79. Work, Energy, and Power in HumansLearning Objectives
Energy Conversion in HumansOur own bodies, like all living organisms, are energy conversion machines. Conservation of energy implies that the chemical energy stored in food is converted into work, thermal energy, and/or stored as chemical energy in fatty tissue. (See Figure 1.) The fraction going into each form depends both on how much we eat and on our level of physical activity. If we eat more than is needed to do work and stay warm, the remainder goes into body fat. Power Consumed at RestThe rate at which the body uses food energy to sustain life and to do different activities is called the Table 1: Basal Metabolic Rates (BMR)
Energy consumption is directly proportional to oxygen consumption because the digestive process is basically one of oxidizing food. We can measure the energy people use during various activities by measuring their oxygen use. (See Figure 2.) Approximately 20 kJ of energy are produced for each liter of oxygen consumed, independent of the type of food. Table 2 shows energy and oxygen consumption rates (power expended) for a variety of activities. Power of Doing Useful WorkWork done by a person is sometimes called If a person needs more energy than they consume, such as when doing vigorous work, the body must draw upon the chemical energy stored in fat. So exercise can be helpful in losing fat. However, the amount of exercise needed to produce a loss in fat, or to burn off extra calories consumed that day, can be large, as Example 1 illustrates. Example 1: Calculating Weight Loss from ExercisingIf a person who normally requires an average of 12,000 kJ (3000 kcal) of food energy per day consumes 13,000 kJ per day, he will steadily gain weight. How much bicycling per day is required to work off this extra 1000 kJ? Solution Table 2 states that 400 W are used when cycling at a moderate speed. The time required to work off 1000 kJ at this rate is then $$\text{Time}=\frac{\text{energy}}{\left(\frac{\text{energy}}{\text{time}}\right)}=\frac{\text{1000 kJ}}{\text{400 W}}=\text{2500 s}=\text{42 min.}$$Discussion If this person uses more energy than he or she consumes, the person’s body will obtain the needed energy by metabolizing body fat. If the person uses 13,000 kJ but consumes only 12,000 kJ, then the amount of fat loss will be $$\text{Fat loss}=(\text{1000 kJ})\left(\frac{\text{1.0 g fat}}{\text{39 kJ}}\right)=\text{26}\phantom{\rule{0.25em}{0ex}}\text{g,}$$assuming the energy content of fat to be 39 kJ/g. Table 2: Energy and Oxygen Consumption Rates (Power)Note: for an average 76kg male.
All bodily functions, from thinking to lifting weights, require energy. (See Figure 3.) The many small muscle actions accompanying all quiet activity, from sleeping to head scratching, ultimately become thermal energy, as do less visible muscle actions by the heart, lungs, and digestive tract. Shivering, in fact, is an involuntary response to low body temperature that pits muscles against one another to produce thermal energy in the body (and do no work). The kidneys and liver consume a surprising amount of energy, but the biggest surprise of all it that a full 25% of all energy consumed by the body is used to maintain electrical potentials in all living cells. (Nerve cells use this electrical potential in nerve impulses.) This bioelectrical energy ultimately becomes mostly thermal energy, but some is utilized to power chemical processes such as in the kidneys and liver, and in fat production. Section Summary
Conceptual QuestionsExercise 1Explain why it is easier to climb a mountain on a zigzag path rather than one straight up the side. Is your increase in gravitational potential energy the same in both cases? Is your energy consumption the same in both? Exercise 2Do you do work on the outside world when you rub your hands together to warm them? What is the efficiency of this activity? Exercise 3Shivering is an involuntary response to lowered body temperature. What is the efficiency of the body when shivering, and is this a desirable value? Exercise 4Discuss the relative effectiveness of dieting and exercise in losing weight, noting that most athletic activities consume food energy at a rate of 400 to 500 W, while a single cup of yogurt can contain 1360 kJ (325 kcal). Specifically, is it likely that exercise alone will be sufficient to lose weight? You may wish to consider that regular exercise may increase the metabolic rate, whereas protracted dieting may reduce it. Problems & ExercisesExercise 1(a) How long can you rapidly climb stairs (116/min) on the 93.0 kcal of energy in a 10.0g pat of butter? (b) How many flights is this if each flight has 16 stairs? Show/Hide Solution Solution(a) 9.5 min (b) 69 flights of stairs Exercise 2(a) What is the power output in watts and horsepower of a 70.0kg sprinter who accelerates from rest to 10.0 m/s in 3.00 s? (b) Considering the amount of power generated, do you think a welltrained athlete could do this repetitively for long periods of time? Exercise 3Calculate the power output in watts and horsepower of a shotputter who takes 1.20 s to accelerate the 7.27kg shot from rest to 14.0 m/s, while raising it 0.800 m. (Do not include the power produced to accelerate his body.) Show/Hide Solution Solution641 W, 0.860 hp Exercise 4(a) What is the efficiency of an outofcondition professor who does $2\text{.}\text{10}\times {\text{10}}^{5}\text{J}$ of useful work while metabolizing 500 kcal of food energy? (b) How many food calories would a wellconditioned athlete metabolize in doing the same work with an efficiency of 20%? Exercise 5Energy that is not utilized for work or heat transfer is converted to the chemical energy of body fat containing about 39 kJ/g. How many grams of fat will you gain if you eat 10,000 kJ (about 2500 kcal) one day and do nothing but sit relaxed for 16.0 h and sleep for the other 8.00 h? Use data from Table 2 for the energy consumption rates of these activities. Show/Hide Solution Solution31 g Exercise 6Using data from Table 2, calculate the daily energy needs of a person who sleeps for 7.00 h, walks for 2.00 h, attends classes for 4.00 h, cycles for 2.00 h, sits relaxed for 3.00 h, and studies for 6.00 h. (Studying consumes energy at the same rate as sitting in class.) Exercise 7What is the efficiency of a subject on a treadmill who puts out work at the rate of 100 W while consuming oxygen at the rate of 2.00 L/min? (Hint: See Table 2.) Show/Hide Solution Solution14.3% Exercise 8Shoveling snow can be extremely taxing because the arms have such a low efficiency in this activity. Suppose a person shoveling a footpath metabolizes food at the rate of 800 W. (a) What is her useful power output? (b) How long will it take her to lift 3000 kg of snow 1.20 m? (This could be the amount of heavy snow on 20 m of footpath.) (c) How much waste heat transfer in kilojoules will she generate in the process? Exercise 9Very large forces are produced in joints when a person jumps from some height to the ground. (a) Calculate the magnitude of the force produced if an 80.0kg person jumps from a 0.600–mhigh ledge and lands stiffly, compressing joint material 1.50 cm as a result. (Be certain to include the weight of the person.) (b) In practice the knees bend almost involuntarily to help extend the distance over which you stop. Calculate the magnitude of the force produced if the stopping distance is 0.300 m. (c) Compare both forces with the weight of the person. Show/Hide Solution Solution(a) $3\text{.}\text{21}\times {\text{10}}^{4}\text{N}$ (b) $2\text{.}\text{35}\times {\text{10}}^{3}\text{N}$ (c) Ratio of net force to weight of person is 41.0 in part (a); 3.00 in part (b) Exercise 10Jogging on hard surfaces with insufficiently padded shoes produces large forces in the feet and legs. (a) Calculate the magnitude of the force needed to stop the downward motion of a jogger’s leg, if his leg has a mass of 13.0 kg, a speed of 6.00 m/s, and stops in a distance of 1.50 cm. (Be certain to include the weight of the 75.0kg jogger’s body.) (b) Compare this force with the weight of the jogger. Exercise 11(a) Calculate the energy in kJ used by a 55.0kg woman who does 50 deep knee bends in which her center of mass is lowered and raised 0.400 m. (She does work in both directions.) You may assume her efficiency is 20%. (b) What is the average power consumption rate in watts if she does this in 3.00 min? Show/Hide Solution Solution(a) 108 kJ (b) 599 W Exercise 12Kanellos Kanellopoulos flew 119 km from Crete to Santorini, Greece, on April 23, 1988, in the Daedalus 88, an aircraft powered by a bicycletype drive mechanism (see Figure 5). His useful power output for the 234min trip was about 350 W. Using the efficiency for cycling from Section 77, calculate the food energy in kilojoules he metabolized during the flight. Exercise 13The swimmer shown in Figure 6 exerts an average horizontal backward force of 80.0 N with his arm during each 1.80 m long stroke. (a) What is his work output in each stroke? (b) Calculate the power output of his arms if he does 120 strokes per minute. Figure 6 Show/Hide Solution Solution(a) 144 J (b) 288 W Exercise 14Mountain climbers carry bottled oxygen when at very high altitudes. (a) Assuming that a mountain climber uses oxygen at twice the rate for climbing 116 stairs per minute (because of low air temperature and winds), calculate how many liters of oxygen a climber would need for 10.0 h of climbing. (These are liters at sea level.) Note that only 40% of the inhaled oxygen is utilized; the rest is exhaled. (b) How much useful work does the climber do if he and his equipment have a mass of 90.0 kg and he gains 1000 m of altitude? (c) What is his efficiency for the 10.0h climb? Exercise 15The aweinspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high, with a mass of about $7\times {10}^{9}\phantom{\rule{0.25em}{0ex}}\text{kg}$. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging.) Historians estimate that 20,000 workers spent 20 years to construct it, working 12hour days, 330 days per year. (a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at onefourth its height. (b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps (see Figure 7), bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 kcal/h. What does your answer imply about how much of their work went into blocklifting, versus how much work went into friction and lifting and lowering their own bodies? (c) Calculate the mass of food that had to be supplied each day, assuming that the average worker required 3600 kcal per day and that their diet was 5% protein, 60% carbohydrate, and 35% fat. (These proportions neglect the mass of bulk and nondigestible materials consumed.) Show/Hide Solution Solution(a) $2\text{.}\text{50}\times {\text{10}}^{\text{12}}\text{J}$ (b) 2.52% (c) $1\text{.}4\times {\text{10}}^{4}\text{kg}$ (14 metric tons) Exercise 16(a) How long can you play tennis on the 800 kJ (about 200 kcal) of energy in a candy bar? (b) Does this seem like a long time? Discuss why exercise is necessary but may not be sufficient to cause a person to lose weight.
