Do Skateboard Tricks Defy the Laws of Physics? - by Eugene Horsch
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Do Skateboard
Tricks Defy the
Laws of Physics?
by Eugene Horsch
Table of Contents Abstract…………………………………………………………………………….....2 Problem, Hypothesis, Procedure…………………………………………………..….3 Background……………………………………………………………………….…..4 Bibliography………………………………………………………………................19 Pictures……………………………………………………………………................20 Drawing………………………………………………………………………..…….23 Preparation…………………………………………………………………………...24 Analysis………………………………………………………………………………25 Conclusions…………..………………………………………………………………29
Abstract
Many skateboard tricks seem to defy the laws of physics. For example when you
do an " OIlLe," the board seems to rise with the rider 's feet as he jumps into the air, as if it
was fastened to them. In reality the board is nor attached to the rider's feet in any way. In
my experiment I tried to find out if skateboard tricks really do defy the laws of physics.
My hypothesi s was that they do no! defy the laws of physics .
I took a video of a rider doing an "Ollie. " Then. I used a computer to enhance and
print out all the individual frames for the trick . After this I analyzed the frames to see
what was actually happening. r measured the distance that the different parts of the board
travel from frame to frame. Then 1used the elapsed time between frames to compute
speeds. Finally, I diagrammed the motion from frame to frame. computed the forces on
the board, and found the corresponding laws of physics such as acceleration and inertia
that explained what was happen ing. I found that there was a reason that the board
behaved the way it did and seemed to rise with the rider's feet.
TIle conclusion that [ have reached from this experiment is that skateboard tricks
are complicated illusions that actually do nor defy the laws of physics .
:2
Problem
Do skateboard tricks defy the laws of physics?
Many skateboard tricks seem to defy the laws of physics. For example when you do an
"O llie" , the board seems to rise with your feet. as if it was a part of them.
Hypothesis
Skateboard tricks are illusions that do not really violate the laws of physics.
Procedure
I. Take a video of the trick.
2. Use a computer to print out all the indiv idual frames for the trick.
3. Label each frame as I. 2, .3 ...etc.
4. Analyze the frames to see what is actually happening.
A. Measure the distance that different parts of the board travel from frame to
frame.
B. Compute the forces on the board from frame to frame.
C. Diagram the forces and the motion from frame to frame .
D. Write a detailed description of what is happening during the trick and why
it is happening.
5. Conclude whether or not the board is following the laws of physics .
..,
.J
BACKGROUND
Eadweard Muybridge
The Englishman Eadweard Muybridge, b. Edward James Muggeridge, Apr 9,
1830, d. May 8,1904, one of the great photographers of the American West, became even
better known for his pioneering photographic studies of motion. Photographing
throughout California in the 1860s and '70s, he made the large, impressive landscapes of
the Yosemite wilderness that won him initial fame. In 1872, Leland Stanford, the former
governor of the state, bet a friend that once in every stride all four of the horse's feet are
off the ground at one time. He hired Muybridge to provide evidence to settle the bet, and
in 1877 Muybridge's pictures, which recorded the horse's motion in sequential frames,
proved Stanford right. (The work took 5 years because it was interrupted while
Muybridge was tried and acquitted for the murder of his wife's lover.) This was the first
use of photographic motion analysis.
In 1879, Muybridge invented the zoopraxiscope, a machine that reconstructed
motion from his photographs and a forerunner of cinematography. After a European tour,
during which his work was acclaimed by artists and scientists alike, he continued (1884-
86) his photographic motion studies; Animal Locomotion (1887), containing 781 groups
of sequential frames, was the first of several such publications, which also included The
Human Figure in Motion (1901). ("Muybridge. Eadweard")
4
To understand more about the physics of human motion, scientists are using a
wide variety of mathematical models, computer programs, and robotics to study "human
dynamical behavior."
Body motions, whether as simple as walking or as complex as arborne pirouettes,
depend on fine control of the nervous system, but also on simple physics.
Mont Hubbard, a mechanical engineer at the University of California, says,
"Sports scientists generally want a deeper understanding of what goes on physically and
psychologically when an athlete refines· a dynamic task. They want to know what factors
enhance or limt performance, whether it's muscle strength or sensory overload" (Lipkin
426).
Understanding the mechanics of athletic performance well enough to model it
mathematically, may help athletes hone their training.
"Athletes have always sought answers in an empirical mode of trial and error.
But if you have a model that tells you exactly what is going on, it's easier to get clear,
unambiguous answers to subtle questions that are often difficult to test in the real world"
(Lipkin 426).
To grasp the biomechanics of many sports movements has led Hubbard's research
team to derive mathematical models for a wide variety of events, from pole vaulting,
skijumping, and javelin throwing to skateboarding and, most recently, golf.
"Sports are about optimization," he adds. "They're about learning to do
something better than you did it last time better than you did it last time or better than you
5
did it last time or better than you did it last time or better than your opponent has done.
Ultimately, our aim is to use scientific methods to help athletes improve their
performances" (Lipken 427)
Through few sports are into tradition as baseball, the game is now being invaded
by high-technology. At the college and amateur levels of play the old ash wood bat has
been supplanted by high-performance metal and fiber-composite bats, and bating coaches
can now use computerized motion analysis systems and instrumented bats to dissect
player's swings.
Before designing his bat, Baum spent several years using sophisticated labortatory
analysis tools such as high-speed cameras, precision timers, force senors, and
mechanical-property testing devices to invesigate what makes a bat "trick't-a surprisingly
subtle problem considering the seeming simplicity of a baseball bat.
Analyzing the batting swing is likewise difficult. Some of the key factors
governing how a ball will be hit are bat speed, mass of the ball in relation to mass.of the
bat, location of the hit of the bat, angle of the hit, ball rotation, weather conditions,
rebound charateristics of the marked variation in player's swings. Several high-tech
systems have been developed to analyze baseball swings.
Baseball coaches can now disect a pitcher's delivery with a motion-analysis
system developed by Bio-Kinetics Inc. Digitized video images of a pitch create a
multicolored, multiple-exposure stick figure computer model that embodies the pitcher's
motion. (Ashley 108-109)
6Most people who've been in an auto accident never forget that moment when time
and space effectively blur. To help carmakers understand exactly what happens during
collisions, Eastman Kodak Co. has devised a motion analysis system that can withstand
40-mph crashes.
A rugged, steel-encased electronic carmera mounted in the test vehicle sends
images in computer-compatible digital format to a remote system that can record up to
12,00 pictures per second. Carmarkers can thus watch collisions, then replay them is
slow motion. "With this, we can do something instantly that generally took us two days,"
said James Moon-Dupree, a safety expert at Ford Motors Co. in Dearborn, Michaghan.
("A Driver's - Eye View of Car Crashes" 86)
Kodak marketer Gerald Lilly estimates the new system will seeI for more tan
$60,000. But the system means that auto markers don't have to destroy as many cars in
crash tests. Moreover, having this information in digital form lays the groudwork for
future test crashes done in the computergenerated world known as virtual reality.
Scientific Methods Used in Physics
Physics attempts to describe and explain the physical universe. Physicists
therefore try to discover one or more laws (meaning invariable principles of nature at
work) which will explain a large class of phenomena. Newton's law of gravitation is a
fine example. Another is the law of mirrors "the angle of incidence is equal to the angle
of reflection."
7Physicists express these laws in some exact mathematical form, which can serve
later as a basis for measurements and calculations. For example, Newton's law of
gravitation states that the force of gravitational attraction (Fg) between two separate
masses depends, first, upon the amount of mass (m) in each one, and second, upon the
distance (d) between the masses. The masses must be multiplied together, and the pull
diminishes with the square of the distance. If the distance is doubled, the pull is only one
fourth as great. The whole law can be stated in the short formula: Fg = gmlm2/d2, where
g is known as the gravitational constant.
This formula can be used in turn to give answers to a host of problems. Newton
used it to help explain why Kepler's laws worked out. A modem designer of space ships
or rockets would use it to help predict what will happen as the rocket flies farther and
farther away from the Earth.
Whenever possible, physicists try to discover laws and prove them true by
experiments in which the variables involved can be controlled or measured accurately.
Although a number of important discoveries in mechanics were made during the
next 18 centuries, it was Galileo who opened the door to an entirely new world of
physics. At the age of 19 he timed with his pulse the swings of a great chandelier in the
cathedral at Pisa and found that the swing always took the same time, even though the
size of the excursion became smaller. He then invented a simple pendulum for measuring
time. This was a great improvement over the sand and water clocks then in use.
8Galileo studied the motions of falling bodies and, in contradiction to Aristotle's
claim, found that heavy bodies fall at exactly the same speeds as lighter ones when air
frict ion is discounted. He also studied accelerated motion by rolling balls down inclined
planes. His experiments laid the foundation for modern mechanics.
Earlier workers such as Roger Bacon had insisted upon careful observation and
experiment as the way to win knowledge, rather than depending upon mere appearances.
Nonetheless Galileo is considered the father of the experimental, or scientific, method
because he devised the critical experiments which forced conviction even though the
results contradicted earlier authorities.
The force that causes objects to drop and water to run downhill is the same
force that holds the Earth , the sun, and the stars together and keeps the moon and artificial
satellites in their orbits. Gravitation, the attraction of all matter for all other matter, is
both the most familiar of the natural forces and the least understood.
Gravity is the weakest of the four forces that are currently known to govern the
way physical objects behave. The other three forces are electromagnetism, which governs
such familiar phenomena as electricity and magnetism; the "strong force," which is
responsible for the events in nuclear reactors and hydrogen bombs; and the "weak force ,"
which is invol ved with radioactivity. Because of its weakness, gravity is difficult to study
in the laboratory.
An example shows why gravity is called a weak force . A drop of strong glue can
bond two pieces of chain so tightl y that they can then be used to lift an automobile. That
9means that the chemical forces in the drop of glue , which are basically electromagnetic in
nature, are stronger than the gravitational attraction between the car, weighing a billion
times more than the drop , and the Earth,-which is a million, trillion, trillion (1030) times
bigger than the drop.
Despite its weakness, gravitation is important because, unlike the other three
forces, it is universally attractive and also acts over an infinite distance. Electromagnetic
forces are both attractive and repulsive and as a result generally cancel out over long
distances. The strong and weak forces operate onl y over extremely small distances inside
the nuclei of atoms. Thus, over distances ranging from those measurable on Earth to those
in the farthest parts of the universe, gravitational attraction is a significant force and, in
many cases, the dominant one.
Both Sir Isaac Newton in the 17th century and Albert Einstein in the 20th century
initiated revolutions in the stud y and observation of the universe through new theories of
gravity. The subject is today at the forefront of theoretical physics and astronomy.
The Acceleration of Gravity
The first scientific studies of gravity were performed by the Italian astronomer
Galileo at the end of the 16th century. Gal ileo measured the speed of falling objects by
timing metal balls rolling down an inclined plane. He concluded that gravity imposes a
constant acceleration on all objects. That is, with each second of fall an object acquires a
constant additional downward velocity. On Earth this acceleration of gravity is 32 feet
10(9.75 meters) per second per second. Thus , at the end of one second, a falling object is
moving at a velocity of 32 feet p~r second and at the end of two seconds, 64 feet (19 .5
meters) per second, and so on, before any adjustment for the resistance of the air it passes
through. The distance a body falls can be determined by calculus and is Oat2 in which a is
the acceleration and t the time.
Galileo found , contrary to the speculations of the Greek philosopher Aristotle
centuries earlier, that all objects are accelerated by gravity in the same way . A feather
falls more slowly than a rock not because its acceleration from gravity is less but because
air resistance slows it more . The force of air resistance varies with the surface area of an
object, so that an object that spreads its weight over a greater area suffers more resistance
and thus drops more slowly. This is the principle used in the parachute.
Late in the 17th century ewt on put forward the fundamental hypothesis that the
gravity that makes objects fall to Earth and the force that keeps the planets in their orbits
are the same. In the earl y 1600s the German astronomer Johannes Kepler described three
laws : first , all planets move in ellipses with the sun at one focus ; second, a line between
the sun and a planet would sweep out equal areas of the ellipse during equal times; and
third, the square of the period of any planet (the quantity of the time it takes to go around
the sun multiplied by itself) is proportional to the cube of its average distance to the sun
that is, the averagedistance multiplied by itself twice.
In his book 'Principia .Mathematica', published in 1687, Newton showed that both
Kepler's laws and Galileo's observations of Earth's gravity could be explained by a single
11simple law of universa l gravitation. Every celestial body in the universe attracts every
other celestial body with a force described by
in which F is the force, m I and m2 are the masses of the two gravitating objects, R is the
distance between them , and G is the universal gravitational constant (6.670 10-8 dyne
cm2/gm2 ).
Also in the 'Principia Mathematica' Newton mathematically defined the concept
of "force" to be equal to the mass of an object on which the force is applied, multiplied by
the acceleration that resu lts from the force, or F = MA, in which A is acceleration. .
Because the gravitational force increases proportionately to the mass of the object that is
accelerated, any object, no matter what its mass, accelerates equally if placed at the same
distance from another mass. Galileo observed that all objects on the Earth are accelerated
by the planet's gravity to the same extent.
Newton demonstrated mathematically that the law of gravitation he proposed
predicts that the planets follow Kepler 's three laws. Newton's vision of a world governed
by simple, unalterable laws exerted a powerful influence for more than a century.
("Gravation")
Newton's Monumental Contributions
In the year Galile o died (1642), there was born in England one of the greatest
scientists of all time, Isaac ewton. His studies of falling bodies and of the solar system
12led to his celebrated law of universal gravitation. Not only did he discover many of the
basic laws of mechanics , including the fundamental laws of motion, but he also
developed a special mathematics for treating problems in mechanics . Thus he became one
of the discoverers of calculus. The other was Gottfried Wilhelm Leibniz .
Newton provided firm bases for expressing natural laws as mathematical
formulas . His method started with locating objects in space with measurements made to
three axes at right angles to each other through a chosen point called the origin. Such
measurements are called Cartesian coordinates after the man who devised them. Newton's
next working principle was that objects remain motionless or in uniform motion (same
\
speed in a straight line) unless something happens to produce a change. Newton called
this something a force, and he provided methods for measuring mechanical forces.
(Compton's Interactive Encylopedia, Physics)
MOTION
An intuitive definition of motion is "a continuous change in time" ("Motion").
Such a description was used by the ancient Greek philosophers, for whom the
interpretation of the concept of change in general constituted a great problem. Zeno of
Elea (c.490-430 BC) devised the paradox of the arrow: a body occupying a space equal
to its volume is at rest; a flying arrow occupies at any moment a space equal to its
volume', thus , at any moment the arrow is at rest; therefore it is at rest all the. This
paradox was not resolved until the 17th century, following the development of
13CALCULUS, which finally enabled mathematicians to distinguish infinitesimally small
changes from zero.
The description of motion in classical mechanics requires the use of mathematics.
In order to be .able to analyze motion systematically, precise definitions for the concepts
of velocity and acceleration must be formulated , and if the values for these quantities are
known for an object at every moment , its complete trajectory can be determined. In this
way it is possible to solve most problems of motion, from the motion of atoms to that of
planets.
VELOCITY
The velocity of an object can be calculated from the distance it travels within a
certain time . Distance divided by elapsed time is then called the average velocity, given
in units such as meters per second (In/sec) or miles per hour (mph). The average velocity
of an object during a particular period of time conveys only a rough impression of the
way the object actually moved during that period. To obtain the velocity v for a
particular moment in time (instantaneous velocity), one must know the infinitesimal
change in position, dr, that occurs in an infinitesimally short moment dt; then, v = dr/dt.
Velocity is a vector quantity; it has not only magnitude but also direction. When
the velocity of an object remains in the same direction and has constant magnitude, that
object is moving with uniform motion . Such motion is quite common; once airplanes,
trains , and ships have come up to speed, they endeavor to continue their journey at
14constant speed and- -ifthe route permits--in a constant direction. Uniform motion is
special because it is the only motion in nature that can be achieved without a net
force of any kind. A passenger in a vehicle undergoing uniform motion will neither be
pressed into his or her chair nor pulled to one side . This explains the preference for
uniform motion in transportation.
ACCELERATION
As soon as forces that do not cancel each other out act on an object, uniform
motion no longer takes place. A simple idea of the concept of acceleration can be
obtained when the change in velocity occurs only in the direction of the velocity itself.
The acceleration is usually expressed as the change in speed , say, in m/sec, that takes
place in one second; in this case, in meters per second per second. An automobile that
accelerates from r~st up to 72 km/hr in 10 seconds has undergone an acceleration of 2 rn
per second per second. The force responsible for the acceleration is provided by the
motor, and the occupant undergoes the same accelerating force by being pressed into the
seat. A deceleration slows the car. Unless an occupant is secured by a seat belt , there is
no decelerating force on him or her, and he or she persists in the forward motion.
Acceleration is also a vector. If the force causing the acceleration does not act in
the same line as the velocity, the acceleration may be divided into two perpendicular
components. The component in the direction of the velocity is called the tangential
acceleration. The average tangential acceleration is equal to the change in velocity.
15The component of acceleration perpendicular to the velocity is the radial
acceleration. It is equal to vvlr, where r is the radius of the (imaginary or not) circular
path under which the object is traveling at the moment of consideration. (An arbitrary
trajectory can always be regarded as bits of a circular path linked together, and
the radius r of the circle can be different at every point of the trajectory.) Even ifan object
is undergoing uniform motion, its path will become curved under the influence of radial
acceleration.
CALCULATING POSITION
The exact location of an object moving uniformly along a straight line can easily
be calculated from x = vt, where x is the distance covered. The same units must be used
on both the left and the right side of the formula; if the velocity i expressed in kilometers
per hour (km/h), then the time has to be stated in hours and the distance in kilometers. If,
however, the velocity is in meters per second (m/sec), then the time has to be in seconds
and the distance in meters.
The velocity of an object that was initially at rest and subsequently exposed to a
uniform acceleration can also be calculated from v = at. Again, calculations have to be
made consistently with meters and seconds or whatever units of measure are being us~d.
A uniformly accelenited motion is the motion caused when an object is constantly
accelerated at the same rate, such as by gravity. Such an object's motion is determined by
x = 1/2 X a X tt. The distance covered thus increases with the square of the time . If the
16object in question was already in motion at the time that acceleration began, then the
distance covered prior to that time has to be included and x = that distance . The initial
velocity need not be in the same direction as the acceleration. In such a case a distance
equal to that covered prior to the time when acceleration began is covered in one direction
and at the same time a distance equal to 1/2 xaX tt is covered in
another direction.
FALLING MOTION
A well-known case of objects being subjected to a uniform acceleration is when
they are released in the gravitationa l field of the Earth. The velocity of such an object
increases every second by an amou.nt of 9.8 m/sec. The acceleration of gravitational
force is in fact not a constant , but up to an altitude of 30 krn the deviations of this value
are less than 1%. An object that is thrown horizontally will move uniformly in a straight
line across the Earth's surface and at the same time undergo the accelerating falling
motion caused by gravity. The actual motion resulting from these two motions is then no
longer a straight line, and the object will traverse increasingly greater distances
downward in proportion to forward; a parabolic trajectory is thus formed.
The height in meters at which an arbitrarily thrown object is located after a
particular time t may be calculated from the previous formula for distance by adding its
starting height to h: h = distance covered prior to acceleration - 1/2(9.8) tt. If distance is
,
measured in feet, 32.2 is substituted for 9.8. Because the last factor in this formula will
17ultimatel y always gain the upper hand, the height will eventually decrease in the end and
the object will ultimatel y lend on the Earth. The initial horizontal velocity is different
from the initial vertical velocity. Air resistances and other forces are not included in this
calculation.
The vertical velocity with which an object released at height h hits the ground also
represents the velocity with which an object needs to be thrown upwards in order to
just reach height h. At high velocities air resistance ultimately prevents any further
increase in rate of fall. A sky diver, for instance, will attain a constant free-fall velocity
(terminal speed) that will--depending on the position of his or her body--lie between 180
and 250 km/h (110 and 160 mph). (Motion")
18Bibliography
1. "A Driver' s - Eye View of Car Crashes. " Business Week 23 March 1992: p. 86
2. Ashley, Steven. "High Tech up at Bat." Popular Science May 1992: pp. 108-109
3. Lipkin, Richard. "Bodies in Motion. " Science News December 23-30, 1995:
pp .426-427
4. "Physics." Compton's Interactive Encvclo pedia . 1994.
5. "Gravitation." Compton's Interacti ve Encvclopedia. 1994.
6. "Motion." Grolier Multimedia Encvclopedia. 1994.
7. "Muybridge, Eadweard" Grolier Multimedia Encyclopedia. 1994
19) )
I 1 1/3 2/3 0 .5 0
i ·DISTANCE IN METERt · ·
~ 7'
o •
Front Wheel Rear Wheel
(Yellow) (Blue)
SKATEBOARDPreparation
The individual frames from the "Ol lie" were digitized and fed into a computer.
Then. each frame was sharpened on the computer to bring out the most detail. Each
frame was used in a drawing program and the position of the skateboard was plotted. The
vertical and horizontal distances were depicted in a grid. The time interval between
frames was exactly 1130 of a second.
24Analysis
KNOWN FACTORS:
a. Velocity of the skateboard or the rider (or any particular point on the board or
rider) between any two frames can be computed by measuring the distance
involved and using the knowledge that the time interval between frames is
1130 second. The formula v= d/t.
b. Acceleration at any given point can also be determined by using the formula
A= dv/dt.
c. The kinetic energy of the board or the rider can also be computed at any frame
2
using the formula E= Y2(mv ) and the knowledge that the board has a mass of
:2 kg. And the rider 65 kg. Similarly, the forces involved can be expressed in
Newtons (N) or the force needed to accelerate one kilogram one meter per
second.
POINT 1:
The skateboard approached the ramp. By measuring the distance traveled between frames.
it was determined that the board was traveling about 5/6 meter every five frames or 1/6
second. By using the formula velocity = distance 1 time (v = d/t), it was determined that
the speed of the board was 5 meters per second or about 18 km. per hour. The rider was
crouched on the board with his weight mostly toward the rear wheels.POINT 2:
At this point on the diagram, the rider abruptly jumps into the air. This is one of the most
critical points of the trick. He jumps almost entirely with his rear leg while
simultaneously raising his front leg into the air. His weight pushes down on the
skateboard at a point just behind the rear axle. Several important things happen at this
point:
a. The rider springs into the air using energy supplied by his leg muscles. The
amount of force supplied raises his 65kg mass approximately 5/6 meter into
the air in about 1/5 second. This can be expressed in as approximately 10.8 N.
b. The force of 10.8 N generated by the rider pushes downward on the board
because of Newtons third law which states that for every reaction there is an
equal and opposite reaction. The rear wheel of the board acts as a fulcrum and
the front of the board is accelerated vertically raising almost a meter in only 3
frames or 111 0 second.
c. The downward force also compresses the rubber wheels of the skateboard' s
rear. When the rider springs into the air, the potential energy of the
compressed and rubber wheels suppl ies enough force to raise the rear of the
skateboard approxima tely 1Jl meter in about one frame.
26POINTS 2-3:
Between points 2 and 3 is where the magic of the trick is observed.
a. The front of the board rises with the rider 's front foot because of the lever
action raising the front of the board . It seems attached to the rider's foot , but it
is not.
b. Because the mass of the rider is much greater than that of the board, the rider
is able to stop the rise of the front of the board. The riders front foot becomes
the fulcrum of a lever that transfers the excess kinetic energy from the front of
the board to the rear and causes the rear of the board to continue to rise .
NOTE: A very puzzling illusion that seems to happen as the board rises into the air. The
forward motion of the board (which was going about 18 krn/hr) seems to almost stop.
Then after the front of the board has risen, the forward motion seem s to resume at about
13 krn/hr. I wonde red how this could be un til I looked at t he motion of the rear wheels
and realized that the board as a whole didn't slow down and forward motion actually
continued at a uniform rate!
POINT 3:
At point #3 on the diagram. the rider pushes down on the front of the board with his front
foot. Again , because of inertia, th e rear of the board continues to rise until the entire
board is approximately level.
27POINT 4:
At point #4 on the diagram , the board is level and at the apex of its trajectory. From this
point on, both the board and the rider fall toward the ground accelerating at ] 0.31 rn/sec,
due to the force of gravity. The board and the rider still seem to be attached because they
are falling together.
POINT 5:
At point #5 on the diagram the board and the rider land. The force of impact absorbs
some of the board s kinetic energy and forward speed is reduced to about .3125 meters in
4/30 second or about 2.34 rn/sec or 8.43 kmlhr.
28Conclusion
The conclusion that I have reached from this experiment is that skateboard tricks
are complicated illusions that actually do not defy the laws of physics.
~-
29You can also read
