People power: the physics of human performance

Size: px
Start display at page:

Download "People power: the physics of human performance"

Transcription

1 People power: the physics of human performance Blake Laing, Ph.D. and Harold Meyer, Ph.D., MPH, Southern Adventist University OBJECTIVES 1. Calculate the mechanical power required to move a mass up an inclined plane at a constant velocity 2. Learn three measures of power expenditure of the human body: Calories/unit time The volume rate of oxygen consumption V O 2 by the body Metabolic Equivalent of Task (MET), defined as the rate of oxygen consumption at rest. 3. Learn how to estimate your own (V O 2 ) max from the Rockport 1-mile test. 4. Use a linear response approximation and proportional reasoning to estimate your own V O 2 rate from a measured heart rate and estimated (V O 2 ) max 5. Calculate the efficiency of human motion. 6. Prescribe an exercise program for two patients/clients using the ACSM walking equation. INTRODUCTION Would you be more likely to engage in cardiovascular exercise if you knew your target heartrate for optimal cardiovascular benefit? What if you could think beyond the gym and engage in any outdoor activity to meet that target HR? Do you already use, or have you considered purchasing, a fitness tracking device or smartphone app which magically generates motivational numbers and graphs? How would you like to understand these simple measurements and become a power user? You can easily calculate your current V O 2 max with a Rockport 1-mile test ( Duckwalk ). You may use a simple Google Docs spreadsheet which calculates your new target HR for each new V O 2 max measurement, no purchase necessary. How would you like to become a more discerning consumer, understanding which products can generate more meaningful data? A good app, such as Polar Flow, should let you enter a current V O 2 max to personalize your training targets. Your knowledge of the physics of work and energy, combined with some knowledge of exercise physiology, can be used to empower the stewardship of your own wellness. You can assess and track your cardiovascular fitness by estimating your V O 2 max, and you can adjust your fitness program by including elevation gain.

2 THEORY 1. MECHANICAL WORK Mechanical work is defined as the change in energy of a system due to external forces. The mechanical work is the product of an opposing force times the displacement along the line of force: (Eq. 1) W = F d = Fd cos θ Where θ is the angle between F and d. For example, work required to move a mass m a distance d up an inclined plane of angle φ due to the opposing force of gravity is (Eq. 2) W = mg h = mgd sin φ, The SI unit of work (or energy) is the Joule (J), where 1 J = 1 N m. 2. MECHANICAL POWER Mechanical power is defined as the rate at which mechanical work performed. The power required to perform an amount of work W in a time interval Δt is (Eq. 2) P = W t. The SI unit of power is the watt, where 1 W = 1 J/s. The mechanical power required to move a mass at a speed v up a hill with incline angle φ is (Eq. 3) P = mg Δd sin φ = mgv sin φ Δt 3. EFFICIENCY How much power is required for a body at rest to remain at rest, or for a body to remain at rest, or remain moving at a constant velocity? You know that you must expend power to walk on a level surface. You require power just to sit still and breathe! Then why would your physics professor insist that it takes no mechanical power at all for a body to move at a constant velocity with no opposing force? The reason is that the human body or a machine does not translate power to motion with 100% efficiency. (Eq. 4) what you get Efficiency = what you paid 100% Mechanical power is defined as the rate of mechanical work performed. A machine operating at 50% efficiency will exert 2 Joules of work (requiring 2 Joule of energy) for every 1 Joule of mechanical work performed, so such a machine will require 2 watts of power for every 1 watt of mechanical power. 4. UNITS OF POWER AND ENERGY IN HUMAN PERFORMANCE All athletes who finish a race have performed the same amount of work per kg bodyweight. To win the race, an athlete has to generate the most power per kg, because the work of finishing is performed in a shorter time.

3 Cardiovascular performance can be quantified in units of power. The SI unit of power is the watt, but power can also be measured as a rate of oxygen consumption. All aerobic organisms generate energy from food and oxygen in the citric acid cycle. The amount of energy generated in this cycle can be measured in Joules, calories, or volume of oxygen consumed. The (little-c) calorie is a unit of energy used to quantify the energy the body derives from food. The number of calories is measured by burning food in a calorimeter (1 cal = 4.19 J). Each 1 Liter O 2 consumed is used to metabolize 5,000 calories (5 kcal) of energy. In this sense, volume of oxygen consumed can be converted to calories burned: 1mL O 2 = 5 cal. Absolute Oxygen consumption V O 2 : the rate of oxygen consumption, or the volume of oxygen consumed by the person per minute. The dot over the V to indicates a time derivative, so V O 2 is not the volume of oxygen consumed, but the rate at which oxygen is consumed [1]. The units of absolute V O 2 are ml min. Relative Oxygen consumption V O 2 : The rate of oxygen consumption per kilogram of body weight[1]. The units of relative V O 2 are ml kg/min. Metabolic Equivalents (METs): A simpler unit of power for clinical professionals. A MET is an abbreviation for a metabolic equivalent [of task]. One MET is equivalent to the relative Oxygen consumption rate at rest. [1] 1 MET = 3.5 ml kg min. Summary of useful units and conversions Profession Units of energy/work Units of power Conversion Physical Science Joule (J), calorie (cal) Watt (W) 1 W = 1 J/s Nutrition 1 Cal = 1 kcal kcal/time 1 cal = 4.19 J Physiology ATP or VO 2 (no dot) V O 2 1mL O 2 = 5 cal Medicine, Therapy Metabolic Equivalent (MET) 1 MET = 3.5 ml O 2 kg min Also, 1 mile = km. 5. THE ACSM WALKING EQUATION Your V O 2 (and therefore power performance) can be directly measured in a laboratory with a respirator which measures how much oxygen is missing from the air you breathe out. Measurements like this have been analyzed using linear regression techniques such as we use in lab to create the American College of Sports Medicine (ACSM) walking equation. The walking equation is a model which can be used to estimate your relative V O 2 when walking at a certain speed on a certain grade. It is simply the sum of the power costs of moving horizontally, vertically, and just staying alive. V O 2 = (horizontal) + (vertical) + (resting) Adding these two components to the resting component (3.5 ml kg min) results in the ACSM walking equation. (Eq. 5) ml V O 2 ( kg min ) = v c h + v c v grade + c r

4 Where v is the walking speed in m/min and the coefficients c h, c h, and c h are given in the table below 1. c h = 0.1 ml m kg c v = 1.8 ml m kg ml c r = 3.5 min kg Work cost per horizontal meter Work cost per vertical meter Power cost of resting (1 MET) Note that grade is in decimal form: grade = rise/run. For example, a 15% grade in decimal form is DERIVING THE P-LAB WALKING EQUATION Physics students can recognize that the vertical part of the walking equation should depend on the vertical component of velocity. Consider the velocity vector of a person moving up an inclined plane of angle θ at a velocity v. Then the power cost due to the horizontal and vertical components of that velocity are horizontal = c h v cos θ vertical = c h v sin θ. Why does the ACSM walking equation not have cos θ? Why does it have grade instead of sin θ? Putting together the above pieces, we could write the P-Lab walking equation as Eq. 4. V O 2 (ml kg min) = c h v cos θ + c v v sin θ + c r (Eq. 6) V O 2 (ml kg min) = cos θ (v c h + v c v tan θ) + c r Notice that tan θ is equal to the grade of the slope ( rise over run, right?). Apparently, the ACSM walking equation assumes that the grades that people typically walk on is small enough that cos θ 1. On a flat grade then we obtain the same result as the ACSM walking equation. Suppose that we went for a walk on a 20% grade. Then cos θ = , so the ACSM walking equation is a decent way to estimate V O 2 (ml kg min) without the need for trigonometry. 7. BASIC EXERCISE PHYSIOLOGY The maximum heart rate (HR) max can be directly measured in a maximal test, calculated from a submaximal test, or simply estimated using a regression model. A simple and commonly-used model is (Eq. 7) (HR) max = 220 age. Heart rate reserve HRR is the difference between your maximum and resting heart rate Similarly, the maximal oxygen uptake reserve VO2R HRR = (HR) max (HR) rest. 1 The 2007 ACSM has 1.8 ml/min/m but these units are clearly incorrect.

5 VO2R = (V O 2 ) max (V O 2 ) rest, where (V O 2 ) max can be measured directly or calculated using a submaximal test such as the Rockport-1 mile test. The resting rate (V O 2 ) rest can be directly measured or estimated to be 3.5 ml/kg/s. While some fitness literature and fitness apps display HR as a percentage of (HR) max, a more accurate metric is %HRR as well as %VO2R, where %HRR = HR (HR) rest V O 2 (V O 2 ) HRR %VO2R = rest VO2R It turns out that HRR is linearly related to VO2R. Any person at rest is at 0% of HRR and 0% of VO2R. Any person at the anerobic threshold is at 100% of HRR and 100% of VO2R. For many people the relationship %HRR = %VO2R holds in between these extremes as well: (Eq. 9) %HRR = HR (HR) rest HRR = V O 2 (V O 2 ) rest VO2R = %VO2R Thus V O 2 (which requires expensive equipment) can be estimated by measuring HR (which only requires counting heart beats). PROCEDURE 1. YOUR ROCKPORT (V O 2 ) max AND KARVONEN THR CALCULATIONS 1. Follow the instructions at the end of this document for the Rockport 1-mile test. Record your data in Data Table How hard were you working 2?) Rate your relative perceived exertion (RPE) on a scale of 1-10 on the first row of the table in Data Table 3 ( Relate your HR to Power Expenditure ) 3. Estimate (V O 2 ) max using the Rockport 1-mile regression formula (Eq. 10) (V O 2 ) max = [weight(lbs)] [age(years)] [for males only] [time(minutes)] [heart rate (bpm)] 4. Determine your fitness level and the appropriate training intensity decimal for you using the table on the fitness plan. 5. Calculate your target heart rate (THR) for optimal cardiovascular benefit using the Karvonen formula THR = HRR Intensity + (HR) rest 2 To say I was working hard is a statement about power (work per unit time), not work. To say I m working hard when climbing a hill really means that I m performing the work required to climb that hill relatively quickly, exerting more power but not performing more work.

6 2. RELATE YOUR HR TO POWER EXPENDITURE 1. Using a treadmill, adjust the incline to the maximum incline position. Many treadmills display a number indicating the incline, but you need to accurately measure the grade using a meter stick or tape measure. Then you ll know what that number means! Record in Data Table Choose a speed that would allow for you to comfortably carry on a conversation. Maintain that speed for 10 minutes, or until your HR reaches a stable warmed-up value. Record your speed, HR, and RPE in Data Table You are exercising at your own risk. Talk to the instructor if you don t believe that it would be a good idea to exercise at your THR, or exercise at a HR you are comfortable with. Find the speed that causes your HR to stay close to your THR for about 5 minutes. Record your speed, HR, and RPE. 4. Now make the treadmill flat and maintain your HR at your THR. Record your speed, HR, and RPE. You may find a spreadsheet helpful for the remaining calculations. Still, fill in the calculation sheet provided. 5. For each row in Data Table 3, calculate %HRR. Do you notice a relationship between %HRR and RPE? It turns out that many people often subjectively rate their power expenditure rather close to their actual %HRR. 6. Calculate your V O 2 for each row using the assumption that %HRR = %VO2R (Eq. 9). Were you exercising at your maximum HR? No? Then you are not calculating (V O 2 ) max here. 7. Calculate your power expenditure in METs. 8. Calculate the mechanical power required for each row and calculate your efficiency. Don t expect it to be high: your body was doing a lot of other things besides walking! TAKE IT TO THE NEXT LEVEL (FOR YOUR BENEFIT ONLY) 1. You can have your (V O 2 ) max measured directly. For instance, students at Southern Adventist University can ask to take this measurement in the human performance lab for free. 2. Would you like to learn more about using empirical models in sports medicine? You might start with Reference 1 (available in the campus library) or by perusing the freely-available ACSM 2011 standards [2]. 3. Would you like to read more about prescribing exercise to cardiac patients? You might start with Reference 3. REFERENCES [1] S. Glass, G.B. Dwyer, ed., ACSM's Metabolic Calculations Handbook, Lippincott Williams & Wilkins, Philadelphia, PA (2007). [2] C.E. Garber, et al., Quantity and Quality of Exercise for Developing and Maintaining Cardiorespiratory, Musculoskeletal, and Neuromotor Fitness in Apparently Healthy Adults: Guidance for Prescribing Exercise Medicine & Science in Sports & Exercise 43,1334 (2011). [3] M. Jetté, K. Sidney, G. Blümchen, Metabolic equivalents (METS) in exercise testing, exercise prescription, and evaluation of functional capacity. Clinical Cardiology, 8 (1990).

7

8 Data and Calculations 3. ROCKPORT (V O 2 ) max AND KARVONEN THR CALCULATIONS Data Table 1: (V O 2 ) max and THR calculations Time (min:s) HR max and HR rest Time (decimal min) Heart rate (bpm) (V O 2 ) max ( ml min /kg) HRR Training intensity THR 4. RELATE YOUR HR TO POWER EXPENDITURE What does the Incline number on the treadmill mean? Indicate on the drawing precisely where you measured rise and run (from where to where?) Data Table 2 Max Incline displayed Measured Rise Rat Race Treadmill Co. Run grade Treadmill walk *Use your judgement to exercise at your own risk. If it is not possible or advisable for you to reach your calculated target HR (THR), either use a lower HR within your comfort zone or talk to the Instructor. Data Table 3 Speed (mph) Rockport 0 Grade RPE HR (bpm) %HRR V O 2 ( ml min /kg) METs Effort (W/kg) Mech. Power (W/kg) Efficiency Incline Incline THR* Flat THR* 0

9 DISCUSSION 1. Cooter fell out of his tree-stand while hunting and broke both arms. Cooter has been training for the Mississippi Coast Half-marathon on November 24, but he can't run right now with two casts. Prescribe a reasonable treadmill walking exercise that will help him train at his goal of V O 2 = 38 ml min kg. You ll have to make reasonable choices, as in real life. 2. Prescribe a walking exercise program for Su-Yun, a 55-year old cardiac patient. Su-Yun prefers to walk outside on a level sidewalk downtown, where there are 20 city blocks per mile. She should exercise at 2.5 METs and walk for 30 minutes. Calculate her ideal walking speed and convert to the most convenient units for Su-Yun.

10 Name: PRELABORATORY INVESTIGATIONS Show your work. 1. What is the mechanical work required to move a 1.0-kg mass up a 10 degree inclined plane (such as a treadmill) which is 1.4 meters long? 2. A comfortable walking speed for many people is 1.4 m/s. What is the mechanical power required to move a 1.0-kg mass up a 10 degree inclined plane at this speed? Draw a vector diagram of the velocity, showing the components in the vertical and horizontal directions. Use SI units. 3. Before you got to sleep, put some kind of timer next to your bed. Measure your resting heart rate before rolling out of bed and record it here. If you forget, guess 60 bpm. 4. If you perform the Rockport 1-mile test (called the Duckwalk at SAU) on your own, you can skip that in lab. Record your time and heart rate here. 5. Come to lab dressed appropriately. The school gymnasium requires that you must wear closed-toed shoes. Jeans or riveted pockets are not allowed in the gym.

11 ROCKPORT ONE-MILE WALKING TEST INSTRUCTIONS Preparation: 1. Use your heart rate monitor if you have one. Otherwise, you can check out a heart rate monitor from the desk at the gym at SAU, or simply use a stopwatch. 2. Warm up thoroughly. Procedure: The goal is to get your heartrate up above 120 bpm, not to race. 1. Walk for one mile (4 laps on a quarter mile track, such as the one at SAU). Use the inside track for the most accurate results. 2. Stop walking after one mile (4 laps). 3. Record your time: : (minutes:seconds) 4. Record your heart rate: (bpm).

W = Fd cos θ. W = (75.0 N)(25.0 m) cos (35.0º) = 1536 J = J. W 2400 kcal =

W = Fd cos θ. W = (75.0 N)(25.0 m) cos (35.0º) = 1536 J = J. W 2400 kcal = 8 CHAPTER 7 WORK, ENERGY, AND ENERGY RESOURCES generator does negative work on the briefcase, thus removing energy from it. The drawing shows the latter, with the force from the generator upward on the

More information

Introductory Energy & Motion Lab P4-1350

Introductory Energy & Motion Lab P4-1350 WWW.ARBORSCI.COM Introductory Energy & Motion Lab P4-1350 BACKGROUND: Students love to get to work fast, rather than spending lab time setting up and this complete motion lab lets them quickly get to the

More information

CONDITIONS OF EQUILIBRIUM

CONDITIONS OF EQUILIBRIUM CONDITIONS OF EQUILIBRIUM Introduction Aim: To investigate the conditions required for an object to be in equilibrium This exercise looks at a rigid object which is in both translational and rotational

More information

Watch:

Watch: Physics 106 Everyday Physics Fall 2013 Energy and Power Prelab Media links are provided in each section. If the link doesn t work, copy and paste URL into your browser window. Be patient with the ads you

More information

Conservation of Energy 1 of 8

Conservation of Energy 1 of 8 Conservation of Energy 1 of 8 Conservation of Energy The important conclusions of this chapter are: If a system is isolated and there is no friction (no non-conservative forces), then KE + PE = constant

More information

LINEAR KINETICS (PART 2): WORK, ENERGY, AND POWER Readings: McGinnis Chapter 4

LINEAR KINETICS (PART 2): WORK, ENERGY, AND POWER Readings: McGinnis Chapter 4 LINEAR KINETICS (PART 2): WORK, ENERGY, AND POWER Readings: McGinnis Chapter 4 1 WORK: Another way of expressing the effect of a force. Mechanically, work is done on an object when a force causes a change

More information

Rolling marble lab. B. Pre-Lab Questions a) When an object is moving down a ramp, is its speed increasing, decreasing, or staying the same?

Rolling marble lab. B. Pre-Lab Questions a) When an object is moving down a ramp, is its speed increasing, decreasing, or staying the same? IP 614 Rolling marble lab Name: Block: Date: A. Purpose In this lab you are going to see, first hand, what acceleration means. You will learn to describe such motion and its velocity. How does the position

More information

Force on a Free Body Lab 5.1

Force on a Free Body Lab 5.1 Purpose To investigate the relationship among mass, force, and acceleration Required Equipment Meter stick or meter tape Masking tape Timer Discussion In this experiment, you will investigate how increasing

More information

Name: School: Class: Teacher: Date:

Name: School: Class: Teacher: Date: ame: School: Class: Teacher: Date: Materials needed: Pencil, stopwatch, and scientific calculator d v λ f λ λ Wave Pool Side View During wave cycles, waves crash along the shore every few seconds. The

More information

Pre-Lab 0.2 Reading: Measurement

Pre-Lab 0.2 Reading: Measurement Name Block Pre-Lab 0.2 Reading: Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You

More information

Section Distance and displacment

Section Distance and displacment Chapter 11 Motion Section 11.1 Distance and displacment Choosing a Frame of Reference What is needed to describe motion completely? A frame of reference is a system of objects that are not moving with

More information

PHY2048 Physics with Calculus I

PHY2048 Physics with Calculus I PHY2048 Physics with Calculus I Section 584761 Prof. Douglas H. Laurence Exam 1 (Chapters 2 6) February 14, 2018 Name: Solutions 1 Instructions: This exam is composed of 10 multiple choice questions and

More information

Basic Math Problems Unit 1

Basic Math Problems Unit 1 Basic Math Problems Unit 1 Name Period Using fractions: When you are using fractions in science, we need to convert them into decimals. You can do this by dividing the top number by the bottom number.

More information

Different Forces Act on Objects

Different Forces Act on Objects Have you heard the story about Isaac Newton sitting under an apple tree? According to the story, an apple fell from a tree and hit him on the head. From that event, it is said that Newton discovered the

More information

Measurement and Uncertainty

Measurement and Uncertainty Measurement and Uncertainty Name: Date: Block: There is uncertainty in every measurement due to of accuracy and precision. Accuracy: how close the instrument measures to an accepted. Precision: how closely

More information

Ch06. Energy. Thermochemistry, understanding energy, heat & work. version 1.5

Ch06. Energy. Thermochemistry, understanding energy, heat & work. version 1.5 Ch06 Energy Thermochemistry, understanding energy, heat & work. version 1.5 Nick DeMello, PhD. 2007-2016 Ch06 Accounting for Energy Energy Definitions Classifications Units Kinetic, Potential, Thermal

More information

1 Work, Power, and Machines

1 Work, Power, and Machines CHAPTER 13 1 Work, Power, and Machines SECTION Work and Energy KEY IDEAS As you read this section, keep these questions in mind: What is work, and how is it measured? How are work and power related? How

More information

MEASUREMENT IN THE LABORATORY

MEASUREMENT IN THE LABORATORY 1 MEASUREMENT IN THE LABORATORY INTRODUCTION Today's experiment will introduce you to some simple but important types of measurements commonly used by the chemist. You will measure lengths of objects,

More information

Unit 01 Motion with constant velocity. What we asked about

Unit 01 Motion with constant velocity. What we asked about Unit 01 Motion with constant velocity Outline for this unit: Displacement, Velocity: numerically and graphically Mechanics Lecture 1, Slide 1 What we asked about Would like to see more practice problems

More information

To determine the work and power required to walk and then run through one floor stairs. To determine the energy burned during that exercise

To determine the work and power required to walk and then run through one floor stairs. To determine the energy burned during that exercise Essentials of Physics: WORK AND POWER Purpose To determine the work and power required to walk and then run through one floor stairs. To determine the energy burned during that exercise Theory In this

More information

Physics in the Classroom (Physics 304)

Physics in the Classroom (Physics 304) Physics in the Classroom () Timothy D. Usher Ph.D. CSUSB Please write down your responses to the following. Why are you hear? Go deeper by asking why to your response and writing that answer down. Continue

More information

Calculating Average Speed and Comparing Kinetic and Potential Energy

Calculating Average Speed and Comparing Kinetic and Potential Energy Calculating Average Speed and Comparing Kinetic and Potential Energy Author: Matthew Kurth Grade Level: pre-ap 6 th grade Science (45 minute class) Sources: CPO Science (Force and Motion) o Curriculum

More information

AP PHYSICS 1. Energy 2016 EDITION

AP PHYSICS 1. Energy 2016 EDITION AP PHYSICS 1 Energy 2016 EDITION Copyright 2016 National Math + Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. 1 Pre-Assessment Questions Consider a system which could

More information

Chapter 7: Work, Power & Energy

Chapter 7: Work, Power & Energy Chapter 7: Work, Power & Energy WORK My family owned at one point a Paletria in Tucson, AZ. As many already know, it is very hot in Tucson (usually have 100+ days over 100 o F or 40 o C) and therefore,

More information

Review of Scientific Notation and Significant Figures

Review of Scientific Notation and Significant Figures II-1 Scientific Notation Review of Scientific Notation and Significant Figures Frequently numbers that occur in physics and other sciences are either very large or very small. For example, the speed of

More information

Newton s Wagon. Materials. friends rocks wagon balloon fishing line tape stopwatch measuring tape. Lab Time Part 1

Newton s Wagon. Materials. friends rocks wagon balloon fishing line tape stopwatch measuring tape. Lab Time Part 1 Newton s Wagon Overview: The natural state of objects is to follow a straight line. In fact, Newton s First Law of Motion states that objects in motion will tend to stay in motion unless they are acted

More information

F = ma W = mg v = D t

F = ma W = mg v = D t Forces and Gravity Car Lab Name: F = ma W = mg v = D t p = mv Part A) Unit Review at D = f v = t v v Please write the UNITS for each item below For example, write kg next to mass. Name: Abbreviation: Units:

More information

Chapter 10-Work, Energy & Power

Chapter 10-Work, Energy & Power DULLES HIGH SCHOOL Chapter 10-Work, Energy & Power Energy Transformations Judy Matney 1/12/2016 In this chapter, we will study the concepts of force and work; we will understand the transformations of

More information

Page 1. Name:

Page 1. Name: Name: 3834-1 - Page 1 1) If a woman runs 100 meters north and then 70 meters south, her total displacement is A) 170 m south B) 170 m north C) 30 m south D) 30 m north 2) The graph below represents the

More information

PHYSICS 15a, Fall 2006 SPEED OF SOUND LAB Due: Tuesday, November 14

PHYSICS 15a, Fall 2006 SPEED OF SOUND LAB Due: Tuesday, November 14 PHYSICS 15a, Fall 2006 SPEED OF SOUND LAB Due: Tuesday, November 14 GENERAL INFO The goal of this lab is to determine the speed of sound in air, by making measurements and taking into consideration the

More information

Lesson 1 Exit Ticket 4 2

Lesson 1 Exit Ticket 4 2 Lesson 1 Exit Ticket 4 2 1. Complete the conversion table. Distance 71 km m km 30,000 m 81 m cm m 400 cm 2. 13 km 20 m = m 3. 401 km 101 m 34 km 153 m = 4. Gabe built a toy tower that measured 1 m 78 cm.

More information

Chapter 3 Acceleration

Chapter 3 Acceleration Chapter 3 Acceleration Slide 3-1 Chapter 3: Acceleration Chapter Goal: To extend the description of motion in one dimension to include changes in velocity. This type of motion is called acceleration. Slide

More information

Physics 231. Topic 5: Energy and Work. Alex Brown October 2, MSU Physics 231 Fall

Physics 231. Topic 5: Energy and Work. Alex Brown October 2, MSU Physics 231 Fall Physics 231 Topic 5: Energy and Work Alex Brown October 2, 2015 MSU Physics 231 Fall 2015 1 What s up? (Friday Sept 26) 1) The correction exam is now open. The exam grades will be sent out after that on

More information

WORK, POWER, & ENERGY

WORK, POWER, & ENERGY WORK, POWER, & ENERGY In physics, work is done when a force acting on an object causes it to move a distance. There are several good examples of work which can be observed everyday - a person pushing a

More information

Experiment 4 Free Fall

Experiment 4 Free Fall PHY9 Experiment 4: Free Fall 8/0/007 Page Experiment 4 Free Fall Suggested Reading for this Lab Bauer&Westfall Ch (as needed) Taylor, Section.6, and standard deviation rule ( t < ) rule in the uncertainty

More information

Chapter 9: Circular Motion

Chapter 9: Circular Motion Text: Chapter 9 Think and Explain: 1-5, 7-9, 11 Think and Solve: --- Chapter 9: Circular Motion NAME: Vocabulary: rotation, revolution, axis, centripetal, centrifugal, tangential speed, Hertz, rpm, rotational

More information

Purpose of the experiment

Purpose of the experiment Kinematics PES 1160 Advanced Physics Lab I Purpose of the experiment To measure a value of g, the acceleration of gravity at the Earth s surface. To understand the relationships between position, velocity

More information

1. Type your first name. * 2. Type your last name. * 3. Choose the block I teach you for science. * Mark only one oval. Block 1.

1. Type your first name. * 2. Type your last name. * 3. Choose the block I teach you for science. * Mark only one oval. Block 1. Hippenmeyer Physics Assessment 1 Your email address (khippenmeyer@ncmcs.net) will be recorded when you submit this form. Not khippenmeyer? Sign out * Required 1. Type your first name. * 2. Type your last

More information

WORK, POWER, & ENERGY

WORK, POWER, & ENERGY WORK, POWER, & ENERGY In physics, work is done when a force acting on an object causes it to move a distance. There are several good examples of work which can be observed everyday - a person pushing a

More information

Chemistry 104 Chapter Two PowerPoint Notes

Chemistry 104 Chapter Two PowerPoint Notes Measurements in Chemistry Chapter 2 Physical Quantities Measurable physical properties such as height, volume, and temperature are called Physical quantity. A number and a unit of defined size is required

More information

LAB: MOTION ON HILLS

LAB: MOTION ON HILLS LAB: MOTION ON HILLS Introduction In this three-part activity, you will first study an object whose speed is changing while it moves downhill In this lab, the two variables you are focusing on are time

More information

Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis

Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis TAKING MEASUREMENTS The accuracy of a measurement depends on two factors: the skill of the individual taking the

More information

1.1 Units and unit conversions

1.1 Units and unit conversions Fundamentals This chapter reviews four important mathematical concepts and techniques that will be helpful in many quantitative problems you re likely to encounter in a college-level introductory astronomy

More information

Momentum, Impulse, Work, Energy, Power, and Conservation Laws

Momentum, Impulse, Work, Energy, Power, and Conservation Laws Momentum, Impulse, Work, Energy, Power, and Conservation Laws 1. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second.

More information

Introduction to Measurements of Physical Quantities

Introduction to Measurements of Physical Quantities 1 Goal Introduction to Measurements of Physical Quantities Content Discussion and Activities PHYS 104L The goal of this week s activities is to provide a foundational understanding regarding measurements

More information

Mathematics in Contemporary Society Chapter 10

Mathematics in Contemporary Society Chapter 10 City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College Fall 2015 Mathematics in Contemporary Society Chapter 10 Patrick J. Wallach Queensborough

More information

Analyzing Motion: Enrichment

Analyzing Motion: Enrichment Chapter 2 Analyzing Motion: Enrichment Note to Teachers: The concepts involved in motion position, velocity, acceleration, and time should be developed using the four modes of representation: visual, numeric,

More information

? 4. Like number bonds, a formula is useful because it helps us know what operation to use depending on which pieces of information we have.

? 4. Like number bonds, a formula is useful because it helps us know what operation to use depending on which pieces of information we have. UNIT SIX DECIMALS LESSON 168 PROBLEM-SOLVING You ve covered quite a distance in your journey through our number system, from whole numbers through fractions, to decimals. Today s math mysteries all have

More information

Bellringer Day In your opinion, what are the five most important lab safety rules?

Bellringer Day In your opinion, what are the five most important lab safety rules? Bellringer Day 01 1. In your opinion, what are the five most important lab safety rules? Lab Safety Video Lab Safety Map See if you can identify the lab safety equipment around the room. You can discuss

More information

Astronomical Distances. Astronomical Distances 1/30

Astronomical Distances. Astronomical Distances 1/30 Astronomical Distances Astronomical Distances 1/30 Last Time We ve been discussing methods to measure lengths and objects such as mountains, trees, and rivers. Today we ll look at some more difficult problems.

More information

L ESSON P LAN:DETERMINING THE E FFECT OF D ISTANCE (PART 1) AND I NCLINATION (PART 2)

L ESSON P LAN:DETERMINING THE E FFECT OF D ISTANCE (PART 1) AND I NCLINATION (PART 2) L ESSON P LAN:DETERMINING THE E FFECT OF D ISTANCE (PART 1) AND I NCLINATION (PART 2) In the activity at the heart of this lesson, the students will measure the effect of distance and inclination on the

More information

(UNIT I) Measuring Activity Name

(UNIT I) Measuring Activity Name (UNIT I) Measuring Activity Name Purpose: To become more familiar with the metric system (SI) of measurement. Make estimates first and then measure it. Pre Lab reading: http://www.cnn.com/tech/space/9909/30/mars.metric.02/#1

More information

4.1 - Acceleration. What is acceleration?

4.1 - Acceleration. What is acceleration? 4.1 - Acceleration How do we describe speeding up or slowing down? What is the difference between slowing down gradually and hitting a brick wall? Both these questions have answers that involve acceleration.

More information

3rd Grade. Forces and Motion Review. Slide 1 / 106 Slide 2 / 106. Slide 4 / 106. Slide 3 / 106. Slide 5 / 106. Slide 6 / 106. Motion and Stability

3rd Grade. Forces and Motion Review. Slide 1 / 106 Slide 2 / 106. Slide 4 / 106. Slide 3 / 106. Slide 5 / 106. Slide 6 / 106. Motion and Stability Slide 1 / 106 Slide 2 / 106 3rd Grade Motion and Stability 2015-11-09 www.njctl.org Slide 3 / 106 Slide 4 / 106 Table of Contents Forces and Motion Review Balanced and Unbalanced Forces Motion prediction

More information

LAB 6: WORK AND ENERGY

LAB 6: WORK AND ENERGY 93 Name Date Partners LAB 6: WORK AND ENERGY OBJECTIVES OVERVIEW Energy is the only life and is from the Body; and Reason is the bound or outward circumference of energy. Energy is eternal delight. William

More information

Real Numbers and an Introduction to Algebra

Real Numbers and an Introduction to Algebra ChaPter 1 Real Numbers and an Introduction to Algebra Objectives In this chapter you will learn how to do the following: 1. Read mathematical symbols. 2. Distinguish between different sets of numbers.

More information

AP Physics 1 First Semester Final Exam Review

AP Physics 1 First Semester Final Exam Review AP Physics First Semester Final Exam Review Chapters and. Know the SI Units base units.. Be able to use the factor-label method to convert from one unit to another (ex: cm/s to m/year) 3. Be able to identify

More information

10 Work, Energy, and Machines BIGIDEA

10 Work, Energy, and Machines BIGIDEA 10 Work, Energy, and Machines BIGIDEA Write the Big Idea for this chapter. Use the What I Know column to list the things you know about the Big Idea. Then list the questions you have about the Big Idea

More information

https://njctl.org/courses/science/ap-physics-c-mechanics/attachments/summerassignment-3/

https://njctl.org/courses/science/ap-physics-c-mechanics/attachments/summerassignment-3/ AP Physics C Summer Assignment 2017 1. Complete the problem set that is online, entitled, AP C Physics C Summer Assignment 2017. I also gave you a copy of the problem set. You may work in groups as a matter

More information

3rd Grade Motion and Stability

3rd Grade Motion and Stability Slide 1 / 106 Slide 2 / 106 3rd Grade Motion and Stability 2015-11-09 www.njctl.org Slide 3 / 106 Table of Contents Forces and Motion Review Balanced and Unbalanced Forces Motion prediction from patterns

More information

MEI Conference Preparing to teach Projectiles. Kevin Lord.

MEI Conference Preparing to teach Projectiles. Kevin Lord. MEI Conference 2016 Preparing to teach Projectiles Kevin Lord Kevin.lord@mei.org.uk Session notes 2 Horizontal Motion Vertical Motion 3 Observing projectile motion From Mechanics in Action M. Savage and

More information

********************************************************************************************************

******************************************************************************************************** QUESTION # 1 1. Let the random variable X represent the number of telephone lines in use by the technical support center of a software manufacturer at noon each day. The probability distribution of X is

More information

Chapter 3 - Measurements

Chapter 3 - Measurements Chapter 3 - Measurements You ll learn it in the summer, If not, it ll be a bummer. You ll need to know conversions, For units, Euro version. Metrics are powers of ten, And you might cry when, You re forced

More information

Graphing Skill #1: What Type of Graph is it? There are several types of graphs that scientists often use to display data.

Graphing Skill #1: What Type of Graph is it? There are several types of graphs that scientists often use to display data. Graphing Skill #1: What Type of Graph is it? There are several types of graphs that scientists often use to display data. They include: Pie Graphs Bar Graphs Histograms Line Graphs Scatter Plots Dependent

More information

Pre Comp Review Questions 7 th Grade

Pre Comp Review Questions 7 th Grade Pre Comp Review Questions 7 th Grade Section 1 Units 1. Fill in the missing SI and English Units Measurement SI Unit SI Symbol English Unit English Symbol Time second s second s. Temperature Kelvin K Fahrenheit

More information

Free Response- Exam Review

Free Response- Exam Review Free Response- Exam Review Name Base your answers to questions 1 through 3 on the information and diagram below and on your knowledge of physics. A 150-newton force, applied to a wooden crate at an angle

More information

Physics 8 Wednesday, October 19, Troublesome questions for HW4 (5 or more people got 0 or 1 points on them): 1, 14, 15, 16, 17, 18, 19. Yikes!

Physics 8 Wednesday, October 19, Troublesome questions for HW4 (5 or more people got 0 or 1 points on them): 1, 14, 15, 16, 17, 18, 19. Yikes! Physics 8 Wednesday, October 19, 2011 Troublesome questions for HW4 (5 or more people got 0 or 1 points on them): 1, 14, 15, 16, 17, 18, 19. Yikes! Troublesome HW4 questions 1. Two objects of inertias

More information

Efficiency = power out x 100% power in

Efficiency = power out x 100% power in Work, Energy and Power Review Package 1) Work: change in energy. Measured in Joules, J. W = Fd W = ΔE Work is scalar, but can be negative. To remember this, ask yourself either: Is the object is losing

More information

SCIENCE 1206 Unit 3. Physical Science Motion

SCIENCE 1206 Unit 3. Physical Science Motion SCIENCE 1206 Unit 3 Physical Science Motion Section 1: Units, Measurements and Error What is Physics? Physics is the study of motion, matter, energy, and force. Qualitative and Quantitative Descriptions

More information

Which one of the following is an SI base unit? (a) gram (c) newton (e) kilogram

Which one of the following is an SI base unit? (a) gram (c) newton (e) kilogram chapter INTRODUCTION AND MATHEMATICAL CONCEPTS Section 1. Units Section 1.3 The Role of Units in Problem Solving 1. Which one of the following is an SI base unit? (a) gram (c) newton (e) kilogram (b) slug

More information

Unit 1: Equilibrium and Center of Mass

Unit 1: Equilibrium and Center of Mass Unit 1: Equilibrium and Center of Mass FORCES What is a force? Forces are a result of the interaction between two objects. They push things, pull things, keep things together, pull things apart. It s really

More information

PHYSICS Kinematics in One Dimension

PHYSICS Kinematics in One Dimension PHYSICS Kinematics in One Dimension August 13, 2012 www.njctl.org 1 Motion in One Dimension Return to Table of Contents 2 Distance We all know what the distance between two objects is... So what is it?

More information

Momentum, Impulse, Work, Energy, Power, and Conservation Laws

Momentum, Impulse, Work, Energy, Power, and Conservation Laws Momentum, Impulse, Work, Energy, Power, and Conservation Laws 1. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second.

More information

Work and the Work-Energy Theorem

Work and the Work-Energy Theorem Work and Energy Click on the topic to go to that section Energy and the Work-Energy Theorem Work and Energy 2009 by Goodman & Zavorotniy Forces and Potential Energy Conservation of Energy Power Conservation

More information

Galileo & Friction 2000 yrs prior to inertia idea, the popular belief was that all objects want to come to a rest. BUT 1600's: Galileo reasoned that

Galileo & Friction 2000 yrs prior to inertia idea, the popular belief was that all objects want to come to a rest. BUT 1600's: Galileo reasoned that Galileo & Friction 2000 yrs prior to inertia idea, the popular belief was that all objects want to come to a rest. BUT 1600's: Galileo reasoned that moving objects eventually stop only because of a force

More information

PHY 221 Lab 7 Work and Energy

PHY 221 Lab 7 Work and Energy PHY 221 Lab 7 Work and Energy Name: Partners: Goals: Before coming to lab, please read this packet and do the prelab on page 13 of this handout. Note: originally, Lab 7 was momentum and collisions. The

More information

3.3 Acceleration An example of acceleration Definition of acceleration Acceleration Figure 3.16: Steeper hills

3.3 Acceleration An example of acceleration Definition of acceleration Acceleration Figure 3.16: Steeper hills 3.3 Acceleration Constant speed is easy to understand. However, almost nothing moves with constant speed for long. When the driver steps on the gas pedal, the speed of the car increases. When the driver

More information

Experimenting with Forces

Experimenting with Forces A mother hears a loud crash in the living room. She walks into the room to see her seven-year-old son looking at a broken vase on the floor. How did that happen? she asks. I don t know. The vase just fell

More information

Linear Motion with Constant Acceleration

Linear Motion with Constant Acceleration Linear Motion 1 Linear Motion with Constant Acceleration Overview: First you will attempt to walk backward with a constant acceleration, monitoring your motion with the ultrasonic motion detector. Then

More information

Physics 101. Hour Exam I Fall Last Name: First Name Network-ID Discussion Section: Discussion TA Name:

Physics 101. Hour Exam I Fall Last Name: First Name Network-ID Discussion Section: Discussion TA Name: Last Name: First Name Network-ID Discussion Section: Discussion TA Name: Instructions Turn off your cell phone and put it away. This is a closed book exam. You have ninety (90) minutes to complete it.

More information

LAB 3: WORK AND ENERGY

LAB 3: WORK AND ENERGY 1 Name Date Lab Day/Time Partner(s) Lab TA (CORRECTED /4/05) OBJECTIVES LAB 3: WORK AND ENERGY To understand the concept of work in physics as an extension of the intuitive understanding of effort. To

More information

Final Project Physics 590. Mary-Kate McGlinchey MISEP Summer 2005

Final Project Physics 590. Mary-Kate McGlinchey MISEP Summer 2005 Final Project Physics 590 Mary-Kate McGlinchey MISEP Summer 2005 Lesson Objectives: Students will be able to Identify the relationship between motion and a reference point. Identify the two factors that

More information

AP Physics C Mechanics Summer Assignment

AP Physics C Mechanics Summer Assignment AP Physics C Mechanics Summer Assignment 2018 2019 School Year Welcome to AP Physics C, an exciting and intensive introductory college physics course for students majoring in the physical sciences or engineering.

More information

PHY 221 Lab 9 Work and Energy

PHY 221 Lab 9 Work and Energy PHY 221 Lab 9 Work and Energy Name: Partners: Before coming to lab, please read this packet and do the prelab on page 13 of this handout. Goals: While F = ma may be one of the most important equations

More information

3 Tools and Measurement

3 Tools and Measurement CHAPTER 1 3 Tools and Measurement SECTION The Nature of Life Science BEFORE YOU READ After you read this section, you should be able to answer these questions: How do tools help scientists? How do scientists

More information

Draft Proof - Do not copy, post, or distribute

Draft Proof - Do not copy, post, or distribute 1 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1. Distinguish between descriptive and inferential statistics. Introduction to Statistics 2. Explain how samples and populations,

More information

July 19 - Work and Energy 1. Name Date Partners

July 19 - Work and Energy 1. Name Date Partners July 19 - Work and Energy 1 Name Date Partners WORK AND ENERGY Energy is the only life and is from the Body; and Reason is the bound or outward circumference of energy. Energy is eternal delight. William

More information

If I see your phone, I wil take it!!! No food or drinks (except for water) are al owed in my room.

If I see your phone, I wil take it!!! No food or drinks (except for water) are al owed in my room. DO NOW Take a seat! Chromebooks out (if charged) SILENCE YOUR PHONE and put it in the pocket that has your number in the bulletin board (back wall). NO EXCEPTION! If I see your phone, I will take it!!!

More information

Physics Midterm Review KEY

Physics Midterm Review KEY Name: Date: 1. Which quantities are scalar? A. speed and work B. velocity and force C. distance and acceleration D. momentum and power 2. A 160.-kilogram space vehicle is traveling along a straight line

More information

Module VII: Work. Background/Support Information

Module VII: Work. Background/Support Information Background/Support Information NAME: DATE: Module VII: Work OBJECTIVES/PURPOSE Students will: define the concept of work as force times distance distinguish the relation of work to energy apply the concept

More information

Coulomb s Law. 1 Equipment. 2 Introduction

Coulomb s Law. 1 Equipment. 2 Introduction Coulomb s Law 1 Equipment conducting ball on mono filament 2 conducting balls on plastic rods housing with mirror and scale vinyl strips (white) wool pads (black) acetate strips (clear) cotton pads (white)

More information

Chapter 9- Static Equilibrium

Chapter 9- Static Equilibrium Chapter 9- Static Equilibrium Changes in Office-hours The following changes will take place until the end of the semester Office-hours: - Monday, 12:00-13:00h - Wednesday, 14:00-15:00h - Friday, 13:00-14:00h

More information

ALBERTA WEIGHTLIFTING ASSOCIATION AFFILIATED WITH THE C.W.F.H.C. AND I.W.F. SINCLAIR BODYWEIGHT CORRECTION FORMULA

ALBERTA WEIGHTLIFTING ASSOCIATION AFFILIATED WITH THE C.W.F.H.C. AND I.W.F. SINCLAIR BODYWEIGHT CORRECTION FORMULA SINCLAIR BODYWEIGHT CORRECTION FORMULA 1. Forward It is with a heavy heart that I put together this current Sinclair Coefficients (S.C.) package. It feels just like yesterday when Dr. Roy Sinclair asked

More information

Lab 3 Acceleration. What You Need To Know: Physics 211 Lab

Lab 3 Acceleration. What You Need To Know: Physics 211 Lab b Lab 3 Acceleration Physics 211 Lab What You Need To Know: The Physics In the previous lab you learned that the velocity of an object can be determined by finding the slope of the object s position vs.

More information

INTRODUCTION AND MATHMATICAL Concepts. 1. Which one of the following is an SI base unit? (a) gram (c) newton (e) kilogram

INTRODUCTION AND MATHMATICAL Concepts. 1. Which one of the following is an SI base unit? (a) gram (c) newton (e) kilogram chapter INTRODUCTION AND MATHMATICAL Concepts Section 1.2 Units Section 1.3 The Role of Units in Problem Solving 1. Which one of the following is an SI base unit? (a) gram (c) newton (e) kilogram (b) slug

More information

Energy, Work, and Power

Energy, Work, and Power Energy, Work, and Power I. Energy - kinetic and potential - conservation II. Work - dot product - work-energy relations III. Springs IV. Power - machines and efficiency The student will be able to: 1 Define

More information

5 Energy and Machines

5 Energy and Machines 5 Energy and Machines 5-1 Work and Power Vocabulary Work: The product of the component of the force exerted on an object in the direction of displacement and the magnitude of the displacement. work (force)(displacement)

More information

PH7_UnitPacketCompleteKey

PH7_UnitPacketCompleteKey Page 1 of 45 Page 2 of 45 Unit Packet Contents 1. Unit Objectives 2. Notes: Potential / Kinetic Energy 3. Guided Practice: Potential and Kinetic Energy 4. Independent Practice Potential and Kinetic Energy

More information

Chapter 4 Force and Motion

Chapter 4 Force and Motion Chapter 4 Force and Motion Units of Chapter 4 The Concepts of Force and Net Force Inertia and Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion More on Newton s Laws:

More information

Bay Area Scientists in Schools Presentation Plan

Bay Area Scientists in Schools Presentation Plan Bay Area Scientists in Schools Presentation Plan Lesson Name: We Love Gravity! Presenter(s) Virginia Lehr, Laura Hidrobo Grade Level 5 Standards Connection(s) Solar System and Gravity Teaser: Gravity is

More information