Work and energy in athletics

Work. The word ‘work’, as used in everyday life or in athletics, refers to the overcoming of resistance. No matter how hard and exhausting the struggle or the physical benefit derived therefrom, if an athlete attempts to lift a 300-lb barbell and fails—then he has done no mechanical work! For in order to do work, in the scientific sense, a force must move an object through some distance. Work — Force X Distance.

This formula can also be applied (somewhat academically, perhaps, from the point of view of the coach or athlete) to the working of a single muscle. If its force of contraction is unknown then this is computed from its proportional cross-section and the distance is represented by the distance through which the fibres shorten—a distance usually estimated at half their resting length.

Without equipment found only in the laboratory it is impossible to measure accurately the work done by athletes; for in such calculations great care must be taken to ensure that only the force acting in the direction of motion is considered, and to remember that the effective forces exerted in athletic movement are continually changing from one instant to another.

However, it is sometimes useful and of interest to make a rough assessment, measuring force in pound-wt and the distance in feet—calling the unit of work the foot-pound. Thus, from films it could be calculated approximately that a high-jumper applied his take-off force over a vertical distance of 11/2 ft before leaving the ground and if, say, it was estimated that he exerted a 350-lb force then his work at take-off would be 1 ½ X 350 = 525 foot-pounds. Similarly, a javelin thrower who in the actual throwing action pulled the implement over a distance of 6 ft, using a 130-lb force, would do 780 foot-pounds of work, and so would another thrower applying 260 lb-wt over 3 ft.

Energy. Work must be performed in order to accelerate an athlete or throwing implement. Conversely, a moving athlete, discus, shot, hammer or javelin possesses a certain capacity to do work (called energy) by giving up velocity, i.e. by coming to rest. The energy an object has by virtue of its motion is called kinetic energy; it is the kinetic energy of a javelin which drives it several inches into the ground; a hurdler’s kinetic energy sends the hurdle flying when he hits it. This type of energy depends directly on the object’s mass; for a given velocity, the greater mass will have more energy. It depends, too, on the square of the velocity; i.e. if an object’s velocity is doubled then the kinetic energy becomes four times as great. In linear motion the kinetic energy of a body is given by the formula e = /mv, where v is the linear velocity of the mass. Unlike momentum, energy is a non-vectorial quantity, which explains why kinetic energy can be satisfactorily used, whatever its direction.

There is also the energy of position or condition—potential energy. A drawn bow is ready to do work and therefore possesses potential energy. Likewise, a high-jumper in mid-air, a pole vaulter high up over the bar or a shot at the high point of its trajectory all have potential energy by virtue of their positions. // appears to be one of the natural laws that energy can be neither created nor destroyed. No machine—and no athlete—can use more energy than has already been absorbed.

Since energy is the capacity for doing work, it is measured in units of work—i.e. in foot-pounds. If, for example, an athlete during weight training lifts 200 lb 5 ft off the floor, the barbell’s potential energy is 200 x 5 or 1000 foot-pounds. If the barbell is then dropped, its potential energy is changed into the kinetic energy of motion, and at the instant of striking the ground it still has 1000 foot-pounds of kinetic energy; the potential energy has gone. But after the weight has struck the ground the kinetic energy disappears, to be changed into other forms of energy.

When track and field athletic techniques are performed on a sound mechanical basis they require the least possible expenditure of energy or, as in sprinting, enable athletes to utilise large amounts in short periods. However, from a purely practical point of view the techniques of running, jumping, vaulting and throwing are best studied and analysed through the concept of momentum rather than energy.

Power

In athletics it is not merely the work performed which is important but also the time taken to do it. Thus, in terms of mechanical work accomplished, a quarter-miler does as much in running 440 yards in 50 seconds as when dawdling round the track in 75 seconds; but to win races he must speed up his rate of working. Again, in many track and field events an athlete has very little time in which to do his work; a long-jumper moving at great horizontal speed over the eight-inch takeoff board, for example, has but a fraction of a second in which to drive downward; he must work very quickly.

Even with regard to the development of strength and muscular endurance in training, the rate of exercising is important to athletes, for, as Steinhaus maintains in formulating the principle of progressive overloading, ‘Muscle hypertrophy is in proportion, not to actual work done, but to the work done per unit of time.’

In mechanics, the rate at which work is done is called power. Therefore power = work — time. The more work that is done in a given time the greater the power; and the quicker it is done then the greater is the power used. Here it is important to note the difference between the more precise mechanical meaning and the word’s looser meaning in everyday parlance—when, usually, it refers to force.

The measurement of power can be expressed in different ways, but kinesiologists, physiologists and others concerned with the analysis of human motion use the foot-pound per second as the smaller unit of measurement and the horse-power as the larger. It was James Watt, the Scottish inventor, who originally assessed the value of horse-power at 33,000 foot-pounds per minute, or 550 foot-pounds per second.

To take a simple case: the horse-power of a man running up a flight of stairs can be calculated if his weight, time and the height of the stairs are known. If, then, he weighs 154 lb and takes 4 seconds to climb 14 ft, his rate of working (i.e. his horse-power) is:

From a mechanical standpoint the measurement of power in track and field athletics is exceedingly difficult because, as already maintained, it is usually impossible to assess with accuracy the amount of work—in particular the ever-changing effective force of an athlete’s movement. In sprinting, for example, the distance run and time taken are easily come by, but how, without the most complicated of equipment, is the runner’s effective force—which changes with each stride— to be calculated?

Even if it were possible to obtain such figures, the result would make no allowance for additional work against gravity, air resistance, ground friction, positive and negative acceleration of the limbs, and the internal resistances due to muscle viscosity and the friction of various body tissues one against another.

It is for this reason that physiologists find it more convenient to think in terms of the energy used in exercise, and have calculated from the rate of oxygen usage that an average sprinter at top speed develops approximately thirteen horse-power.

Clearly, the ability to work quickly—i.e. powerfully—depends partly upon an athlete’s neuro-muscular co-ordination and also upon his attitude of mind, e.g., the absence of inhibition through fear of failure or injury, his determination and concentration. However, although muscular effort has so often to be exerted as quickly as possible, it is essential not to lose sight of the importance of work. Misunderstanding often leads to an omission of whole phases of forceful movement in an effort to produce speed. Thus, the athlete fails to attain maximum effect.

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