Medical Physics - Energy, Work, and Power of Human Body.pdf

Medical Physics Medical Physics Energy, Work, and Power of Human Body Energy, Work, and Power of Human Body Contents : The Concept of Energy 3 Energy Changes in Human Body 9 Oxygen Consumption 15 Basal Metabolic Rate (BMR) 19 Work and Kinetic Energy 25 Potential Energy 35 Total mechanical energy 39...

Medical Physics Medical Physics Energy, Work, and Power of Human Body Energy, Work, and Power of Human Body Contents : The Concept of Energy 3 Energy Changes in Human Body 9 Oxygen Consumption 15 Basal Metabolic Rate (BMR) 19 Work and Kinetic Energy 25 Potential Energy 35 Total mechanical energy 39 Power 42 Heat Losses From Human Body 44 The Energy to Run (Homework) 50 Energy, Work, and Power of Human Body The Concept of Energy: All the activities of the body, including thinking, is come from energy conversions (Oxygen Consumption). Food is the fuel for the body which is use the released energy to: 1. Operate its varies organs. 2. Maintain the body with constant temperature. 3. Do the external work. The energy used to operate the organs appears as body heat. Some of this heat is useful in maintaining the body at its normal temperature. Energy, Work, and Power of Human Body The Concept of Energy: Other energy source can help maintain body temperature. Radiant solar energy and Heat energy from our surrounding environment. Under resting conditions about: 25% of the body s̓ energy is being used by skeletal muscles & the heart. 19% is being used by the brain. 10% is being used by the kidneys. 27% is being used by the liver and spleen. 5% is being used by the feces and urine. Any energy that is left over is stored as body fat. Energy, Work, and Power of Human Body The Concept of Energy: The law of conservation of energy. This law states that there exists a numerical quantity called “energy” that remains fixed in any process that occurs in nature. Energy comes in many forms. Mechanical energy, Electrical energy, Chemical energy, Nuclear energy, and Thermal energy. In this lecture we study only the conversion of energy in the body, the work don by and power of the body and how the body loses heat. Energy, Work, and Power of Human Body The Concept of Energy: Conservation of Energy in the Body. Change in stored energy in the body (i.e. food energy, body fat, and body heat) = Heat lost from the body + Work done. This is known as the first law of thermodynamics: Δ𝑈𝑈: is the stored energy. Δ𝑄𝑄: is the heat lost or gained. Δ𝑊𝑊: is the work done by the body in some interval of time. Energy, Work, and Power of Human Body The Concept of Energy: A body that is doing no work (Δ𝑊𝑊 = 0) and at a constant temperature, continues to lose heat to surrounding environment, i.e., Δ𝑄𝑄 = −𝑣𝑣𝑒𝑒. Therefore, Δ𝑈𝑈 is also −𝑣𝑣𝑒𝑒. , indicating a decrease in stored energy. It is useful to consider the change of Δ𝑈𝑈, Δ𝑄𝑄, 𝑎𝑎𝑛𝑛𝑑𝑑 Δ𝑊𝑊 in a short interval of time Δ𝑡𝑡. Energy, Work, and Power of Human Body : is the rate of change of stored energy. : is the rate of heat loss or gain. : is the rate of doing work (Mechanical Power). Energy Changes in Human Body Energy, Work, and Power of Human Body Energy Changes in Human Body: Energy of the Human body is the measure of its ability to do work. Several energy and power units are used in relation to the body. Physiologist: 1. Kilocalories (kcal) for food energy. 2. Calorie (C) is actually a kilocalorie. 3. Kilocalories (kcal) per minute for the rate of heat production Diet of 2500 C/day is 2500 kcal/day. Energy, Work, and Power of Human Body Energy Changes in Human Body : Physics: Unit for energy in 𝑀𝑀𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟, 𝐾𝐾𝑖𝑖𝑙𝑙𝑜𝑜𝑔𝑔𝑟𝑟𝑎𝑎𝑚𝑚, 𝑆𝑆𝑒𝑒𝑐𝑐𝑜𝑜𝑛𝑛𝑑𝑑 (𝑆𝑆𝐼𝐼) system is 𝑁𝑁𝑒𝑒𝑤𝑤𝑡𝑡𝑜𝑜𝑛𝑛. 𝑚𝑚𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟 (𝑁𝑁. 𝑚𝑚) ,or 𝐽𝐽𝑜𝑜𝑢𝑢𝑙𝑙𝑒𝑒 (𝐽𝐽) And in 𝐶𝐶𝑒𝑒𝑛𝑛𝑡𝑡𝑖𝑖𝑚𝑚𝑒𝑒𝑡𝑡𝑒𝑒𝑟𝑟, 𝐺𝐺𝑟𝑟𝑎𝑎𝑚𝑚, 𝑆𝑆𝑒𝑒𝑐𝑐𝑜𝑜𝑛𝑛𝑑𝑑 (𝐶𝐶𝐺𝐺𝑆𝑆) system is the 𝑒𝑒𝑟𝑟𝑔𝑔, (1 𝑒𝑒𝑟𝑟𝑔𝑔 = 10−7𝐽𝐽). Power is given in (𝐽𝐽/𝑠𝑠) or Watt (𝑊𝑊). Energy, Work, and Power of Human Body Energy Changes in Human Body : 𝑀𝑀𝐸𝐸𝑇𝑇 (metabolic equivalents) is a convenient unit for expressing the rate of energy consumption of the body. Metabolic rate refers to the chemical process by which your body converts food and drinks into energy. It plays a crucial role in determining how many calories you need to function and how much energy you use for basic and physical activities. Energy, Work, and Power of Human Body Energy Changes in Human Body : 1𝑀𝑀𝐸𝐸𝑇𝑇 is the energy you spend sitting at rest - your resting or basal metabolic rate. 𝑀𝑀𝐸𝐸𝑇𝑇 defined as: 50 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑚𝑚2 of body surface area per hour. For normal person the energy consumption is 1 𝑀𝑀𝐸𝐸𝑇𝑇 under resting conditions. Atypical man has about 1.85 𝑚𝑚2 of surface area (a woman has 1.4 𝑚𝑚2), and thus for a typical man 1 𝑀𝑀𝐸𝐸𝑇𝑇 is about 92 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/ℎ𝑟𝑟 𝑜𝑜𝑟𝑟 107 𝑊𝑊. Energy, Work, and Power of Human Body Energy Changes in the Body : 1 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙 = 4184 𝐽𝐽. 1 𝐽𝐽 = 107 𝑒𝑒𝑟𝑟𝑔𝑔. 1 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/min = 69.7 𝑊𝑊 = 0.094 ℎ𝑝𝑝 (horsepower). 100 𝑊𝑊 = 1.43 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙 / min. 1 ℎ𝑝𝑝 = 642 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙 / ℎ𝑟𝑟 = 746 𝑊𝑊. 1 𝑀𝑀𝐸𝐸𝑇𝑇 = 50 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑚𝑚2. ℎ𝑟𝑟 = 58 𝑊𝑊/𝑚𝑚2. 1 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙 / ℎ𝑟𝑟 = 1.162 𝑊𝑊. Oxygen Consumption Energy, Work, and Power of Human Body Oxygen Consumption : Food oxidation The oxidation occurs in the cell of the body which increased during the process of digestion. In the oxidation process by combustion, heat is released as an energy of metabolism. The rate of oxidation is called metabolic rate. The oxidation equation for 𝟏𝟏 𝒎𝒎𝒐𝒐𝒍𝒍𝒆𝒆 (𝟏𝟏𝟖𝟖𝟎𝟎 𝒈𝒈) of glucose (𝐶𝐶6𝐻𝐻12𝑂𝑂6) in common intravenous feeding is: Energy, Work, and Power of Human Body 1 𝑚𝑚𝑜𝑜𝑙𝑙𝑒𝑒 of gas has a volume of 22.4 𝑙𝑙𝑖𝑖𝑡𝑡𝑡𝑡𝑒𝑒𝑟𝑟 (at constant temperature & pressure). Kilocalories of energy released per gram of fuel = 686 / 180 = 3.8 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑔𝑔. Kilocalories released per liter of 𝑂𝑂2 used = 686 / ( 6 × 22.4 ) = 5.1 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑙𝑙. Liters of 𝑂𝑂2 used per gram of fuel = 6 × 22.4 / 180 = 0.75 𝑙𝑙/𝑔𝑔 Liters of 𝐶𝐶𝑂𝑂2 produced per gram of fuel = 6 × 22.4 / 180 = 0.75 𝑙𝑙/𝑔𝑔 Energy, Work, and Power of Human Body Oxygen Consumption : The various types of food gives various energy released per liter of oxygen consumed. Therefore, by measuring the oxygen consume by the body we can get a good estimate of the energy released. Stored energy (at constant temp.) = Extracting energy from food + Body fat. Note: Not all of this energy is available to the body because part is lost in incomplete combustion (feces, urine, and gas) Basal Metabolic Rate (BMR) Energy, Work, and Power of Human Body Basal Metabolic Rate (BMR): At rest, the typical person consumes energy at a rate of about 92 kcal/hr (107 W or 1 met). This lowest rate of energy consumption, called Basal Metabolic Rate (BMR). BMR defined as the amount of energy needed to perform minimal body function such as Breathing Pumping the blood through the arteries under resting conditions. Clinically BMR compared to normal values for a person of the same sex, age, height, and weight. Energy, Work, and Power of Human Body BMR depends primarily upon: 1. Thyroid function, a person with an overactive thyroid has a higher BMR than a person with normal thyroid function. 2. Temperature of the body, a small change in temperature can Produce a large change in chemical reactions. Every 1 ̊𝐶𝐶 change cause 10% change in BMR. 3. BMR change fast with surface area. 4. BMR is proportional to mass of the body. Energy, Work, and Power of Human Body Weight loss through dieting and physical exercise discussed in following example: Example 1: Suppose you wish to lose 4.54 𝑘𝑘𝑔𝑔 either through physical activity or by dieting. How long would you have to work at an activity of 15 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/min to lose 4.54 𝑘𝑘𝑔𝑔 of fat ? Energy, Work, and Power of Human Body Fats the maximum rate of energy 9.3 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑔𝑔. If you worked for 𝑇𝑇 𝑚𝑚𝑖𝑖𝑛𝑛𝑢𝑢𝑡𝑡𝑒𝑒𝑠𝑠, then 𝑇𝑇 min × 15 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙 / min = 4.54 × = 4.2 × 104 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙 𝑇𝑇 = 2810 min = 47 ℎ𝑟𝑟 103 𝑔𝑔 × 9.3 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑔𝑔 Note: Note that a great deal of exercise is needed to lose a few kg. Energy, Work, and Power of Human Body It is usually much easier to lose weight by reducing your food intake. If you normally use 2500 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑑𝑑𝑎𝑎𝑦𝑦, how long must you diet at 2000 𝑘𝑘𝑐𝑐𝑎𝑎𝑙𝑙/𝑑𝑑𝑎𝑎𝑦𝑦 to lose 4.54 𝑘𝑘𝑔𝑔 of fat? Note: From the oxygen consumption: BMR is sometimes determined when resting. We can estimate the food energy used in various physical activities. Work and Kinetic Energy Energy, Work, and Power of Human Body Work and Kinetic Energy: Energy stored in the body is converted into external mechanical work. When a force acts through a distance, we say, “The force does work.” More precisely, the work 𝑾𝑾 done by a constant force 𝑭𝑭 acting on a body moving in a straight line is defined to be the product of the force component 𝐹𝐹𝑥𝑥 in the direction of motion times the distance ∆𝑥𝑥 the body moves: Energy, Work, and Power of Human Body Work and Kinetic Energy: If a body does not move, ∆𝒙𝒙 = 𝟎𝟎, and so, even though forces may act on the body, no work is done by those forces (Figure a). No work is done on a moving body by any force that is perpendicular to the direction of the body’s motion (Figure b), since such a force has a zero component in the direction of motion. (Figure a) (Figure b) Energy, Work, and Power of Human Body Work and Kinetic Energy: The unit of work is the unit of force times the unit of distance the Nm in SI. This unit is given the name “joule” (abbreviated J), in honor of James Joule, who demonstrated by numerous experiments in the nineteenth century that heat is a form of energy: In the cgs system the unit of work is the erg, defined as a dyne-cm. Since 1 𝑁𝑁 = 105 𝑑𝑑𝑦𝑦𝑛𝑛𝑒𝑒 and 1 𝑚𝑚 = 102 𝑐𝑐𝑚𝑚 , 1 𝑁𝑁 − 𝑚𝑚 107 𝑑𝑑𝑦𝑦𝑛𝑛𝑒𝑒 − 𝑐𝑐𝑚𝑚 or Energy, Work, and Power of Human Body Example 1: Pulling a Suitcase: An airline passenger pulls his suitcase a horizontal distance of 40.0 m, exerting a force F of magnitude 25.0 N, directed 30.0° above the horizontal. Find the work done by the force F. Energy, Work, and Power of Human Body Example 2: Lifting a Box: A woman slowly lifts a box weighing 40.0 N from the floor to a shelf 1.50 m above a) Find the work done by the force 𝐹𝐹 the woman exerts on the box. b) Find the work done on the box by its weight 𝑤𝑤. c) Find the net work done on the box. Energy, Work, and Power of Human Body Example 2: Lifting a Box: (a) (b) (c) The net work done on the box is the sum of the work done by each of the forces acting on the box. Net work equals zero: Energy, Work, and Power of Human Body Work and Kinetic Energy: Kinetic Energy A body’s kinetic energy 𝐾𝐾 is defined to be half its mass 𝑚𝑚 times the square of its speed 𝑣𝑣. Energy, Work, and Power of Human Body Work and Kinetic Energy: Kinetic energy is conserved. A more interesting example of conservation of kinetic energy occurs in the game of pool. Ball has a mass of 0.2 𝑘𝑘𝑔𝑔 and is initially moving at 10 𝑚𝑚/𝑠𝑠, its initial kinetic energy Energy, Work, and Power of Human Body Work and Kinetic Energy: The other balls are initially at rest and so have no kinetic energy. Just after the collision, the kinetic energy of 10 𝐽𝐽 is shared among all balls Work and Potential Energy Energy, Work, and Power of Human Body Work and Potential Energy: Constant Gravitational Force The work done on a body on or near the earth’s surface by the constant force of gravity. Work always equals the decrease in a quantity called “gravitational potential energy,” which depends on the body’s elevation. When gravity is the only force doing work on a body, the sum of the body’s kinetic energy plus its gravitational potential energy is conserved. Energy, Work, and Power of Human Body Work and Potential Energy: Work is done by the gravitational force Gravitational potential energy The work equals the difference in the values of the gravitational potential energy Energy, Work, and Power of Human Body Work Potential Energy: For example, suppose a roller coaster weighing 104 𝑁𝑁 starts at an elevation of 40 𝑚𝑚 , where its potential energy 𝑚𝑚𝑔𝑔𝑦𝑦 = 4 × 105 𝐽𝐽, and falls to an elevation of 10 𝑚𝑚, where its potential energy 𝑚𝑚𝑔𝑔𝑦𝑦 = 105𝐽𝐽. No matter what path the roller coaster follows, the gravitational force does work on it equal to its decrease in potential energy of 3 × 105 𝐽𝐽. Total mechanical energy Energy, Work, and Power of Human Body Total mechanical energy: We define the total mechanical energy 𝐸𝐸 to be the sum of the kinetic and gravitational potential energies: As a simple example of conservation of mechanical energy, consider a body in free fall. Energy, Work, and Power of Human Body Total mechanical energy: As a body falls, its speed increases. Its kinetic energy increases while its potential energy decreases, so that the sum of the two the total mechanical energy remains constant. This is illustrated in Fig. for a 1 kg body falling from rest through a distance of 1 m. Power Energy, Work, and Power of Human Body Power: The rate at which work is performed by a force is defined to be the power output of the force. The average power, denoted by 𝑃𝑃, is the work divided by the time ∆𝑡𝑡 over which the work is performed. The SI unit of power is the 𝐽𝐽/𝑠𝑠 , which is called the “ 𝑤𝑤𝑎𝑎𝑡𝑡𝑡𝑡 ” (abbreviated 𝑊𝑊), in honor of James Watt, the inventor of the steam engine. Heat Losses From Human Body Energy, Work, and Power of Human Body Heat Losses From Human Body : The normal body contains stored heat and constant temperature 37 ̊𝐶𝐶. The body should have certain mechanism to keep this temperature constant despite of fluctuations in the environment temperature. These mechanisms are: 1. Radiation 2. Convection 3. Perspiration 4. Respiration Energy, Work, and Power of Human Body Heat Losses From Human Body : Radiation Body emit electromagnetic radiation of energy proportional to the fourth power of absolute temperature. This given by Stefan Boltzmann Law: The emissivity e in the infrared region is independent of the color of the skin and is very nearly equal to 1. Energy, Work, and Power of Human Body Heat Losses From Human Body : The body receives radiant energy from surroundings objects. The approximate difference between the heat radiated by the body and the heat absorbed from surroundings can be given by: 𝐻𝐻𝑟𝑟: the rate of energy loss (or gain) due to radiation. 𝐴𝐴𝑟𝑟: effective area of the body emitting radiation. 𝑇𝑇𝑠𝑠: skin temperature. 𝑇𝑇𝑤𝑤: wall surrounding temperature. 𝐾𝐾𝑟𝑟 : radiation coefficient or constant that depends upon various physical parameters = 5 kcal/m2. hr. ˚C. Energy, Work, and Power of Human Body Heat Losses From Human Body : The heat loss due to convection (𝐻𝐻𝑐𝑐) can be given by: 𝐻𝐻𝑐𝑐: Heat loss due to convection. 𝐾𝐾𝑐𝑐: convection coefficient or constant that depends upon the movement of the air and equal to 2.3 kcal /m2. hr. ˚C when the body is resting and there is no apparent wind. 𝐴𝐴𝑐𝑐: the effective surface area. 𝑇𝑇𝑠𝑠: the temperature of the skin. 𝑇𝑇𝑎𝑎: the temperature of the air. Energy, Work, and Power of Human Body Heat Losses From Human Body : The previous mechanisms of losing heat depends upon: 1. Temperature. 2. Humidity. 3. Motion of the air. 4. Physical activity of the body. 5. The amount of body exposed. 6. The amount of insulation of body (clothes and fat). The hypothalamus of the brain contains the body ̓ s thermostat. For example, if the core temperature rises, the hypothalamus initiates sweating and vasodilatation, which increases the skin temperature The Energy to Run Energy, Work, and Power of Human Body The Energy to Run: Why is it so much harder to run than to ride a bicycle at the same speed? When you ride a bicycle, it is after all your own body that produces your motion, just as when you run. And yet cycling requires much less effort than running. After 30 minutes or an hour of running along a level road at a moderate pace, even a well conditioned runner may tire, whereas a cyclist can keep the same pace with little effort. Energy, Work, and Power of Human Body The Energy to Run: We say that “running burns calories” or that “running uses a lot of energy.” To understand the physical basis of such expressions, to see why running requires so much energy and is so much less energy efficient than bicycle riding, we shall apply concepts of work and energy to the human body. Also extend concepts of work and energy to systems of particles such as human bodies and machines. In general, how energy is used by the body when muscles contract and specifically how that energy is used in running and cycling. Energy, Work, and Power of Human Body The following are some general properties of work and energy associated with muscular exertion: 1. Work Done by Muscles Muscles consist of bundles of muscle fibers. Under tension, these fibers can shorten, or “contract,” as protein filaments within the fibers slide over each other. Contraction of a muscle fiber means that a force (the tension in the muscle fiber) acts through a distance (the distance the fiber contracts). The direct effect of a muscle’s contraction may be to move one of the body’s limbs. Energy, Work, and Power of Human Body The Energy to Run: For example, if you hold a weight in your hand and contract the biceps muscle in your arm, your hand and forearm swing upward, raising the weight. The work done by your biceps muscle is approximately equal to the work done by the force your hand exerts on the weight. The effect of this work is to increase the weight’s gravitational potential energy. Energy, Work, and Power of Human Body 2. Heat Generated by the Body When Muscles Contract Heat, a disordered form of energy, is generated whenever muscles do work. Typically the quantity of heat generated when muscles contract is about three times as great as the work done by the muscles. When your muscles do very much work, you can usually feel the heat generated by your body. You may begin to sweat, which is a way the body gets rid of excess heat. Energy, Work, and Power of Human Body 3. Internal Energy of the Body The body’s internal energy is the total energy of all the particles within the body. Chemical reactions within the body provide the energy necessary to produce muscle contraction. The energy released by these chemical reactions produces the work and heat associated with muscle contraction. Conservation of energy implies that the body’s loss of internal energy equals the sum of the work and heat generated. Loss of internal energy = Work done by muscles + Heat generated Energy, Work, and Power of Human Body When your body loses much internal energy in a short time interval, you tend to feel tired. Your body’s internal energy is replenished by the consumption of food. Now we can use these basic concepts of work and energy to understand why cycling requires less energy than running. Suppose you ride a bicycle with, well-inflated tires and very little friction in its moving parts. Riding over flat, level pavement at 10 km/h, requires little effort. Energy, Work, and Power of Human Body Once moving, both the kinetic energy and the gravitational potential energy of the bicycle and your body stay constant with just a little pedaling required. Consequently, only a little work needs to be done by your legs as they push against the pedals and your body loses little internal energy in producing this small amount of work. The work that is done by your legs is needed to compensate for the small negative work done by friction and air resistance. If you did not pedal at all, your bike would gradually slow down. Energy, Work, and Power of Human Body In contrast to riding a bike, when you run on a flat, level surface, your kinetic energy and gravitational potential energy can never be exactly constant. Watch a runner and you will see that the runner’s head moves up and down somewhat, an indication of some change in elevation of the runner’s center of mass. This means that the runner’s gravitational potential energy is not constant. Energy, Work, and Power of Human Body Some of that energy is lost each time the runner’s body moves downward, and this energy must then be supplied as the body moves up - ward again. More efficient runners, bob up and down less than average runners do and there by use less energy. A runner’s center-of-mass kinetic energy also necessarily varies somewhat, again in contrast to that of a cyclist. Energy, Work, and Power of Human Body This effect is more difficult to see, a runner’s center of mass continually alternates between speeding up and slowing down with each stride. The variation in center-of-mass speed is slight, it does require a significant amount of work for the legs to increase the center of mass kinetic energy from the minimum value to the maximum value during each stride.