Download Newton`s Second Law of Motion

Physics Chapter 5 Forces
A team of skydivers can form beautiful patterns as they plummet toward Earth at
high speeds of up to 120mph. How do the skydivers control their velocities?
Bad news around 60 sky divers a year use the ground - Fatalities by Year
due to sky diving accidents
2004 (70)
2006 (60)
2005 (62)
2007 (61)
2008 (61)
updated
http://adventure.howstuffworks.com/skydiving.htm
1
Chapters 3 and 4 were limited to a discussion of the study of how objects move,
kinematics. Galileo devised many ingenious experiments that allowed him to
effectively describe motions but not to explain them. Chapter 5 introduces the
subject of dynamics. The study of why objects move as they do. Dynamics can
answer such questions as, "Why do sky divers accelerate rather than fall at a
constant rate?"
The causes of acceleration were first studied by Sir Isaac Newton (1642-1727).
The connection between acceleration and its cause can be summarized by three
statements known, after the man who formulated them, as Newton's laws of
motion.
http://www.neatorama.com/2007/08/08/ten-strange-facts-about-newton/
(Ten strange facts about Newton)
5-1 LAWS OF MOTION
Isaac Newton started work on his laws of motion in 1665, but did not publish them
until 1687. More than three hundred years later, his three laws still summarize the
relationship between acceleration, and its cause, force.
Forces http://videos.howstuffworks.com/discovery/4867-physics-primal-forcesvideo.htm (Four forces of Matter)
Video 4 number 1 forces
What is a force? Force can be defined as a push or a pull. When you hang your
jacket on a coat-hook, the hook pulls upward on your jacket. If you place a coin on
your palm, the coin pushes downward on your hand. These forces occur when
one object touches another. On the other hand, if you drop the coin, it will fall to
the ground, pulled by a force called gravity. Gravity is a force that acts between
objects even when they are not touching. Sometimes forces, like that of gravity on
a coin, cause accelerations; other times forces stretch, bend, or squeeze an
object. All forces are vectors - they not only have magnitude but they also have
direction. in fact, we define "down" as the direction gravity pulls.
Although you can think of hundreds of different forces, physicists group them all
into just four kinds. The force that Newton first described, the gravitational force, is
an attractive force that exists between all objects. The gravitational force of Earth
on the moon holds the moon in its orbit. The gravitational force of the moon on
Earth causes tides. Despite its effects on our daily lives, the gravitational force is
the weakest of the four forces.
The forces that give materials their strength, their ability to bend, squeeze, stretch,
or shatter, are examples of the electromagnetic force. These forces result from a
basic property of particles called electric charge. Charged particles at rest or in
motion exert electric forces on each other. When charged particles are in motion
they produce magnetic forces on each other. Electric and magnetic forces are
both considered to be aspects of a single force, the electromagnetic force. It is
2
very large compared to the gravitational force.
The two remaining forces are less familiar because they are evident mainly over
distances the size of the nucleus of an atom. The third force is the strong nuclear
force that holds the particles in the nucleus together. It is the strongest of the four
forces - hundreds of times stronger than the electromagnetic force. But it only acts
over distances the size of the nucleus. The fourth force is called the weak force. It
is actually a form of electromagnetic force, and is involved in the radioactive decay
of some nuclei (Boson).
Scientists have discovered and used mathematical laws to describe forces each
mathematical law works well in its own domain, but sometimes seem to contradict
each other when dealing with different forces. For instance, in normal scales,
gravity uses one law, but for very small objects, another law is needed. For this
reason scientists have tried to develop a theory that could be used to describe all
forces.
Electricity and magnetism were unified into a single force in the 1870s. Recently
the electromagnetic force has been linked with the weak force. This suggests to
physicists that all forces are different aspects of a single force. They have
constructed theories called Grand Unification Theories (GUTs) and
Supersymmetric theories that try to demonstrate this unification. Latest model is
the String Theory that shows the most promise of unifying a theory to describe all
forces. String Theory describes matter as strings instead of individual particles like
grains of sand. Based on 10 to 24 dimensions only see 4. At this time all theories
that unify forces are incomplete and do not fully agree with experiments.
Newton's First Law of Motion
http://videos.howstuffworks.com/hsw/19126-roller-coaster-physics-the-thrill-of-it-all-video.htm
Video 2 #1
Suppose you place a cart on the incline and let it gravity pull it down the incline
onto a carpet. The carpet fibers push backwards on the cart wheels , and the cart
will stop moving soon after it leaves the incline. If you use a smooth wooden floor
instead of the carpet, the smooth surface pushes back less, and the cart will roll
farther. If you have an extremely smooth floor and wheels that produce very little
resistance to motion, very little backward force is exerted on the wheels, and the
cart may roll at almost constant speed for a long distance without any additional
pushes from you. Galileo speculated that if a perfectly smooth object were on a
perfectly smooth horizontal surface it might travel forever in a straight line. Air
Hockey Table
It was left to Newton, however, to develop Galileo's idea more fully. Imagine an
3
object with no force on it. If it is moving at constant speed in a straight line, it will
continue to do so. If it is at rest, it will remain at rest, because rest is a special
name for zero velocity. This behavior of objects is described in Newton's first law.
The law states that an object with no force acting on it moves with constant
velocity. This Referred to as Inertia. Turn corner with ball and cart
Objects often have more than one force acting on them. The sum of all the forces
acting on an object is known as the net force. Think of the rope used in a tug-ofwar. The members of one team pull the rope in one direction and the people on
the other team pull it in the opposite direction. If the two teams pull with equal
strength, the rope will experience no net force, even though there are obviously
forces acting on it, it will not move. If one team pulls harder than the other a net
force exists and the rope will begin to accelerate in the direction of the net force.
To understand the effects of forces in two directions, we assign signs: positive for
forces to the right, negative for forces to the left. All the forces pulling to the right
combine to produce one large positive force. In the same way, forces to the left
combine into a large negative force. If the team pulling to the right is stronger, the
net force is positive. If the other team is stronger, the net force is negative. Thus,
our method of finding the net force on an object is to sum all the forces, keeping
track of signs. If the rope starts at rest, it does not begin to move if the net force is
zero. It has a constant – zero - velocity. Thus, we state Newton's first law more
carefully: an object with no net force acting on it remains at rest or moves with
constant velocity in a straight line. (Law of Inertia)
Newton's Second Law of Motion
http://science.howstuffworks.com/newton-law-of-motion.htm/printable
http://videos.howstuffworks.com/hsw/19113-exploring-motion-newtons-second-law-of-motion-video.htm
Video 2 #2
Newton's first law states that if there is no net force on an object, there is no
acceleration. In other words, the object moves at constant velocity. But how much
will an object accelerate when there is a net force? Think about pushing a bowling
ball. The harder you push, the faster the velocity of the ball will change. The larger
the force, the larger the acceleration, the rate of change in velocity. Acceleration is
found to be directly proportional to force.
Acceleration also depends on the mass of an object. Masses of bowling balls vary;
some are small, others large. If you exert the same force on a less massive ball,
its acceleration will be larger. In fact, if the mass is half as much, the acceleration
will be twice as large. The acceleration is inversely proportional to the mass.
These relationships are true in general and are stated in Newton's second law: the
acceleration of a body is directly proportional to the net force on it and inversely
4
proportional to its mass. Newton's second law may be summarized as
a = F/m, or m = F/a or, more commonly, F = ma.
If an object has a net force exerted on it, it will accelerate. Force and acceleration
both have direction as well as size. The acceleration is in the same direction as
the force causing it. If the force is in the positive direction, so will be the
acceleration. Similarly, if the force is in the negative direction, so will be the
acceleration.
By reducing the mass of a racecar, car builders get maximum acceleration from
the available force. The fastest top fuelers can attain terminal speeds of over
530 km/h (329 mph) while covering the quarter mile (402 m) distance in roughly
4.45 seconds. It is often related that Top Fuel dragsters are the fastest
accelerating vehicles on Earth; quicker even than the space shuttle launch vehicle
or catapult-assisted jet fighter
According to Newton's second law, a net force on an object causes it to
accelerate. In addition, the larger the mass of the object, the smaller the
acceleration. For this reason, we say that a massive body has more inertia than a
less massive body.
The following simple experiment demonstrates Newton's second law. Lay an index
card over a drinking glass. Place a penny on the card, centered over the glass.
With the flick of a finger, give the card a quick horizontal push. The card moves
away, but the penny drops into the glass. Why doesn't the penny accelerate with
the card? The penny has more mass (we say it has more inertia), and a horizontal
force is needed to accelerate it. The card is too smooth to exert much horizontal
force on the penny. With very little horizontal force on it, the penny has little
5
sideways acceleration. As soon as the card is no longer under it, however, the
upward force of the card is removed. There is mostly a net downward force, the
force of gravity, so the penny accelerates downward, falling into the glass.
Beakers of water paper pull - Table cloth and dishes inertia and second law
combined.
The Unit of Force
Newton's second law gives us a way to define the unit of force. A force that
causes a mass of one kilogram to accelerate at a rate of one meter per second
squared is defined as one newton (N). That is
F = ma = (1.00 kg)(1.00 m/s2) = 1.00 N.
N = kgxm/s2
Newton's Second Law of Motion
The Unit of Force
Example Problem - Using Newton's Second Law to Find the Net Force on an
Accelerating Object
What net force is required to accelerate a 1500-kg racecar at +3.00 m/s2?
Example Problem - Finding Force When Acceleration Must Be Calculated
An artillery shell has a mass of 55.0 kg. The shell is fired from a cannon, leaving
the barrel with a velocity of + 770.0 m/s. The cannon barrel is 1.50 m long.
Assume that the force, and thus the acceleration, of the shell is constant while the
shell is in the cannon barrel. What is the force on the shell while it is in the cannon
barrel?
Do Practice Problems 5-1
Newton’s Third Law of Motion
http://videos.howstuffworks.com/hsw/19114-exploring-motion-newtons-third-law-of-motion-video.htm
Video 4 #4 and #5
If you try to accelerate a bowling ball by kicking it, you may become painfully
aware of Newton's third law. As you kick the ball, your toes will feel the equal force
the ball is exerting on you. If you exert a force on a baseball to stop it, the ball also
exerts a force on you. These are examples of the forces described in Newton's
third law: When one object exerts a force on a second object, the second exerts a
force on the first that is equal in magnitude but opposite in direction.
According to Newton's third law, if you exert a small force on the ball, it exerts a
small force on you. The larger the force you exert on the ball, the stronger its force
is on you. The magnitudes are always equal. These two forces are often called
action-reaction forces.
6
By analyzing the forces, using Figure 5-6, involved when you pick up a bowling
ball up from the ground. When the ball is resting on the ground – the gravitational
force between the ball and the Earth pull the ball toward the center of the earth –
when the ball is in contact with the ground the upward force of the ground is equal
to the downward force of gravity - your hand exerts a force on the ball, the ball
exerts a force on your hand that is the same size, but in the opposite direction.
These two forces are action-reaction forces. As you examine the diagram, note
the two equal but opposite forces acting on two different objects, your hand and
the ball, the ball and Earth.
Why does the ball accelerate upward? After all, the force your hand exerts on
the ball is the same magnitude as the force the ball exerts on your hand. Where is
the net upward force that causes the acceleration? To answer that question, we
need to isolate the bowling ball and examine only the forces that act on it. There
are two forces acting on the ball, the force of your hand directed upward and the
force of gravity pulling downward. When you lift the ball, the force exerted by your
hand is greater than the force of gravity, so the ball accelerates upward. Only the
forces on the ball determine its acceleration.
Do Concept Review 5-1
5.2 USING NEWTON'S LAWS
http://videos.howstuffworks.com/hsw/19112-exploring-motion-newtons-firstlaw-of-motion-video.htm review 1st law and friction
A track can only exert force on a car through the tires. This force will be
transmitted only if there is enough friction between track and tires. If you have
ever tried to accelerate a car on icy or wet roads, you know that the existence of
friction is not guaranteed. Among the applications of Newton's laws we will explore
7
in this section is friction.
Drag racers "smoke" their tires before a race to increase the friction between the
tires and the track. They rev the engine just enough to get the tires spinning, then
let the tires spin for about 5 seconds just long enough to smoke the tires over.
That's long enough because the purpose of the burnout is to clean off the surface,
and to put heat in them for traction. Some racers mistakenly boil the tires off, or
spin the tires for 15-20 seconds. This destroys the tires, and makes them slicker,
not stickier, because overheating the tires draws the oils and resins to the tread
surface.
Mass and Weight
While walking on the sidewalk at Old Fashion Days, you see a box and you give it
a good kick. If the box goes sailing, you know it has a small mass. If the box
hardly accelerates at all, it must have a large mass. Suppose you pick up the box
and then let it drop. It will accelerate downward. Thus, Earth must be exerting a
downward force on it. The gravitational force exerted by a large body, usually
Earth, is called weight. Weight is measured in newtons like all other forces. A
medium-sized apple weighs about one newton.
The weight of an object can be found using Newton's second law of motion. On
the surface of Earth, objects that have only the force of gravity acting on them fall
downward with an acceleration of 9.80 m/s2. This acceleration is so important that
we give it a special symbol and write g = 9.80 m/s2 in the downward direction.
The force of gravity on an object is present whether the object is falling, resting on
the ground, or being lifted. Earth still pulls downward on it. The force of gravity is
given by the equation F = mg. This force is called the weight of an object and is
given the symbol W. Therefore, we write
W = mg since g is acting downward (-) W is (-)
On the surface of Earth, the weight of an object with a 1.00-kg mass is - 9.80 N.
The weight of any object is proportional to its mass. Weight is a vector quantity
8
pointed toward the center of Earth. If we assign "up" to be the positive direction,
then weight would be negative. More often we will use the word "down" instead of
a minus sign (-) when direction is needed.
Example Problem - Calculating Weight
Find the weight of a 2.26-kilogram bag of sugar.
Do practice problems 5-2
You do not really "feel" your weight. What you do feel are the forces exerted on
you by objects that touch you. When standing, you don't feel the force you exert
on the floor, you feel the force the floor exerts on you. The larger your weight, the
larger the force exerted by the floor will be on you. When sitting, you feel the force
of the chair. If you do a pull-up, you feel the force of the bar on your hands. When
you are at rest, or moving at constant velocity, these forces are equal in
magnitude to your weight, but in the opposite direction. Gravity is the force pulling
you down the normal force pushes back against you. (-) W and (+) FN
Mass and weight are not the same. Weight depends on the acceleration due to
gravity, and thus may vary from location to location. A person weighs a very small
amount less on top of a high mountain, even though he or she has the same
mass. A bowling ball with a mass of 7.3 kg weighs 71 N on Earth, but only 12 N on
the moon, where the acceleration due to gravity is 1.6 m/s2. If you tried to kick a
bowling ball across the surface of the moon, however, it would be just as hard to
accelerate as on Earth because its mass would be the same.
Two Kinds of Mass
We discussed one way of determining mass by measuring the amount of force
necessary to accelerate it, that is, its inertia. The inertial mass of an object is the
ratio of the net force exerted on the object and its acceleration,
m = F/a
A second method of finding mass is to compare the gravitational forces exerted on
two objects, one with an unknown mass, and the other with a known mass. The
object with the unknown mass is placed on one pan of a beam balance. The
object with the known mass is placed on the pan at the other end of the beam.
When the pans balance, the force of gravity is the same on each pan. Then the
masses of the objects on either side of the balance must be the same. The mass
measured this way is called the gravitational mass.
Suppose you apply the same force to two different objects and find that the
acceleration of one object is twice that of the other. You would conclude that the
mass of the first object is half that of the second. If you put the same objects on a
pan balance, you would find the gravitational force on the first object is half the
gravitational force on the second. Very precise experiments indicate that inertial
9
mass and gravitational mass of objects are equal within the accuracy of the
experiments . In 1916 Albert Einstein (1879-1955) used the equality of inertial and
gravitational masses as one foundation for his general theory of relativity.
http://www.jca.umbc.edu/~george/html/courses/glossary/mass_inertial_vs_grav.ht
ml
A body's Inertial
Mass
is
is measure of how strongly the body is
accelerated (by A) by a given force.
It is the mi in Newton's 2nd-law:
Force = mi A
A body's Gravitational
Mass is
is measure of how strongly the body is
affected by the force of Gravity
It is the mg in Newton's universal law of
gravitation when the body is a distance R
from another body of mass M:
Force = G mg M R-2

The inertial mass mi determines how the body accelerates as a results of
the application of any force.

The gravitational mass mg determines how the body "feels" a gravitational
force (and how much of a gravitational force it generates).
The fact that:
mi A =G mgM r2 if mi equals mg then it is apparent that the acceleration (due to the
force of gravity) is independent of mass.
Simply put, gravitational mass is that property of an object that causes it to attract
other massive objects. An objects inertial mass is its resistance to changes in
motion.
http://www.exploratorium.edu/ronh/weight/ your weight on other planets
Friction
Slide your hand across a tabletop. The force you feel opposing the movement of
your hand is called friction. It acts when brakes slow a bike or car, when a sailboat
moves through water, and when a skydiver falls through the air. If there were no
friction, whenever you tried to walk, you would slip as if you were on ice. Without
friction, tires would spin and cars would not move. An eraser could not grip your
homework paper and remove a mistake.
Friction is the force that opposes the motion between two surfaces that are in
contact. The direction of the force is parallel to the surface and in a direction that
opposes the slipping of the two surfaces. To understand the cause of friction, you
must recognize that on a microscopic scale, all surfaces are rough. When two
surfaces rub, the high points of one surface temporarily bond to the high points of
the other. The electromagnetic force causes this bonding.
10
If you try to push a heavy box along the floor, you will find it very hard to start it
from rest, Figure 5-11. If two objects are not in relative motion, static friction is the
force that opposes the start of motion. Static friction forces have maximum values.
When the magnitude of your push on the box is greater than the maximum value
of the static friction between the floor and the box, the box starts moving. When
the box starts to move, the force of friction will decrease. The force between
surfaces in relative motion is called sliding friction. The force of sliding friction is
less than that of static friction. Thus, a car will stop faster if the wheels are not
skidding. (anti-lock brakes)
How large is the force of sliding friction? Slide your book across the desk. It slows
down. To keep it moving at constant velocity, you must exert a constant force that
is just the same size as the frictional force, but in the opposite direction. See
Figure 5-12. (No net force if no acceleration so FA = Ff)
By measuring the force you exert, called the applied force, FA , you can find the
force of friction, Ff.
Ff = FA
Experimentally it has been found that the force of friction depends primarily on the
force pushing the surfaces together, FN, and on the nature of the surfaces in
contact. This result can be expressed as
Ff = FN.
11
In this equation  (mu), called the coefficient of friction, is a constant that depends
on the two surfaces in contact. FN is the force pushing the surfaces together. It is
called the normal force, where "normal" means perpendicular. In the example
above, the normal force on the book is the force exerted by the table,
perpendicular to its surface. When the book is resting on a horizontal surface, the
normal force of the table on the book is numerically equal to the weight of the
book (W). The normal force of the table on the book is also equal to the force of
the book on the table, since they are action-reaction forces. If you use your hands
to exert an extra force, F, down on the book, the force of the book on the table
increases to W + F. By Newton's third law, the normal force of the table upward on
the book also increases to W + F.
W + F. = FN
Notice that when we are studying the friction between two objects, such as a book
lying on a horizontal table, there are two sets of forces. The first set is parallel to
the surfaces that are touching. This set consists of the force that moves the object
and the opposing frictional force. The second set of forces acts perpendicular to
the two surfaces. The downward force may be just the object's weight, the
downward force of gravity. Often, though, other forces are exerted on the object. A
person might push the object down, or perhaps lift up on it. A second object might
be placed on top of the first. The sum of all vertical forces is the total downward
force. The other force in this set is the equal but upward force exerted on the
object by the table. That force is the normal force on the object. In many cases,
the coefficient of sliding friction for two surfaces in contact is very nearly
independent of the amount of surface area in contact and the velocity of motion.
The problems we solve will make this assumption.
PROBLEM SOLVING STRATEGY
When solving problems involving more than one force on an object:
1. Always start by sketching a neat drawing of the object.
2. Then draw arrows representing all the forces acting on the object.
3. Label each force with the cause of the force. Be specific. Examples are
"weight," "force of string," "normal
force exerted by table," "force of friction."
Evaluate your drawing and compare all the forces to determine the magnitude and
direction of the NET FORCE because that is the force that will cause acceleration.
Example Problem - Static and Sliding Friction
A smooth 40.0N wooden block is placed on a smooth wooden tabletop. You put a
force sensor hook to your lab quest and observe that a force of 18.0N must be
applied to start the block in motion, once it starts to move at a constant velocity
the force applied drops to 14.0N. a. What is the coefficient of static friction and
sliding friction for the block and table? b. If a 20.0-N brick is placed on the block,
12
what force will be required to keep the block and brick moving at constant
velocity?
Do practice problems 5-3
While this general description of friction known as the standard model
has practical utility, it is by no means a precise description of friction.
Friction is in fact a very complex phenomenon, which cannot be
represented by a simple model. Almost every simple statement you
make about friction can be countered with specific examples to the
contrary. Saying that rougher surfaces experience more friction sounds
safe enough - two pieces of coarse sandpaper will obviously be harder
to move relative to each other than two pieces of fine sandpaper. But if
two pieces of flat metal are made progressively smoother, you will reach
a point where the resistance to relative movement increases. If you
make them very flat and smooth, and remove all surface contaminants
in a vacuum, the smooth flat surfaces will actually adhere to each other,
making what is called a "cold weld". But like in most cases in basic,
introductory physics we simplify to gain a general understanding of
nature.
The standard model can be used if the following assumptions are made:
 The frictional force is independent of area of contact
 The frictional force is independent of the velocity of motion
 The frictional force is proportional to the normal force.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
The Net Force Causes Acceleration
13
In Newton's second law of motion, F = ma, the force, F, that causes the mass to
accelerate is the net force acting on the mass. In Figure 5-14a, a 10 kg mass
rests on a frictionless, horizontal surface. A + 100-N force is exerted horizontally
on the mass. The resulting acceleration is
+100 N
a = F/m = +100N/10kg = +10m/s2
If the same mass rests on a rough surface, friction will oppose the motion. In
Figure 5-14b, the frictional force is -20 N. The negative sign indicates that the
force acts in a direction opposite the positive applied force. The acceleration of
any object is the result of the net force acting on it. The net force is the vector sum
of the applied and frictional forces. When you sum forces, which are vectors, you
must pay attention to the signs. That is,
Fnet = Fapplied + Ff
+100 N + (-20 N) = +80 N,
and the resulting acceleration is given by a = Fnet/m = +80N/10kg =+8.0 m/s2
The direction of the acceleration is positive, in the direction of the applied force.
Other forces besides friction act on objects. Consider a 10.0-kg stone lying on the
ground. The stone is at rest; the net force on it is zero. The weight of the stone, W,
is 98.0 N in a downward direction. The ground exerts an equal and opposite force,
98.0 N, upward. The net force is
Fnet = Fground + W
=
+98.0 N + (- 98.0 N)
=0N
How can the stone be given an upward acceleration? Suppose a person exerts a
148-N upward force on the stone. The net force is
Fnet = Fperson + W
=
+148.0 N + (-98.0 N)
= +50.0 N.
The net force acting on the stone is 50 N upward. The acceleration of the stone
14
can now be found from Newton's second law:
a = f/m = +50 N/10 kg = +5 m/s2
The stone will be accelerated upward at +5 mIs2.
Example Problem - Forces on an Accelerating Object
A spring scale hangs from the ceiling of an elevator. It supports a package that
weighs 25.0 N. a. What upward force does the scale exert when the elevator is not
moving? b. What force must the scale exert when the elevator and object
accelerate upward at + 1.50 mIs2? Use Figure 5-16.
That is, the scale exerts a larger force and thus indicates a larger weight when the
elevator accelerates upward.
If you ride an elevator, you "feel" your inertial mass. When the elevator
accelerates upward, you feel the added force of the floor on your feet, accelerating
15
you up. You also feel the forces your muscles exert on your stomach; these forces
may make your stomach feel strange.
Do Practice Problems 5-4
The Fall of Bodies in the Air
Astronauts on the surface of the moon dropped a hammer and a feather together.
These objects hit the surface at the same time. Without any air, all objects fall with
the same acceleration. On Earth, the acceleration is 9.80 m/s2; on the moon it is
1.60 m/s2.
In air, however, an additional force acts on moving bodies. Try this experiment.
Take two pieces of notebook paper. Crumple one into a ball. Now hold them side
by side and drop them at the same time. The two pieces of paper obviously do not
accelerate at the same rate. The flat paper encounters much more air resistance
than the ball. Air resistance, sometimes called the drag force, is a friction-like
force. As an object moves through the air, it collides with air molecules that exert a
force on it. The force depends on the size and shape of the object, the density of
the air, and the speed of motion. (Through air knuckle ball)
Suppose you drop a ping-pong ball. Just after you drop it, it has very little velocity,
and thus very small drag force. The downward force of gravity is larger than the
upward drag force and the ball accelerates downward. As its velocity increases,
so does the drag force. At some later time the drag force equals the force of
gravity. The net force is now zero, and the velocity of the ball becomes constant.
This constant velocity is called the terminal velocity.
The terminal velocity of a ping-pong ball in air is only 9 m/s (20mph). A basketball
has a terminal velocity of 20 m/s (45mph) as does a penny, while a baseball can
fall as fast as 42m/s (94mph). Skiers increase their terminal velocities by
decreasing drag force. They hold their bodies in an "egg" shape and wear very
smooth clothing and streamlined helmets. A skydiver can control terminal velocity
by changing body shape. A spread-eagle position gives the slowest terminal
velocity, about 60 m/s (134mph). By opening the parachute, The skydiver has
become part of a very large object with a correspondingly large drag force. The
terminal velocity is now about 5 m/s 11mph.
http://www.grc.nasa.gov/WWW/K-12/airplane/termv.html
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
freefall with air and without
16