2. List the fundamental measures and the units of measurement for each. 3. Given the appropriate information, calculate force, work and power.

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1 Lab Activity 1 The Warm-Up Interpretations Student Learning Objectives After Completing this lab, you should be able to: 1. Define, explain and correctly use the key terms. 2. List the fundamental measures and the units of measurement for each. 3. Given the appropriate information, calculate force, work and power. 4. Convert units from English to metric. 5. Convert oxygen consumption from L min -1 to ml kg -1 min -1 and vice versa. 6. Interpret correlation coefficients and the results of t-tests and ANOVAs. Equipment Stadiometer Scale Calculator Procedure: Part I All students should familiarize themselves with the following fundamental measures, derived measures, units of measurement and conversions before proceeding to the calculation and experimental portion of the lab.

2 A. Fundamental Measures: The International Metric System Le Systeme International d Unities (SI) There are 5 basic metric units used in exercise physiology: SI Unit Measure Abbreviation English Unit meter length m inches *liter volume L or l fluid ounces kilogram mass kg pounds o celsius temperature o C Fahrenheit second time s second mole amount of substance mol * The liter is a derivative of the meter (0.001 m 3 = 1L). B. Derived Measures: Force, Work, Power and Density Derived measures are those that are derived from the fundamental measures. 1. Force = mass (kg) acceleration (m s -2 ) = mass (kg) velocity (m s -1 ) time(s) = mass [(distance time) time]

3 2. Work = force (N) distance (m) = [mass (distance time) time] distance = mass acceleration distance 3. Power = work (J) time (s) = [mass (distance time) time) distance] time = work time =force velocity 4. Density = mass (kg) volume (L) C. Units of Measurement 1. Force = kg (m s -1 ) s -1 = kg (m s -2 ) = 1 newton (N)

4 A Newton is a force that gives a mass of 1 kg an acceleration of 1 m s -2. An old unit of force is the kilopond (kp). One kp is a force acting on a mass of 1 kg at normal acceleration due to gravity: 1 kp = N. 2. Work = 1 newton (N) meter (m) = 1 joule (J) Work is done when a force acts against a resistance to produce motion. It is the product of the force and the distance moved. One joule of work is done when the force of 1 N moves through a distance of 1 m. Because the effect of gravity on 1 kg is nearly constant at all places on earth, work is expressed in kg m: 1 kgm = J. 3. Power = (N m) s -1 = J s -1 = 1 watt Power is the rate of doing work. It is expressed in watts, but often authors will use kgm min -1. Based on the assumption that the acceleration due to gravity is a constant at all places on earth, 1 kgm min W. 4. Density = mass (kg) volume (m 3 ) Density is the amount of mass per unit volume. In the metric system, water has a density of 1 gram per cubic centimeter (g cc -1 ) or 1000 kg per cubic meter (1000 kg m 3 ).

5 D. Conversion Factors Complete Table 1.0, below. Table 1.0 Conversion Factors for Converting from English to SI units or SI to English Length 1 inch = cm 1 cm = in 1 foot = cm 1 mile = m 1 meter = in 1 km = mile 1 meter = ft 1 yard = m Volume 1 ml = cc 1 liter = quart 1 L = quart 1 fl oz = quart Mass 1 1 kg = lbs 1 kg = newton 1 lb = 1 kg Force 1 kp 2 = 1 kg 1 lb = newton 1 newton = lb Power 1 hp = watts 1 watt = kgm min -1

6 1. The SI unit of measure for mass is the gram or kilogram. Both newton and pounds are units of force, not mass. Because we assume that the acceleration due to gravity on earth is a constant we can convert kilograms to pounds or newtons and vice versa. 2. A kilopond (kp) is an old unit of force and is equal to the force exerted on a mass of 1 kilogram by the normal acceleration of gravity on the surface of the earth (9.81 m s -2 ). It is presented here so that you can make the conversion when you encounter the unit in the older literature. Under normal acceleration of gravity 1 kp is equivalent to 1 kg. E. Metric Prefixes Complete Table 2.0, below. Table 2.0. Prefixes Particularly Relevant to Exercise Physiology, with Values and Examples of Use Prefix (symbol) Value Two Examples of use Mega (M) 10 6 (1,000,000) Megabyte, Kilo (k) 10 3 (1,000) Hecto (h) 10 2 (100) Deca (da) 10 Deci (d) 10-1 (0.1) Centi (c) 10-2 (0.01) Milli (m) 10-3 (0.001) Micro (u) 10-6 ( ) Micrometer,

7 The metric system is an international decimalized system of measurement; based on 10. F. Metric Math 1. When you are working from the base unit to smaller units, move the decimal point to the right, for example 1.0 gram = 1000 mg. 2. When you are working from the base unit to larger units, move the decimal point to the left, for example 1.0 meter = kilometer meters 1 kilometer 1 km 100 meters 1 hectometer 1 hm 10 meters 1 decameter 1 dam Base unit 1 meter 1 m 0.1 meter 1 decimeter 1 dm 0.01 meter 1 centimeter 1 cm meter 1 millimeter 1 mm Examples: 19.6 m = 1960 cm = 19,600 mm = km 1.0 L = 10 dl = 1000 ml

8 3. Within the metric system, as in the English system, values can be expressed in absolute or relative units. Examples: A) Assuming a body weight of 50 kg: 2.1 L min -1 = 2100 ml min kg = 42.0 ml kg -1 min -1 This is a relative unit, in this case relative to body weight. B) Assuming a body weight of 60 kg: 35 ml kg -1 min kg = 2100 ml min ml L -1 = 2.10 L min -1 This is an absolute unit. G. Converting Units using Dimensional Analysis Dimensional analysis is used to convert from one set of units to another and simply involves setting up an equation of equivalencies so that you can cancel original units to get to units needed. Remember that you treat units exactly as you would treat numbers in an equation. For instance, if you have minutes in the denominator and the numerator when multiplying the minutes would cancel out.

9 Examples: A) Convert 80 km hr -1 to m s -1. Equivalencies needed: 1000 m per 1 km; 1 hour per 60 minutes; 1 minute per 60 seconds. 1 hr 1 min = 1 hr 60 min 60 s 3600 s 80 km 1000 m 1 hr 1 hr 1 km 3600 s 80,000 m = 22.2 m s s B) Convert 160 lb to kg. Equivalencies needed. 1 kg per 2.2 pounds. 160 lb l kg 2.2 lb 160 kg = 72.2 kg 2.2 C) Convert 6 feet and 4 inches into meters. Equivalencies needed: 1 m per in = 76 in. 76 in. 1 m = 1.93 m in. D) Convert 10,000 m to miles. Equivalencies needed: 1 mile per 1610 meters. 10,000 m 1 mile = 6.21 miles 1610 m

10 E) If a person lifted 325 lb off the floor, how much force was exerted? Equivalencies needed: 1 N per lbs. 325 lb 1 N = N lb Procedure: Part II Height, weight and age will be obtained from all students, and the data will be used to create scattergrams. Students should work with a partner and measure each other s height and weight. See the Introduction for information about creating different graphs. Protocols A. Height Measurements 1. Remove your shoes. 2. If a stadiometer is used, face away from the wall. If a scale is used, face away from the vertical rod. 3. Stand against the wall with your heels together, and evenly distribute your weight over each foot. Keep your chin level, eyes looking straight ahead and place your hands on hips. 4. Inhale deeply. Your partner should take the measurement at the highest point on the head while gently, but firmly, compressing the hair. The measurement is taken to the nearest 0.1 cm or 0.25 in. Note: After measuring the height, check to make sure the scale was read correctly. 5. Record the height in Data Table 1.0, below.

11 B. Weight Measurement: Control Condition Note: Normal laboratory measurement of weight should always be done without shoes and wearing as little clothing as possible (preferably shorts and a t-shirt). 1. Remove your shoes and step on the center of the scale. 2. Face toward the beam of the scale and evenly distribute your weight over each foot. 3. Your partner stands on the other side of the scale and moves the beam weights until balance is achieved. Weight is recorded to the nearest 0.25 lb. or 0.01 kg. Note: After measuring the weight, check to make sure the scale was read correctly. 4. Return the beam weights to zero. 5. Record the weight in Data Table 1.0. C. Weight Measurement: Experimental Condition 1. Step on the center of the scale with your shoes on. 2. Repeat steps 2-5 from Protocol B. D. Age Conversion 1. Calculate your age in months. 2. Record the age in Data Table 1.0.

12 Data Table 1.0 Subject 1 Height (cm) without shoes Weight (kg) without shoes Weight (kg) with shoes Age (months) Mean (SD)

13 Student Activities Definitions Define the following key terms. For those terms, which are measurable variables, describe in your own words what they mean (not how they are obtained or calculated). Indicate the unit(s) of measurement. 1. Density: 2. Force: 3. Joule: 4. Mass: 5. Newton: 6. Power:

14 7. SI Units: 8. Units of Measurement: 9. Velocity 10. Watt: 11. Work: Analysis 1. Using the class data in Data Table 1.0, graph the following as scattergrams and briefly discuss the relationship between the variables: a. Height versus weight without shoes b. Age versus weight without shoes c. Weight with shoes versus weight without shoes d. Age versus height

15 Interpretation and Discussion 1. Complete the following practice graph scenarios. First, choose which type of graph would be the best graph to depict the data. Then, based on the graph you complete, briefly discuss the relationship between the variables. a. To determine her acute blood pressure response to incremental aerobic exercise, Julie rode the cycle ergometer for 18 minutes. She started at a light workrate, and she increased the workrate every three minutes. The results of her exercise bout are presented in Table A. Graphically show the acute systolic blood pressure (SBP) and diastolic blood pressure (DBP) response to incremental aerobic exercise and briefly discuss the relationship between the variables. Table A Time Workrate SBP DBP (minutes) (kgm min -1 ) (mm Hg) (mm Hg) Rest

16 b. At the same time Marge started an aerobic exercise program, Homer started a strength training program. An exercise physiologist measured the capillary density of Homer and Marge s vastus lateralis before they started their respective training programs and after 6 months of training. Given the results in Table B, graphically show how capillary density changes in response to aerobic training and strength training and briefly discuss the relationship between the variables. Table B. Capillary Density (capillaries mm -2 ) Before Training After Training Homer Marge Application Complete the following problems. Show all of your calculations on set-ups. 1. A person weighing 135 lbs. steps up and down on a bench for 5 minutes at a rate of 30 steps min -1. The bench is 20 cm high. Calculate work and power for the first 30 seconds.

17 2. One person doing a bench press raises 150 lb 0.5 meter 10 times, whereas another person raises 130 lb 0.4 meter 1.5 times. Which person has done more work? 3. A woman holds an 8 lb. shot put 0.34 meter above the floor for 10 seconds. How much work is done holding the shot put?

18 4. According to a simplified model of the human heart, with each pulse approximately 20 g of blood is accelerated from 0.25 m s -1 to 0.35 m s -1 during a period of 0.10 seconds. Given that the 20 g of blood is moved about 0.30 for each beat, and the heart beats about 60 beats min -1, how much work is done by the heart in one day? Hint: Acceleration is the difference between final velocity and initial velocity divided by time. 5. A 70-kg hiker climbs to the top of a 4,200-m mountain. The climb is made in 4.0 hours starting at an elevation of 3,100 m. Calculate work and power output.

19 6. A person pedals a cycle ergometer as fast as possible for 30 seconds against a resistance of 4 kg. If the total number of pedal revolutions completed in 30 seconds is 52.5, calculate work and power (note: on his bike, for each revolution a point on the wheel travels 6 m). Hint: When pedaling a cycle ergometer, the resistance is due to a weight which must be lifted against the force of gravity. 7. A person who weighs 163 lb runs up a stairway 1.02 m high in seconds. Calculate work and power. Hint: Whenever an object (e.g., your body) is lifted against the force of gravity, acceleration is the acceleration due to gravity.

20 Related Readings References 1. Plowman, S.A. & Smith, D.L. (2011) Exercise Physiology for Health, Fitness and Performance. (3 rd ed.). Baltimore: Lippincott, Williams & Wilkins. 2. National Institute of Standards and Technology 3. Bureau International des Poids et Mesures

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