# Work, Power & Conversions

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1 Purpose Work, Power & Conversions To introduce the metric system of measurement and review related terminology commonly encountered in exercise physiology Student Learning Objectives After completing this lab, you should be able too: 1. Define, explain and correctly use key terms. 2. List the fundamental measures, derived measures and the units of measurement for each. 3. Calculate force, work and power. 4. Convert units for English to metric. 5. Convert oxygen consumption from L min -1 to ml kg -1 min -1 and vice versa. Equipment Needed Calibrated balance scale with stadiometer Data Collection Working with a partner, record your weight in pounds (lb) and height in inches (in.) as measured using a calibrated platform scale and stadiometer. Presentation of Data 1. Perform the following conversions: o Weight in lb to weight in kg o Height in in. to height in m o Height in m to height in cm 2. Compare your height and weight data with a standard height weight table. 3. Answer the following questions: o If a man is 5 ft, 10 in. tall, how tall is he in cm? in m? o If a baseball player hits a home run that measures 430 ft, how far did the ball travel in m? o If two football players weigh 200 lb and 240 lb, respectively, what is the difference in their weights, expressed in kg? o If a cross-country runner runs at a 10 mi/h pace, what is his pace expressed in m/s? in km/h? o If another runner runs at a pace of 6.5 min/mi, what is her speed expressed in mi/h? Page 1

2 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. A. Fundamental Measures: The International Metric System There are 5 basic metric units used in Exercise Physiology SI Units Measure Abbreviation English Unit meter *liter length *volume m *L or l inches fluid ounces kilogram mass kg pounds celcius temperature C farenheit second time s second mole amount of substance mol * The liter is a derivative of the meter (0.001 m 3 = 1 L). B. Derived Measures: Force, Work, Power, and Density Derived measures are those that are derived from the fundamental measures. 1. Force = mass (kg) x acceleration (m s -2 ) = mass (kg) x velocity (m s -1 )/time (s) = mass x [(distance/time)/time] 2. Work = force (N) x distance (m) = [mass x (distance/time)/time] x distance = mass x acceleration x distance 3. Power = work (J)/ time (s) =[mass x (distance/time)/time) x distance]/time =work/time =force x velocity 4. Density = mass (kg)/volume (L) Page 2

3 C. Units of Measurement 1. Force = kg x (m s -1 ) s -1 = kg x (m s -2 ) = 1 Newton (N) 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 = Newton (N) x meter (m) = 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 the 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 x m)s -1 = J s -1 = 1 Watt Power is the rate of doing work. It is expressed in kgm min -1 : 1 kgm min -1 = 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 ). D. Conversion Factors 1. Length 1 inch = 2.54 cm 1 cm = in 1 foot = cm 1 mile = 1610 m 1 meter = in 1 km = 0.62 mile 1 meter = 3.28 ft 1 yard = m Page 3

4 2. Volume 1 quart = 0.94 L 1 ml = 1 cc 1 L = 1.06 quarts 1 fl. oz. = 29.5 ml 3. Mass 1 kg = 2.2 lbs. = Newtons* 1 lb. = kg * When gravity equals 9.8 m s m s -2 is the acceleration of an object due to the force of gravity. 4. Force 1 lb. = 4.45 N 1 N = lbs. 1 kg = 1 kp* * Under normal acceleration of gravity. 5. Power 1 horsepower (hp) = 746 W 1 W = 6.12 kp m min -1 E. Metric Prefixes Prefixes particularly relevant to exercise physiology are given below: Prefix Value Symbol Mega 1,000,000 (10 6 ) M Kilo 1,000 (10 3 ) k Hecto 100 (10 2 ) h Deca 10 da Deci 0.1 (10-1 ) D Centi 0.01 (10-2 ) c Milli (10-3 ) m Micro (10-6 ) µ The metric system is based on 10, just like the United States monetary system. 10 mm = 1 cm 10 m = 1 dam 10 cm = 1 dm 10 dam = 1 hm 10 dm = 1 m 10 hm = 1 km Page 4

5 F. Metric Math 1. When you are working form the base unit to smaller units, move the decimal point to the right. 2. When you are working form the base unit to larger units, move the decimal point to the left. Examples: 1000 meters 1 kilometer 1 km 100 meters 1 hectometer 1 hm 10 meters 1 dekameter 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 19.6 m = 196 dm = 1960 cm =19,600 mm 19.6 m = 1.96 dam = hm = km 1 L = 10 dl = 100 cl = 1000 ml 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 -1 = 42.0 ml kg -1 min b) Assuming a body weight of 60 kg: 35 ml kg -1 min -1 x 60 kg = 2100 ml min ml L -1 =2.10 L min -1 Page 5

6 G. Converting Units To convert from one set of units to another, set up an equation of equivalencies which will allow you to cancel unwanted units and leave the desired units. Examples: 1. 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 x 1 min = 1 hr 60 min 60 s 3600 s 80 km x 1000 m x 1 hr 1 hr 1 km 3600s 80,000 m = 22.2 m s s 2. Convert 160 lbs. to kg. Equivalencies needed: 1 kg per 2.2 pounds. 160 lbs x 1 kg 2.2 lbs 160 kg = 72.2 kg Convert 6 feet and 4 inches into meters. Equivalencies needed: 1 m per in. 6 x = 76 in. 76 in x 1 m = 1.93 m 39,73 in 4. Convert 10,000 m to miles. Equivalencies needed: 1 mile per 1610 meters. 10,000 m x 1 mile = 6.21 miles 1610 m 5. If a person lifted 325 lbs. off the floor, how much force was exerted? Equivalencies needed: 1 N per lbs. 325 lbs. x 1 N = N lbs Page 6

8 A. Definitions. Student Activities 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. Mass: 4. Power: 5. Units of Measurement: 6. Velocity: 7. Work: Page 8

9 B. 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 vs. Weight Without Shoes b. Age vs. Weight Without Shoes c. Weight With Shoes vs. Weight Without Shoes d. Age vs. Height Data Table 1.0 Subject Height (cm) Weight (kg) Weight (kg) Age Without Shoes Without Shoes With Shoes (Months) Mean SD Page 9

10 C. Application. Complete the following problems. Show all of your calculation 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. 2. One person doing a bench press raises 150 lbs. 0.5 meters 10 times, while another person raises 130 lbs. 0.4 metes 15 times. Which person has done more work? 3. A woman holds an 8 lb. shot put 0.34 meters above the floor for 10 seconds. How much work is done holding the shot put? Page 10

11 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 m 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. Page 11

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