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Fundamental Mechanical Concepts Relating to Biomechanics
Assignment:
Part A. Summarize the reading below from pages 1 to 4.
Be sure to define and explain each concept fully, with examples and formulas as necessary.
Some form of a ‘homework check’ should be expected.
FORCE
A force can be thought of as a push or pull, a blow exerted by actual contact or the pull of the earth's gravitational attraction on a body within its field. In other words, a force is something that causes or tends to cause a change in the motion or shape of an object or body. Itis measured in pounds (British units) or in Newtons (metric units). For example, you can push on a door with a force of 22 N (-5 lb) to open it.
PRESSURE
The definition of pressure is the amount of force acting over a given area:
p=F/A
where p is pressure, F is force, and A is area.
Pressure is expressed in Newtons per square centimeter or per square meter (N/m2), or pounds per square inch (lb/in2 or psi). Pressure is not synonymous with force. For a given force, if the area is halved, the pressure is doubled. For example, a person weighing 400 N standing on both feet (area = 200 cm2) exerts a pressure of400 N/200 cm2= 2 N/cm2 on the floor. The same person standing on only one foot exerts a pressure of 400 N/100 cm2 = 4 N/cm2.
MASS AND WEIGHT
Any body Is composed of a certain amount of matter, or mass. Mass is common to all material things, whether solid, liquid, or gaseous, and is a measure of a body's resistance to having its state of motion changed. The term given to such a resistance is inertia. Inertia is the property of a body or object that resists changes in the body's motion in any direction. The inertia of a body is related to how much mass the body possesses; the more mass, the more inertia. The inertia of the arm, for example, is less than the inertia of the leg because of the difference in their masses. The inertia, or sluggishness of a body, is measured by how many slugs (British) or kilograms (metric) of mass the body possesses.
Not to be confused with the mass of a body is the weight of the body. A body's weight is a measure of the force with which the earth pulls on the body's mass. Such a weight force always acts in a downward direction, toward the earth's center. A body's mass and weight are directly proportional; that is, the more mass a body has, the greater the earth's force of attraction on it, and therefore, the more it weighs. Mass and weight, however, should not be thought of as the same quantity. Weight is a force; mass is not. A person with a mass of 58 kg would weigh ~569 N. (In British, a mass of 4 slugs would weigh ~128 lb.)
Mass does not have a direction associated with it, nor does the mass of a body alter with changes in the gravitational force. Since the weight force is always directed downward toward the center of the earth, the magnitude of the body's weight will vary slightly according to differences in gravitational attraction. For example, a body will weigh slightly more at the earth's poles than at the equator because the magnitude of gravitational force is slightly greater at the poles.
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VOLUME AND DENSITY
The concept of mass is often confused with that of volume, or size. Volume is the space a body occupies; it has length, width, and height. It is not necessarily true that the larger a body, the greater its mass. Consider, for example, the relative mass of a golf ball and of an inflated balloon. The amount of matter in the golf ball is contained in a smaller volume (e.g., 40 cc) than is the matter in a balloon of 1000 cc (1 liter) of air and rubber. A golf ball also may he compared to a Ping-Pong ball. The golf ball has more mass within the same volume because the material inside is denser than the air inside the Ping-Pong ball. The density of an object or body is its mass per unit volume, or a measure of how compactly the body's matter is contained in its volume. Weight per unit volume is defined as the weight-density of a body.
WD = W/V
where W is weight and V is volume.
For example, the weight-density of water is 9.9 N per liter (62.4 lb/cu ft), and the weight-density of air is about 0.01 N per Alter (0.075 lb/cu ft). The fact that the weight-density of the human body is approximately the same as that of water is an important consideration in studying the buoyancy of the body in water.
Because the human body is composed of a variety of materials, its density is not uniform; that is, each body segment has a somewhat different density. The large
thorax volume is not as massive or heavy as it appears due to the low-density air in the lungs. Bones, muscles, and body fluids are relatively high-density materials in the body, whereas fat and air have lower densities.
CENTER OF GRAVITY
Recall that the earth exerts a force on each segment of a body in direct proportion to each segment's mass. The total effect of the force of gravity on a whole body, or system, is as if the force of gravity were concentrated at a single point called the center of gravity (CG). The center of a system's mass
distribution also is called its center of mass and may be thought of as that point at which all the body's mass seems to be concentrated. The CG also can be thought of as the balance point of a system, since the system's mass balances out on all sides of this point. In a rigid ob'ect of uniform density, the CG Is at the center of the ob'ect. In a segmental body whose parts can be rearranged, however, the location of the CG is dependent on the arrangement of the segments and their relative masses. The figure below shows the locations of the CG for some familiar masses.
Center of gravity locations of some common systems.
WORK
Physical work is the product of force times the distance through which that force moves a load:
W = F X d
where w is work, F is force, and d is distance force is applied. If a force of 10 N moved a body 5 m across a floor, the work done on that body would be 10 N X 5 m = 50 Nm. If the object did not move when the 10 N of force were applied, zero work would have been done even though the effort was felt.
ENERGY
Energy is defined as the ability to do work. Many kinds of energy exist, such as heat, chemical, electrical, and mechanical. Mechanical energy is of primary significance in biomechanies, although in many instances the conversion of mechanical energy into heat occurs.
Mechanical energy has three forms that are useful in understanding how the body interacts with the environment: kinetic energy, gravitational potential energy, and elastic potential energy.
Kinetic energy is the energy a body or object has because of its motion. It is expressedby:
KE = 1/2 rnv2
where KE is kinetic energy, m is mass, and v is speed.
The kinetic energy of a 10-kg medicine ball travelling at 3 rn/sec is 1/2 (10 x 3 2) = 45 Nm, which does work on the catcher who feels the force of impact during the time the ball's motion is brought to zero. The kinetic energy is transformed to heat energy in the catching process.
Gravitational Potential Energy
Whenever a body or object is in a position from which it can fall or be lowered by gravity, it posses potential energy due to its height above the surface on which it will land. Quantitatively, gravitational potential energy is expressed by:
PE = W X h
where PE is gravitational potential energy, W is weight, and h is height above the
surface. A 400-N diver on a 10-m platform has 400 X 10 = 4000 Nm of potential energy before the dive. As the diver descends, the body progressively loses Its potential energy because itis being converted into energy of motion, or kinetic energy. By the time the diver hits the water surface, all the body's energy is kinetic, and. this kinetic energy performs the work of moving a large mass of water during entry as well as creating heat.
Elastic Potential Energy
Elastic energy, or strain energy, is the ability of a body or object to do work while it recoils (or reforms) after being stretched or compressed or twisted. All the implements and balls used in sport have some degree of elasticity, or recoil ability, that provide force. Springboards and trampolines and shoe soles have recoil ability. Human bones, muscles, and connective tissues have some elasticity, fortunately, that contributes significantly to movement efficiency in activities using wind-ups, or sudden stretching during muscle contraction. Kinetic energy is the energy used to deform the body or object, and it is converted into elastic energy and heat.
POWER
In sport, the term power is often misused to describe feats of strength, or force application. Correctly, power Is the product of force times the speed with which that force is applied. A strong, fast muscle contraction is more powerful than that same muscle force applied slowly. From another perspective, power is the rate during which physical work is performed. Both expressions use the same quantities for determining power.
where P is power, F is force applied, d is distance force is applied, t is time force is applied,
and v is speed force is applied.
In Biomechanics, looking at power in terms of force times velocity is meaningful. For example, a force of 100 N applied at a speed of 2 m/sec is a power output of 200 Nmlsec, or 200 watts (1 Nm/sec = 1 watt of power). The greatest power achieved for a particular effort is always a compromise between great force and great speed rather than a maximization of either one at the expense of the other. This is discussed further in the section on power training in Chapter 7.
TYPES OF MOTION EXHIBITED BY A SYSTEM
A system's movement takes the form of linear motion or rotary (angular) motion or a combination of these types of motion.
Linear Motion
When a system is forced to move in a path that is a line, it exhibits linear motion, that is, a change in location from one place to another within a spatial frame of reference. If the path is a straight line, it is called rectilinear, and if the path is curved, it Is called curvilinear. For example, a dropped ball travels a rectilinear path toward the ground, or a jumper travels a curvilinear path over a high bar. The path of a pencil along a ruler is rectilinear; the path of a thrown discus moving through the air is curvilinear. Using only the word linear to mean rectilinear is customary. The distance (d) that a system moves in a straight line is measured in linear measurement units such as meters, feet, centimeters, inches, kilometers, or miles, and is called the linear displacement of a system.
Regardless of what the system is-the human body, a body segment, two body segments, or some object in the environment-we need to use some point in the system that represents the total system and whose motion we can follow. That point is the CG of the system. For example, to describe the path of a jogger's body, we track his CG from moment to moment, and It would form a wavy horizontal as he bounced along his way.
Rotary Motion
If some point within a system is restricted or secured so that the system rotates around this point when it receives a force, that point serves as an axis of rotation,and the motion iscalled rotary or angular motion. In the human body, each segment is connected to one or more adjacent segments to form joints. The joints serve as the location of the axes of rotation for the body segments. For instance, if you hold your elbow in 80 degrees of flexion and receive a weight in your hand, the force of the weight does not cause the entire forearm segment to move linearly downward because it is attached to the rest of the body or restricted from moving at the elbow joint, which provides resistance to downward motion of the elbow end of the forearm; the hand end of the forearm is free to move, however, and consequently rotates about the ML axis of the elbow Joint (Figure B.4a).
The change in location of a rotating body is called its angular displacement and is designated by the Greek letter theta, θ. The path of a rotating body is measured in angular measurement units such as revolutions, degrees, and radians.
(A radian is a proportion of a circle and is equivalent to approximately 57.3 degrees.)
radians = θ/57.3 degrees
where θ is angular displacement (in degrees).
Examples of angular displacement of a system exhibiting rotary motion include the sweeping of the second hand on a clock through 360 degrees with each revolution, shaking the head "no" as it rotates about a longitudinal axis through the neck, and rotating the forearm through 80 degrees as a weight is lowered (Figure B.4a).
Due to the structure of the body's skeletal system and the articulation of the segments, nearly all segmental movements are rotary. As a segment rotates, each single point on the segment describes its own circular path around the Joint axis, as shown In Figure B.4b.
(Figure to follow)
The distance from any point on the rotating segment to the axis of rotation is called that point's radius of rotation and is the radius of the circle formed by that point as the segment rotates. The radius of the point and the length of the circular are that the point forms are measured in linear measurement units (e.g., feet, meters, inches, centimeters) because they are linear distances. The entire rotating segment sweeps along an imaginary surface or plane, and the segment's movement (displacement) is measured in angular measurement units (degrees or radians).
Linear And Angular Motion
In most human movements the whole body or its segments or both move linearly and rotate at the same time. For example, the diver in Figure B.5 (figure to follow) is falling linearly downward while simultaneously rotating around her CG, which serves as the axis of rotation for any rotating object free of support.
Other examples in sport include the legs of a runner moving forward as they rotate around the knee joints, the body of a pole vaulter as he rotates around his grip on the pole while being thrust upward in a curvilinear path, and a gymnast performing a somersault dismount from a balance beam.