acceleration of the skydiver at each instant in time.
The diagrams above illustrate a key principle. As an object falls, it picks up speed. The
increase in speed leads to an increase in the amount of air resistance. Eventually, the force
of air resistance becomes large enough to balances the force of gravity. At this instant in
time, the net force is 0 Newtons; the object will stop accelerating. The object is said to
have reached a terminal velocity.
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