Biomechanics for a Dancer: Chapter 3

1L

1000 cm^3

1 qt

57.75 in^3

Volume

amount of three-dimensional space (width, height, depth) occupied by a body; a unit of volume is a unit of length multiplied by a unit of length multiplied by a unit of length. In mathematical shorthand, this is a unit of length raised to the exponential power of three, or a unit of length cubed. In the metric system, common units of volume are cubic centimeters (cm^3), cubic meters (m^3), and liters (l). In the English system of measurement, common units of volume are cubic inches (in^3) and cubic feet (ft^3), another unit is the quart (qt).

free body

any object, body, or body part that is being focused upon for analysis. (even though a hand must be applying force to a tennis racquet in order for the racquet to forcefully contact a ball, if the racquet is the free body of interest, the hand is represented in the free body diagram of the racquet only as a force vector).

acute loading

application of single force of sufficient magnitude to cause injury to a biology tissue, the causative force in termed macrotrauma

bending

asymmetric loading that produces tension on one side of a body's longitudinal axis and compression on the other side. when an eccentric (or nonaxial) force is applied to a structure, the structure bends, creating compressive stress on one side and tensile stress on the opposite side

force (F)

can be thought of as a push or a pull acting on a body. each force is characterized by its magnitude, direction, and point of application to a given body. body weight, friction, and air or water resistance are all forces that commonly act on the human body. the action of a force causes a body's mass to accelerate. units of force are units of mass multiplied by units of acceleration (a).

deformation

change in shape. when a force acts on an object, there are two potential effects; the first is acceleration and the second is ______ The amount of deformation that occurs in response to a given force depends on the stiffness of the object acted upon. when an external force is applied to the human body, several factors influence whether an injury occurs. among these are magnitude and direction of the force, and the area over which the force is distributed. also, important are the material properties of the loaded body tissues.

surface electrodes

consisting of small discs of conductive material, are positioned on the surface of the skin over a muscle or muscle group to pick up global myoelectric activity.

coplanar vectors

contained on the same plane, a procedure that may be used is the "tip-to-tail" method, in which the tail of the second vector is placed on the tip of the first vector and the resultant is then drawn with its tail on the tail of the first vector and its tip on the second vector.

transducers

devices that detect signals, used in the process of electromyography. known as electrodes, sense the level myoelectric activity present at a particular site over time. depending on the questions of interest, either surface electrodes or fine wire electrodes are used. output from the electrodes is amplified and graphically displayed or mathematically processed and stored by a computer.

axial

directed along the longitudinal axis of a body. pure compression and tension

stress

distribution of force within a body, quantified as force divided by the area over which the force acts. quantified the same way as pressure: force per unit of area over which the force acts. when a blow is sustained by the human body, the likelihood of injury to body tissue is related to the magnitude and direction of the ____ created by the blow. compressive, tensile, and shear ____ are terms that indicate the directing of the acting ____.

myoelectric activity

electric current or voltage produced by a muscle developing tension, known today as electromyography (EMG). used to study neuromuscular function, including indentification of which muscles develop tension throughout a movement and which movements elicit more or less tension from a particular muscle group. it is also used to assess nerve conduction velocities and muscle response in conjunction with the diagnosis and tracking of pathological conditions of the neuromuscular system. also used to study the ways in which individual motor units respond to central nervous system commands.

shear

force directed parallel to a surface. tends to cause one portion of the object to slide, displace, or ____ with respect to another portion of the object.

Pressure (P)

force per unit of area over which force acts; Units of ________ are units of force divided by units of area. Common units of ______ in the metric system are N per square centimeter (N/cm^2) and Pascals (Pa). In the English system, the most common unit of pressure is pounds per square inch (psi or lb/in^2). _______(_) is defined as force (F) distributed over a given area (A): = F/A

torsion

load-producing twisting of a body around its longitudinal axis, typically when one end of the structure is fixed. torsional fractures of the tibia are not uncommon in football injuries and skiing accidents in which the foot is held in a fixed position while the rest of the body undergoes a twist.

failure

loss of mechanical continuity. deformations exceeding the ultimate _____ point produce mechanical failure of the structure, which in the human body means fracturing of bone or rupturing of soft tissues.

density

mass per unit of volume. combines the mass of a body with the body volume. the conventional symbol for density is the Greek letter rho (ρ). density (ρ) = mass/volume. units of ______ are units of mass divided by units of volume. In the metric system, a common unit of density is the kilogram per cub meter (kg/m^3). In the English system of measurement, units of density are not commonly used. Instead, units of specific weight (weight density) are employed.

vector resolution

operation that replaces a single vector with two perpendicular vectors such that the vector composition of the two perpendicular vectors yields the original vector. The two perpendicular components, therefore, are a different but equal representation of the original vector.

scalar

physical quantity that is completely described by its magnitude, have no particular direction associated with them. mass, volume, length, and speed are examples of _____ quantities.

vector

physical quantity that possesses both magnitude and direction. represented by arrow-shaped symbols. the magnitude of a vector is its size. a ____ symbol's orientation on paper represents direction, and its length represents magnitude. force, weight, pressure, specific weight, and torque are kinetic _____ quantities; displacement, velocity, and acceleration are kinematic vector quantities.

center of gravity

point around which a body's weight is equally balanced, no matter how the body is positioned. in motion analyses, the motion of the center of gravity serves as an index of total body motion. from a kinetic perspective, the location of the center of mass determines the way in which which the body responds to external forces. the point where the weight vector is shown to act in free body diagrams, because the point at which weight is assumed to act on a body is the body's center of gravity, the center of gravity is the point where the weight vector is shown to act in free body diagrams.

yield point (elastic limit)

point on the load deformation curve past which deformation is permanent. if the force applied causes the deformation to exceed _______, the response is plastic, meaning that some amount of deformation is permanent.

compression

pressing or squeezing force directed axially through a body. the weight of the body as a compressive force on the bones that support it.

vector composition

process of determining a single vector from two or more vectors by vector adding. when vectors are added together. the composition of two or more vectors that have exactly the same direction results in a single vector that has a magnitude equal to the sum of the magnitudes of the vectors being added. if two vectors that are oriented in exactly opposite directions are composed, the resultant has the direction of the longer vector and a magnitude equal to the difference in the magnitudes of the two original vectors.

impulse (J)

product of force and the time over which the force acts. when a force is applied to a body, the resulting motion of the body is dependent not only on the magnitude of the applied force but also on the duration of force application. J=Ft a large change in an object's state of motion may result from a small force acting for a relatively long time or from a large force acting for a relatively short time.

tension

pulling or stretching force directed axially through a body. the opposite of compression force, also known as tensile force. Muscles produce tensile force that pulls on the attached bones.

repetitive loading

repeated application of a subacute load that is usually of relatively low magnitude. although a single force of this magnitude is not likely to result in a fracture of healthy bone, numerous repetitions of such a force may cause a fracture of an otherwise healthy bone somewhere in the lower extremity. when repeated or chronic loading over a period produces an injury, the injury is called a chronic injury or a stress injury, and the causative mechanism is termed microtrauma.

net force

resultant force derived from the composition of two or more forces; the vector sum of all of the acting forces. when all acting forces are balanced, or cancel each other out, the net force is zero, and the body remains in its original state of motion, either motionless or moving with a constant velocity. when a net force is present, the body moves in the direction of the net force and with an acceleration that is proportional to the magnitude of the net force.

load deformation curve

shows the relationship between the amount of force applied to a structure and the structure's response. with relatively small loads, deformation occurs, but the response is elastic, meaning that when the force is removed the structure returns to its original size and shape. since stiffer materials display less deformation in response to a given load, greater stiffness translates to a steeper slope of the load deformation curve in the elastic region.

combined loading

simultaneous action of more than one of the pure forms of loading. because the human body is subjected to a myriad of simultaneously acting forces during daily activities, this is the most

Inertia

tendency of a body to resist a change in its state of motion; resistance to action or to change. the mechanical definition is resistance to acceleration. the tendency of a body to maintain its current state of motion, whether motionless or moving with a constant velocity. the amount of inertia a body possesses is directly proportional to its mass. the more massive an object is, the more it tends to maintain its current state motion and the more difficult it is to disrupt that state.

-9.81 m/s^2

the acceleration of gravity, the negative sign indicates that the acceleration of gravity is directed downward, or toward the center of the earth.

weight

the amount of gravitational force exerted on a body. since weight is a force, units of weight are units of force either N or lb, also characterized by magnitude, direction, and point of application. the direction in which weight acts is always toward the center of the earth. algebraically, its definition is a modification of the general definition of a force, with weight (wt) being equal to mass (m) multiplied by the acceleration of gravity (a>g): wt = ma>g. As the mass of a body increases, its weight increases proportionally. The factor of proportionality is the acceleration of gravity, which is -9.81 m/s^2

free body diagram

the first step when analyzing, the effects of forces on a body or system of interest. consists of a sketch of the system being analyzed and vector representations of the acting forces

Newton (N)

the most common unit of force in the metric system, which is the amount of force required to accelerate 1 kg of mass at 1 m/s^2. 1 N = (1 kg)(1 m/s^2)

pound (lb)

the most common unit of force is the pound (lb). the amount of force necessary to accelerate a mass of 1 slug at 1 ft/s^2, and 1 lb is equal to 4.45 N. 1 lb = (1 slug)(1 ft/s^2)

mass (m)

the quantity of matter composing a body. the common unit of mass in the metric system is the kilogram (kg), with the English unit of mass being the slug, which is much larger than a kg

torque (T)

the rotary effect created by an eccentric force, moment of force. the angular equivalent of linear force, may be thought of as rotary force. algebraically, it is the product of force (F) and the perpendicular distance from the force's line of action to the axis of rotation. the greater the amount of ____ acting at the axis of rotation, the greater the tendency for rotation to occur. units of ____ in both the metric and the english systems follow the algebraic definition. they are units of force multiplied by units of distance: Newton-meters (N-m) or foot-punds (ft-lb).

resultant

the single vector resulting from a composition of two or more vectors

force platforms and pressure platforms

typically built rigidly into a floor flush with the surface and are interfaced to a computer that calculates kinetic quantities of interest. force platforms are usually designed to transduce ground reaction forces in vertical, lateral, and anteroposterior directions with respect to the platform itself; pressure platforms provide graphical or digital maps of pressures across the plantar surfaces of the feet.

specific weight

weight per unit of volume. proportional to density, as weight is proportional to mass. units of _____ ____ are units of weight devided by units of volume. the metric unit for specfic weight is Newtons per cubic meter (N/m^3), and the English system uses pounds per cubic foot (lb/ft^3).

fine-wire electrodes

when more localized pickup is desired, indwelling, ________ are injected into a muscle.