SEHS Topic 4.3 The Fundamentals of
Biomechanics (Part I)
Intro Intro
• The mathematical quantities that are used to
describe the motion of objects can be divided into
two categories. The quantity is either a vector or a
scalar. These two categories can be distinguished
from one another by their distinct definitions:
• Scalars
• Vectors
Check for Understanding
• Consider the following quantities listed below.
Categorize each quantity as being either a vector or a
scalar. Click the button to see the answer.
• Quantity
Category
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•
•
•
•
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_________________
_________________
_________________
_________________
_________________
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a. 5 m
b. 30 m/sec, East
c. 5 mi., North
d. 20 degrees Celsius
e. 256 bytes
f. 4000 Calories
• Force –
Define the following terms
• In other words, a force can cause an object with mass to
change its velocity (which includes to begin moving from a
state of rest), i.e., to accelerate, or a flexible object to deform.
• A force has both magnitude and direction, making it a vector
quantity.
• It is measured in the SI unit of newtons and represented by
the symbol F
•
Cont’d
• Speed : is a scalar quantity that refers to "how fast an
object is moving."
– Speed can be thought of as the rate at which an object
covers distance. A fast-moving object has a high speed and
covers a relatively large distance in a short amount of time.
Contrast this to a slow-moving object that has a low speed; it
covers a relatively small amount of distance in the same
amount of time. An object with no movement at all has a
zero speed.
– http://www.physicsclassroom.com/mmedia/kinema/trip.cfm
• Velocity- is a vector measurement of the rate and
direction of motion or, in other terms, the rate and
direction of the change in the position of an object
Speed vs. Velocity cont’d
• Imagine a person moving rapidly - one step forward and one step
back - always returning to the original starting position. While this
might result in a frenzy of activity, it would result in a zero
velocity.
• Why?
• Because the person always returns to the original position, the
motion would never result in a change in position. IF a person in
motion wishes to maximize their velocity, then that person must
make every effort to maximize the amount that they are displaced
from their original position.
• Remember: velocity is direction aware.
• It would not be enough to say that an object has a velocity of 55
mi/hr. One must include direction information in order to fully
describe the velocity of the object. For instance, you must describe
an object's velocity as being 55 mi/hr, east.
Speed vs. Velocity cont’d
• The average speed during the course of a motion is
often computed using the following formula:
• In contrast, the average velocity is often computed
using this formula
Check for understanding
• While on vacation, Lisa Carr traveled a total
distance of 440 miles. Her trip took 8 hours.
What was her average speed?
• Displacement –
Cont’d
• To test your understanding of this distinction, consider the motion
depicted in the diagram below. A physics teacher walks 4 meters
East, 2 meters South, 4 meters West, and finally 2 meters North.
• Even though the physics teacher has walked a total distance of 12
meters, her displacement is 0 meters. During the course of her
motion, she has "covered 12 meters of ground" (distance = 12 m).
Yet when she is finished walking, she is not "out of place" - i.e.,
there is no displacement for her motion (displacement = 0 m).
Displacement, being a vector quantity, must give attention to
direction. The 4 meters east cancels the 4 meters west; and the 2
meters south cancels the 2 meters north. Vector quantities such
as displacement are direction aware. Scalar quantities such as
distance are ignorant of direction. In determining the overall
distance traveled by the physics teachers, the various directions of
motion can be ignored
Cont’d
The diagram below shows the position of a cross-country
skier at various times. At each of the indicated times, the
skier turns around and reverses the direction of travel. In
other words, the skier moves from A to B to C to D.
Use the diagram to determine the resulting displacement
and the distance traveled by the skier during these three
minutes.
Check your understanding
• 1. What is the displacement of the cross-country
team if they begin at the school, run 10 miles and
finish back at the school?
• 2. What is the distance and the displacement of
the race car drivers in the Indy 500?
Cont’d
• Remember our physics teacher? What was his
average speed if he walked the perimeter in 24
seconds? And what was his velocity?
Definitions/Concepts Cont’d
• Momentum – is a vector describing a "quantity of motion" or in
mathematical terms p (momentum) = mass (m) X velocity (v).
– As momentum is the product of mass and the velocity, you can increase
momentum by increase either of these elements. Ex… using a heavier bat or
racquet or increasing running speed or hand speed.
• Acceleration –
• A person can be moving very fast and still not be accelerating. Acceleration
has to do with changing how fast an object is moving. If an object is not
changing its velocity, then the object is not accelerating. The data at the
right are representative of a northward-moving accelerating object. The
velocity is changing over the course of time.
•
• http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm
• Impulse –
Cont’d
• Fastball Egg Toss.
PROCEDURE
Hold a flat bed sheet at each of the four corners to provide a large target
for the pitcher. Make a "pocket" in the bottom of the sheet by holding it up
slightly. (You want to prevent the egg from rolling out of the sheet.)
• Throw an egg into the sheet as fast and hard as you can. The object is to
break the egg by throwing it into the sheet. (You may want to place the egg
in a plastic sandwich bag, just in case.)
• An egg cannot be thrown hard enough into a sheet to break the shell
because the sheet, which "gives," transfers the momentum of the egg over
a long period of time, greatly decreasing the force on the egg shell.
• Compare what happens when momentum is transferred abruptly. Drop the
raw egg (in the plastic bag) on a solid surface. Now, time is very short,
making the force much greater.
Analyze velocity-time; distance-time; and
force-time graphs of sporting actions
Final term/concept for Part I
• Center of mass/Center of gravity -
Explain that a change in body position during sporting
activities can change the position of the center of
mass
• The center of gravity is the theoretical point where all the body
weight is concentrated or the theoretical point about which the body
weight is evenly distributed.
• If a body is of uniform density and has a symmetrical shape the
center of gravity is in the geometric center.
• If the object is not symmetrical and does not have uniform density, it
is more difficult to describe the location of its center of gravity.
Cont’d
• In addition to the shifting of the center of gravity caused by body
movements, external loads alter the position of the center of
gravity. When an external load is added, the concern is the
combined center of gravity of the load and the person. When the
person lifts or carries a load, the combined center of balance must
be kept over the base to be in balance. The greater the external
load, the greater the distance the load is held from the person's
body, the farther the combined center of gravity will be from the
person's center of gravity.