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7.9: Work, Energy, and Power in Humans

Energy Conversion in Humans

Our 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. (Figure 7.09.1.) 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.

Figure 7.09.1. Energy consumed by humans is converted to work, thermal energy, and stored fat. By far the largest fraction goes to thermal energy, although the fraction varies depending on the type of physical activity.

Power Consumed at Rest

The rate at which the body uses food energy to sustain life and to do different activities is called the metabolic rate. The total energy conversion rate of a person at rest is called the basal metabolic rate (BMR) and is divided among various systems in the body, as shown in Table. The largest fraction goes to the liver and spleen, with the brain coming next. Of course, during vigorous exercise, the energy consumption of the skeletal muscles and heart increase markedly. About 75% of the calories burned in a day go into these basic functions. The BMR is a function of age, gender, total body weight, and amount of muscle mass (which burns more calories than body fat). Athletes have a greater BMR due to this last factor.

Basal Metabolic Rates (BMR):
Organ Power consumed at rest (W) Oxygen consumption (mL/min) Percent of BMR
Liver & spleen 23 67 27
Brain 16 47 19
Skeletal muscle 15 45 18
Kidney 9 26 10
Heart 6 17 7
Other 16 48 19
Totals 85 W 250 mL/min 100%

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 Figure7.09.1.) Approximately 20 kJ of energy are produced for each liter of oxygen consumed, independent of the type of food. Table shows energy and oxygen consumption rates (power expended) for a variety of activities.

Power of Doing Useful Work

Work done by a person is sometimes called useful work, which is work done on the outside world, such as lifting weights. Useful work requires a force exerted through a distance on the outside world, and so it excludes internal work, such as that done by the heart when pumping blood. Useful work does include that done in climbing stairs or accelerating to a full run, because these are accomplished by exerting forces on the outside world. Forces exerted by the body are non-conservative, so that they can change the mechanical energy \((KE + PE)\) of the system worked upon, and this is often the goal. A baseball player throwing a ball, for example, increases both the ball’s kinetic and potential energy.

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 7.09.1 illustrates.

Example 7.09.1: Calculating Weight Loss from Exercising

If 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 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

\[Time = \dfrac{energy}{\left(\frac{energy}{time} \right)} = \dfrac{1000 \space kJ}{400 \space W} = 2500 \space s = 42 \space min.\]

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

\[ Fat \space loss = (1000 \space kJ) \left ( \frac{1 \space g \space fat}{30 \space kJ} \right) = 26 \space g,\]

assuming the energy content of fat to be 39 kJ/g.

Figure 7.09.2. A pulse oxymeter is an apparatus that measures the amount of oxygen in blood. Oxymeters can be used to determine a person’s metabolic rate, which is the rate at which food energy is converted to another form. Such measurements can indicate the level of athletic conditioning as well as certain medical problems. (credit: UusiAjaja, Wikimedia Commons) 

Energy and Oxygen Consumption Rates:

Activity Energy consumption in watts Oxygen consumption in liters O2/min
Sleeping 83 0.24
Sitting at rest 120 0.34
Standing relaxed 125 0.36
Sitting in class 210 0.60
Walking (5 km/h) 280 0.80
Cycling (13–18 km/h) 400 1.14
Shivering 425 1.21
Playing tennis 440 1.26
Swimming breaststroke 475 1.36
Ice skating (14.5 km/h) 545 1.56
Climbing stairs (116/min) 685 1.96
Cycling (21 km/h) 700 2.00
Running cross-country 740 2.12
Playing basketball 800 2.28
Cycling, professional racer 1855 5.30
Sprinting 2415 6.90

All bodily functions, from thinking to lifting weights, require energy. (See Figure 7.09.3.) 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.

Figure 7.09.3. This MRI scan shows an increased level of energy consumption in the vision center of the brain. Here, the patient was being asked to recognize faces. (credit: NIH via Wikimedia Commons)

Summary

  • The human body converts energy stored in food into work, thermal energy, and/or chemical energy that is stored in fatty tissue.
  • The rate at which the body uses food energy to sustain life and to do different activities is called the metabolic rate, and the corresponding rate when at rest is called the basal metabolic rate (BMR)
  • The energy included in the basal metabolic rate is divided among various systems in the body, with the largest fraction going to the liver and spleen, and the brain coming next.
  • About 75% of food calories are used to sustain basic body functions included in the basal metabolic rate.
  • The energy consumption of people during various activities can be determined by measuring their oxygen use, because the digestive process is basically one of oxidizing food.

Conceptual Questions

Exercise 7.09.1:

Explain 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 7.09.2:

Do you do work on the outside world when you rub your hands together to warm them? What is the efficiency of this activity?

Exercise 7.09.3:

Shivering is an involuntary response to lowered body temperature. What is the efficiency of the body when shivering, and is this a desirable value?

Exercise 7.09.4:

Discuss 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 & Exercises

Exercise 7.09.5:

(a) How long can you rapidly climb stairs (116/min) on the 93.0 kcal of energy in a 10.0-g pat of butter? (b) How many flights is this if each flight has 16 stairs?

[Hide Solution]
 

(a) 9.5 min

(b) 69 flights of stairs

Exercise 7.09.6:

(a) What is the power output in watts and horsepower of a 70.0-kg 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 well-trained athlete could do this repetitively for long periods of time?

Exercise 7.09.7:

Calculate the power output in watts and horsepower of a shot-putter who takes 1.20 s to accelerate the 7.27-kg shot from rest to 14.0 m/s, while raising it 0.800 m. (Do not include the power produced to accelerate his body.)

Figure 7.09.4. Shot putter at the Dornoch Highland Gathering in 2007. (credit: John Haslam, Flickr)

[Hide Solution]

641 W, 0.860 hp

Exercise 7.09.8:

(a) What is the efficiency of an out-of-condition professor who does \(2.10 \times 10^5 \space J\) of useful work while metabolizing 500 kcal of food energy? (b) How many food calories would a well-conditioned athlete metabolize in doing the same work with an efficiency of 20%?

Exercise 7.09.9:

Energy 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 for the energy consumption rates of these activities.

[Hide Solution]
 

31 g

Exercise 7.09.10:

Using data from Table, 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 7.09.11:

What 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.)

[Hide Solution]
 

14.3%

Exercise 7.09.12:

Shoveling 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 7.09.13:

Very 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 80.0-kg person jumps from a 0.600–m-high 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.

[Hide Solution]

(a) \(3.21 \times 10^4 \space N\)

(b) \(2.35 \times 10^3 \space N\)

(c) Ratio of net force to weight of person is 41.0 in part (a); 3.00 in part (b)

Exercise 7.09.14:

Jogging 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 75.0-kg jogger’s body.) (b) Compare this force with the weight of the jogger.

Exercise 7.09.15:

(a) Calculate the energy in kJ used by a 55.0-kg 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?

[Hide solution]
 

(a) 108 kJ

(b) 599 W

Exercise 7.09.16:

Kanellos Kanellopoulos flew 119 km from Crete to Santorini, Greece, on April 23, 1988, in the Daedalus 88, an aircraft powered by a bicycle-type drive mechanism (see Figure). His useful power output for the 234-min trip was about 350 W. Using the efficiency for cycling from [link], calculate the food energy in kilojoules he metabolized during the flight.