Work, Energy, and Power in Humans | Physics

Learning Objectives

By the end of this section, you will be able to:

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• Explain the human body’s consumption of energy when at rest vs. when engaged in activities that do useful work.
• Calculate the conversion of chemical energy in food into useful work.

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. (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 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 1. 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.

Table 1. 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 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 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 nonconservative, 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 1 illustrates.

Example 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 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

[latex]\displaystyle\text{Time}=\frac{\text{energy}}{\left(\frac{\text{energy}}{\text{time}}\right)}=\frac{1000\text{ kJ}}{400\text{ W}}=2500\text{ s}=42\text{ min}\\[/latex]

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

[latex]\displaystyle\text{Fat loss}=\left(1000\text{ kJ}\right)\left(\frac{1.0\text{ g fat}}{39\text{ kJ}}\right)=26\text{ g}\\[/latex],

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

Table 2. Energy and Oxygen Consumption Rates  (Power) 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 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

• 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

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?
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?
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?
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

1. (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?
2. (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?
3. 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.)
4. (a) What is the efficiency of an out-of-condition professor who does 2.10 × 105 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%?
5. 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 2 for the energy consumption rates of these activities.
6. Using 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.)
7. 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 2.)
8. 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?
9. 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.
10. 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.
11. (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?
12. 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 5). His useful power output for the 234-min trip was about 350 W. Using the efficiency for cycling from Table 2 in Conservation of Energy (which is 20%), calculate the food energy in kilojoules he metabolized during the flight.
13. The 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.
14. Mountain 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 10.0-h climb?
15. The awe-inspiring 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 × 109 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 12-hour days, 330 days per year. (a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth 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 block-lifting, 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.)
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.

Glossary

metabolic rate: the rate at which the body uses food energy to sustain life and to do different activities

basal metabolic rate: the total energy conversion rate of a person at rest

useful work: work done on an external system

Selected Solutions to Problems & Exercises

1. (a) 9.5 min; (b) 69 flights of stairs

3. 641 W, 0.860 hp

5. 31 g

7. 14.3%

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9. (a) 3.21 × 104 N; (b) 2.35 × 103 N; (c) Ratio of net force to weight of person is 41.0 in part (a); 3.00 in part (b)

11. (a) 108 kJ; (b) 599 W

13. (a) 144 J; (b) 288 W

15. (a) 2.50 × 1012 J; (b) 2.52%; (c) 1.4 × 104 kg (14 metric tons)

An electric generator is a device that converts a form of energy into electricity. There are many different types of electricity generators. Most electricity generation is from generators that are based on scientist Michael Faraday’s discovery in 1831. He found that moving a magnet inside a coil of wire makes (induces) an electric current flow through the wire. He made the first electricity generator, called a Faraday disk, which operates on the relationship between magnetism and electricity and led to the design of the electromagnetic generators we use today.

Electromagnetic generators use an electromagnet—a magnet produced by electricity—not a traditional magnet. A basic electromagnetic generator has a series of insulated wire coils that form a stationary cylinder—called a stator—surrounding an electromagnetic shaft—called a rotor. Turning the rotor makes an electric current flow in each section of the wire coil, and each section becomes a separate electric conductor. The currents in the individual sections combine to form one large current. This current is the electricity that moves from generators through power lines to consumers. Electromagnetic generators driven by kinetic (mechanical) prime movers account for nearly all U.S. electricity generation.

Turbine driven generators

Most U.S. and world electricity generation is from electric power plants that use a turbine to drive electricity generators. In a turbine generator, a moving fluid—water, steam, combustion gases, or air—pushes a series of blades mounted on a rotor shaft. The force of the fluid on the blades spins (rotates) the rotor shaft of a generator. The generator, in turn, converts the mechanical (kinetic) energy of the rotor to electrical energy. Different types of turbines include steam turbines, combustion (gas) turbines, hydroelectric turbines, and wind turbines.

Steam turbines are used to generate most of the world’s electricity, and they accounted for about 42% of U.S. electricity generation in 2022. Most steam turbines have a boiler where fuel is burned to produce hot water and steam in a heat exchanger, and the steam powers a turbine that drives a generator. Nuclear power reactors use nuclear fuel rods to produce steam. Solar thermal power plants and most geothermal power plants use steam turbines. Most of the largest U.S. electric power plants use steam turbines.

Combustion gas turbines, which are similar to jet engines, burn gaseous or liquid fuels to produce hot gases to turn the blades in the turbine.

Steam and combustion turbines can be operated as stand-alone generators in a single cycle or combined in a sequential, combined cycle. Combined-cycle systems use combustion gases from one turbine to generate more electricity in another turbine. Most combined-cycle systems have separate generators for each turbine. In single-shaft combined-cycle systems, both turbines may drive a single generator. In 2022, combined-cycle power plants supplied about 34% of U.S. net electricity generation.

Combined-heat-and-power plants (CHP) and cogenerators, use the heat that is not directly converted to electricity in a steam turbine, combustion turbine, or an internal-combustion-engine generator for industrial process heat or for space and water heating. Most of the largest CHP plants in the United States are at industrial facilities, such as pulp and paper mills, but they are also used at many colleges, universities, and government facilities. CHP and combined-cycle power plants are among the most efficient ways to convert a combustible fuel into useful energy.

Hydroelectric turbines use the force of moving water to spin turbine blades to power a generator. Most hydroelectric power plants use water stored in a reservoir or diverted from a river or stream. These conventional hydroelectric power plants accounted for about 6% of U.S. electricity generation in 2022. Pumped-storage hydropower plants use the same types of hydro turbines that conventional hydropower plants use, but they are considered energy storage systems. Other types of hydroelectric turbines called hydrokinetic turbines are used in tidal power and wave power systems.

Wind turbines use the power in wind to move the blades of a rotor to power a generator. There are two general types of wind turbines: horizontal axis (the most common) and vertical-axis turbines. Wind turbines were the source of about 10% of U.S. electricity generation in 2022.

Ocean thermal energy conversion (OTEC) systems use a temperature difference between ocean water at different depths to power a turbine to produce electricity.

Other types of generators

Many different types of electricity generators do not use turbines to generate electricity. The most common in use today are solar photovoltaic (PV) systems and internal-combustion engines.

Solar photovoltaic cells convert sunlight directly into electricity. These cells may be used to power devices as small as wrist watches, or they can be connected to form modules (or panels). Modules are connected in arrays that power individual homes or form large power plants. Photovoltaic power plants are now one of the fastest-growing sources of electricity generation around the world. In the United States, PV power plants were the source of about 3% of total utility-scale electricity generation in 2022.

Internal-combustion engines, such as diesel engines, are used all around the world for electricity generation, including in many remote villages in Alaska. They are also widely used for mobile power supply at construction sites and for emergency or backup power supply for buildings and power plants. Diesel-engine generators can use a variety of fuels, including petroleum diesel, biomass-based liquid fuels and biogas, natural gas, and propane. Small internal-combustion-engine generators fueled with gasoline, natural gas, or propane are commonly used by construction crews and tradespeople and for emergency power supply for homes.

Other types of electricity generators include fuel cells, Stirling engines (used in solar thermal parabolic-dish generators), and thermoelectric generators.

Energy storage systems for electricity generation include hydro-pumped storage, compressed-air storage, electrochemical batters, and flywheels. These energy storage systems use electricity to charge a storage facility or device, and the amount of electricity they can supply is less than the amount they use for charging. Therefore, the net electricity generation from storage systems is counted as negative in EIA reports (Electric Power Monthly and Electric Power Annual) to avoid double counting electricity use for charging the storage system.

Electricity generators by major type and share of total annual U.S. utility-scale net electricity generation in 2022 1 Generator Plant type Main fuel/energy source Share of annual electricity generation Steam turbine Single cycle All sources 42.5% Coal 19.4% Nuclear 18.2% Natural gas   2.6% Biomass (1.0%); Others (1.3%)   2.3% Multiple Combined cycle Natural gas2 33.8% Combustion turbine 21.4% Steam turbine 10.7% Dual/single shaft   1.7% Combustion gas turbine Single cycle Natural gas2   3.6% Wind turbine All types Wind   10.3% Hydroelectric turbine Conventional Water   6.0% Photovoltaic All types Solar   3.3% Others3 Various   < 1% Storage systems4 Various  0.2%

Data source: U.S. Energy Information Administration (EIA), Form EIA-923 Power Plant Operations Report, final data for 2022
Note: Sum of subtotals may not equal totals because of independent rounding of individual data series.
1 Includes generators at power plants with at least one megawatt electricity generation capacity
2 Natural gas accounted for 99% of energy sources in combined-cycle power plants and for 95% of energy sources in single-cycle combustion gas turbines.
3 Other sources include internal combustion engines, fuel cells, and binary-cycle turbines.
4 Storage systems include hydro-pumped storage, electrochemical batteries, compressed-air storage, and flywheels. The percentage share of total utility-scale electricity net generation from energy storage systems for electricity generation is shown as positive in the table above. However, generation from storage systems is published as negative net generation in EIA reports (Electric Power Monthly and Electric Power Annual) to avoid double counting of energy storage charging sources.

Last updated: October 31, 2023, with data available at the time of update.

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