I. How much work can a person do?

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I: How Much Work Can a Person Do? Henry A. Bent North Carolina State University Raleigh, 27650

How much work can a person do, per second-compared, for exam~le,to a horse? ~ u n n i n gup stairs, Benjamin Franklin felt, is the hardest work there is. His contemporary, Charles de Coulomb (of "Coulomb's Law," and, likewise, interested in how much work a person can do), once observed a young man climb an extraordinarily long stairway rising about 150m, in 20 min. The young man's rate of vertical ascent was, thus, about 0.125 mls m c em 150m 1min --X- 0.125-X -= 12.520 min 60s s lo-z s [The prefix "c" in, e.g., "cm," stands for 10-2: c = 10W. Thus, 1.1 as noted above, C I ~ O=- ~

Assuming the young man weighed 70 kg (154 lh; 1kg = 2.20 Ih), one calculates that his increase in potential energy in the 20-min climb was about 103,000 J and that his power output, or rate of increase in mechanical energy, was about 85 W (Box 1). More recently, in a Harvard Step Test on and off a 50.8-cm high bench, a group of young men maintained a vigorous steonine rate of 30 bench s t e ~ s l m i nfor 5 min, or until exha&ted: for a climbing rate oi 25 cmls and a corresponding Dower outout about twice that of Coulomb's slower, but more enduring, stair-climber. During extremely short bursts of stair-climbing, lasting less than a second, a test group of young men reached climbing rates of over 140 cmls. In old English units, they raised around 150 lb 5 ftls, yielding a power output of ahout 750 ft lb/s. Some horses! Real horses, according to James Watt, raise 550 pounds 1 ftls i.e., according to Watt 1h p = 550 ft Ibls. A record weight lift in 1975 of 440 pounds snatched-i.e., raised above the iifter's head (about 7 feet) in about 1s--yields a calculated power output of about 440 X 7 + 550 = 5.6 hp. World-class sprinters generate kinetic energy a t the start of a race a t the rate of about 3-4 hp. Momentarily, jumping vertically off force platforms, young men generate power outputs of 5-6 hp. Maximum power output of human muscle is estimated to he 0.3 hplkg. Thus, the ultimate power output of a 70-kg "Huw Much Wurk Can a I'erson I)oq" is the first of a six-part Interface Series t~tledE n e r e ond Exercise. Part 11, "Oxyg& Consumption, Heat Production and Respiratory Quotients" will appear in the August issue. Interface Series papers deal with various aspects of the interface between chemistry and other areas of knowledge or to topics at the boundaries of secondary schwl and colleee chernistrv. , ., .... Hmry Bent currently i* ChairHenry A. Bent man 01 the Division of Chemical North Carolina State Education. He has been a profewor at North Carolina State University University at Raleigh since 1969. Dr. Bent's personal program of physical fitness provides an especially rich (or is it lean) backmound for these nnnera.

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456 1 Journal of Chemical Education

person who is 45 percent muscle, all muscles fully harnessed, is probably about 9-10 hp. However, 5-6 hp appears to he the maximum achievable output, and that only momentarily (Box 2). It's a law of human's nature: the harder one works the sooner one must stop. Though people like cars, people aren't like cars. True, to run both need fuel and oxygen. Cars, however, can run full-out, for 1s or 5 min, perhaps even 2 hr. People can't-though not

Box 1. Definitionsand Illustrative Examples of the Joule and the Watt (At sea-level, the acceleration due to gravity = 32 n/s2 = 9.8 m/s2 (1m = 3.28n)y

Change in Potential

= (force due to gravity)(changein

altitude)

Energy

= (massX acc. due to grav.)

(changein altitude)

Power Output

=

Change in Mechanical Energy Time

- 103,000J --

Box 2. Llmlts of Power

Activity Single vigorous movementweight lined vertical jump Sprint-likelevel of activity Milequn-like level of activity Marathon-like level of activity Full day of manual labor

'

Duration

Work Output Power Outputs (Power X time) hp kW kcailmin kcal

,gardening7, playing fwtt)nllU,shoveling 10, working w t h an axe 12, cross-country skiing 15. The caloric cost of running at moderate speeds is proportional to one's speed: in kilocalories per minute, about twice one's speed in miles per hour. By extrapolation, jogging 3 mph has a caloric cost of 6 kcallmin, greater than that of walking the same soeed. Indeed. the fastest unassisted transit acrosi the U S . has been achieved by a walker, not a runner. In the long run, it's better to walk. But how about in the short run? Suggested Reading (11 Astrand, P.,and R d a h l , K.."Texlhoak ofwork Physiology."McCraw-Hill BwkCo., New York.1970. (2) Wilke. D. R., "Mao as a Sourecaf Mechanical Power." Elganomics, 3.1 (1960). (3) Davies, C. T. M.. "Human Power Output in Exercise of Short Duration in Relation to

Body Size and Composition,"Ergonomics. 14 121,245 119711. I41 Copfi1l.D. L.,and For. E. L.,"Eneweiin of Marathon Running."M ~ d i c i n ~ o n d S e i s n r r in Sports. 1[21,61 (19691.