PHYSICAL TERMINOLOGY

Biology W3002y -- Structure and function of the vertebrates

Physical terms. The terms and definitions are standard ones in physics. Reference should be made to any college-level physic or mechanics text book for additional clarification and discussion.

A) Force is a push or a pull, be it a contact force or an action-at-a-distance force, which acts to modify the equilibrium of a mass. When a force acts on a mass, that body will be accelerated or decelerated. Forces are vector qualities and hence possess a direction as well as magnitude; hence when they are added, it must be by vector addition in which both the magnitudes and vector directions must be summed.

Forces are measured in pounds in the English system of measures, and in dynes and newtons in the metric system. Grams and kilograms are units of mass in the metric system as are the slug or the poundal (=the standard pound) in the English system. A newton is that force which imparts to a mass of one kilogram an acceleration of one meter per second, per second. A dyne is that force which imparts to a mass of one gram an acceleration of one centimeter per second, per second. One newton is equal to 100,000 (=10⁵) dynes. A pound is that force which imparts to a mass of one slug an acceleration of one foot per second, per second. One newton is equal to 0.224 pounds.

If grams and kilograms are used for units of weight or force, as is commonly done, they should be called gram-weight (gm-wt) or kilogram-weight (kg-wt). One pound is equal to 453.6 gram-weight; or one kilogram-weight is equal to 2.205 pounds.

When muscles contract, they develop force which is correlated with the number of contracting fibers. Muscles do not develop power when they contract, nor is power correlated with the number of contracting fibers, contrary to many statements that you will read.

B) Mass of a body is a quantitative measure of its inertia. It is measured relative to a standard kilogram in the metric system. No standard mass exists in the English gravitational system. The standard pound (or poundal) is defined as a mass equal to 0.45359 kilograms.

C) Work is the product of the displacement (a length measurement) of a body of mass and the component of force in the direction of the displacement. Work is done only when a force exerted on a body moves that body in the direction of a component of the force. If the body is not displaced, or if the body is displaced, but not in the direction of a component of force, then no work is done. Work is a form of energy and is measured in units of foot-pounds in the English system or in units of dyne centimeters or ergs,or newton-meters or joules in the metric system. One joule is equal to 10⁷ ergs, or equal to 0.7376 foot-pounds.

A muscles contracting isotonically would do work, but a muscle contracting isometrically does not shorten and hence does no work regardless of the amount of force developed or the amount of metabolic energy used. Note that work equals force X distance in the direction of the force, and since an isometrically contracting muscle does not shorted (= no distance), it does no work. It does expend energy, however. Because of the operation of muscles in the bone-lever systems, muscles frequently do not shorten and hence do not work. The concept of work is of restricted application in mechanical analyses of the skeletomuscular systems. Heat, which is another form of energy, is important in evaluating muscle systems and their relative adaptations.

D) Power is the rate at which work is done and is work divided by time. It is measured in foot-pounds per second with the commonly used unit being the horsepower which is equal to 500 foot-pounds per second. The unit of power in the metric system is one erg per second, or one joule per second (or one watt). One horsepower is equal to 746 watts. Power can be measured only if work is being done; if no work is done, as in an isometrically contracting muscle, then no power is developed. Power, like work, is not a useful concept in studies of the skeletomuscular system.

When muscles contract, they develop force, not power, which is a common error of morphologists. If a muscle also shortens and moves a body in the direction of a component of its force, then the muscle does work and develops power. The correlation between power output and weight (or volume) of muscles as used by some functional anatomists (e.g. Gray, 1968) is dubious.

Please note that if a muscle does not do any work when contracting, it does no mechanical work. But the muscle does expend energy, all of which is dissipated as heat.

E) Torque or moment of force is the product of a force and the length of its moment arm. The length of the moment arm of a force is the perpendicular distance from the axis of rotation of a body to the line of action (vector) of the force. The consequence of the torque produced by a force is to impart circular acceleration to the body on which the force acts. Torque is a vector quality and is measured in foot-pounds or in centimeter-dynes or meter-newtons. Torque is not however the same as work, but is associated with rotating bodies.

F) Stress results when two equal but opposite forces act on a body and is measured as force per unit area. Tension exists when two forces pull on a body away from one another and tend to pull particles of the body away from each other, Compression exists when two forces push on a body toward one another and tend to push particles of the body together. Shear exists when two forces act on a body (either push or pull) offset from one another (i.e., their vectors do not lie on the same line of action) so that the particles of the body tend to slide past one another.

When a stress is placed upon a body, even one comprised of homogeneous material, by means of a pair of compressive forces, for example, the force does not pass through the body along the path of its original vector direction (line of action). Rather the force is distributed into a pattern of stresses (a stress field) depending upon the shape of the object and the placement of the external forces acting on the object. Most objects (vertebrate bones) are subjected to asymmetrical stresses, hence the pattern of internal stresses is very uneven and some parts of the object are subjected to very high stresses while other parts to low stress.

The pattern of stress within an object can be diagrammed by a pattern of trajectories or lines of forces.

G) Strain is the relative change in dimension of a body subject to a stress. Strain is distortion of a stressed body. It is measured as the ratio of change in dimension relative to the original dimension; hence strain is a pure number.

Stress and strain are closely related concepts, but they mean quite different things and cannot be interchanged.

An elastic modulus is the ratio of a stress to the corresponding strain. Young's modulus, for example, is the stretch modulus and is the longitudinal stress relative to the strain; it is the same for a compressive and tensile stress on the same material.

H) Breaking point is the limit of the strength of a material to be strained under a stress without rupturing. The breaking point of an object depends upon its strength at every point in the object relative to the distribution of stress within the object. Objects which are subjected to asymmetrical stresses must withstand differing amounts of stresses throughout their volume and must be sufficiently strong to withstand the maximum stress experienced at any point, not the average stress on the object.

I) Elasticity is the ability of a material deformed under a stress to return to its original shape after the deforming stress is removed. A perfectly elastic material will return exactly to its original form after the distorting force is removed; a perfectly inelastic material does not return at all A steel ball is a highly elastic object while a putty ball is quite inelastic. Bones and bands of collagenous fibers (tendons and ligaments) are highly elastic materials.

J) Compliance is the ability of a material to be deformed under stress. A highly compliant material deforms readily while an incompliant material deforms little under a stress. Compliancy and elasticity are quite different properties. A rubber band or ball is highly compliant and moderately elastic while a steel ball is incompliant and highly elastic. Collagenous ligaments are incompliant, but highly elastic. Unfortunately many workers use the term elastic when they mean compliant.

K) Momentum of a moving body is the product of its mass and velocity. When two moving bodies collide, the change in the momentum of either body equals the impulse of force exerted on the body. Momentum and impulse of force are best diagrammed as a curve of force versus time with the momentum or impulse of force being equal to the area below the time. Of importance is that for a given momentum, the maximum force during a collision is inversely correlated to the length of time of the collision. If the time of impact increases the maximum force decreases, but the maximum force will increase with the compliancy of the body or system. Hence an incompliant object will suffer a much higher maximum force during impact than a compliant to object possessing the same momentum.