OPEN LESSON SAMPLE LESSONS FOR THE CLASSROOM FROM LAYING THE FOUNDATION Middle Grades Science Running the Stairs Measuring Work, Energy, and Power About this Lesson This activity can be used to introduce and develop the concepts of work and power as each student measures the work performed, potential energy, and power level as they climb a flight of stairs. Having the students actually perform and experience the work is the best way for them to formulate their own definitions of work and power, and is especially suited for kinesthetic learners. This learning experience is also powerful in that the experiential definition of work will remain should the student pursue further learning in a physics course. Objectives Students will: Determine the work done against gravity while running up a flight of stairs Determine the power level at which they performed the work Level Middle Grades: Physical Science Common Core State Standards for Science Content LTF Science lessons will be aligned with the next generation of multi-state science standards that are currently in development. These standards are said to be developed around the anchor document, A Framework for K 12 Science Education, which was produced by the National Research Council. Where applicable, the LTF Science lessons are also aligned to the Common Core Standards for Mathematical Content as well as the Common Core Literacy Standards for Science and Technical Subjects. T E A C H E R Code Standard Level of Thinking Depth of Knowledge (Literacy) RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. Apply II Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. i
Teacher Overview Running the Stairs Code Standard Level of Thinking Depth of Knowledge (MATH) 6.EE.2C Write, read, and evaluate expressions in which letters stand for numbers. Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in realworld problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Apply II (Literacy) RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). Apply II (Literacy) W.1 (MATH) 6.RP.3d Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Apply Apply II II T E A C H E R Connections to AP* AP Physics: II. Newtonian mechanics C. Work, energy, and power *Advanced Placement and AP are registered trademarks of the College Entrance Examination Board. The College Board was not involved in the production of this product. Materials and Resources Each lab group will need the following: meter stick stopwatch string washer, 2 in. Additional teacher materials: bathroom scale Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. ii
Teacher Overview Running the Stairs Assessments The following types of assessments are embedded in this lesson: Assessment of prior knowledge Formative assessment discussions during activity The following additional assessments are located on the LTF website: Short Lesson Assessment: Running the Stairs Middle Grades Physics Assessment: Work, Power and Energy 2006 Middle Grades 8 Posttest, Free Response Question 2 Teaching Suggestions In this activity, each student will measure their work performed, potential energy, and power level as they climb a flight of stairs. The pre-lab should include a discussion of the scientific definition of work contrasted with the common language definition. A sample activity might consist of having students compile a list of situations involving work and then have students call out their examples. The teacher can then respond by identifying if the example fits the scientific definition of work. In this way, students will be encouraged to think of other examples of work and develop an operational definition. The work completed in this activity is in one direction and against gravity, but the definition of work is not confined to this one situation. Help your students further define work by describing situations where work may be done and having them identify if work is in fact being done. To complete the activity. you must find a stairway that is at least one flight or greater and open in such a way that you can measure its height with a string or long tape measure. Have each student stand on a bathroom scale and record their weight, then calculate their mass using the conversion on the datasheet. Take the students to the stairway and choose a few students to measure the height of the stairs by tying a weight to the string, lowering it to the bottom, and measuring the length of the string from the bottom of the stairs to the top. T E A C H E R Alternatively, you could give each student a ruler and have them measure the height of each step, then multiply the average height of a step by the number of steps, or simply add the heights of all of the steps. Be sure and emphasize the use of the proper number of significant digits as discussed in previous lessons. Either stand at the top of the stairs with a stopwatch to time each student as they climb the stairs or assign a student to do so. After giving a student the signal to go, start the clock when their foot touches the first step. Tell the students they must touch each step as they climb. Tell each student their time, and have them perform the calculations on the data sheet and answer the Conclusion Questions. v. 2.0, 2.0 Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. iii
Answer Key Data and Observations Mass and weight conversion: 2.2 lbs = 1 kg Teacher Overview Running the Stairs 1kg 100lbs = 45.5kg 2.2 lbs Height of stairs, h = 5.6 m Time to climb stairs, t = 6.7 s Analysis 1. work = mgh = (45.5 kg)(9.81 m/s 2 ) (5.6 m) = 2497.0 J 2.50 10 3 J (2 sig. figs.) A joule (J) is the product of the units (newton meters) and is a result of the product of force and displacement. work 2497.0 J 2. P 372.7 W 370 W t 6.7s Round the value to two significant figures unless your stopwatch measures to the hundredth of a second. T E A C H E R Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. iv
Answer Key (continued) Teacher Overview Running the Stairs Conclusion Questions 1. Potential energy = work done in climbing the stairs to the top = 2.50 10 3 J 2. a. The work done in climbing the stairs does not depend on the time. b. The work done in climbing the stairs does not depend on the time. 3. a. b. work 2 work P, which yields twice the power 1 t t 2 Work P, which yields half the power 2t 4. a. Potential energy = work done = mgh 2mgh = 2(45.5 kg)(9.81 m/s 2 )(5.6 m) = 4994.0 J 5.0 10 3 J (2 sig. figs.) work 4994.0 J b. P 372.7 W 370 W (2 sig. figs.) t 2 6.7s Thus, Brutus operates at the same power level as the student because he does twice the work in twice the time. 5. a. 2500J 1kilocalorie b. 4184 J 0.60 kilocalories (2 sig. figs.) 0.60kilocalories % of the energy bar used = 100 1.2% 50.0kilocalories 6. If the height of the stairs was measured larger than its actual value, the power would appear to be greater than it actually was. If the height was measured smaller than its actual value, the power would appear to be less than it actually was. If the stopwatch was started too late, the power would appear to be greater than its actual value. If the stopwatch was started too early, the power would appear to be less than its actual value. If several steps were measured and an average step height was used to find the total height of the stairway, the power may be greater if a number of the steps were shorter than the average, or the power may be less if a number of the steps were taller than the average. T E A C H E R Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. v
Middle Grades Science Running the Stairs Measuring Work, Energy, and Power Any time work is performed on an object, the energy of that object is changed. When you climb stairs, you do work on your body s mass and increase your potential energy. The amount of work you do is equal to the change in your potential energy. Power is the rate at which work is done. If you climb the stairs quickly, you operate at a high power level. If you climb the stairs slowly, your power level is low. Work and energy are measured in joules (J), and power is measured in watts (W). The equation for the work done in lifting a mass from the ground level to a height h is work = mgh (Eq. 1) where m is the mass of the object in kilograms, g is the acceleration due to gravity (9.81 m/s 2 ), and h is the height to which the mass is lifted in meters. The equation for power, P, is the work done divided by time t, work P (Eq. 2) t Purpose You will be timed while running up a flight of stairs, and will determine the work done against gravity and the power level at which you performed the work. Materials Each lab group will need the following: meter stick stopwatch string washer, 2 in. SAFETY ALERT!» Use caution when running up the stairs.» Do not skip any steps, but step on each one as you climb the stairs.» Be sure your shoestrings are securely tied. Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. 1
Procedure Student Activity Running the Stairs 1. Stand on a bathroom scale to determine your weight. Find the mass that corresponds to your weight by using the conversion given on your student answer page. 2. Find a stairway that has a vertical height of at least one floor. 3. Measure the height of the stairway in meters by attaching a weight to a string and lowering it from the top of the stairs to the bottom. Measure the length of the string with the tape measure or several meter sticks. Alternatively, measure the height of each step and find the sum of the heights of all the steps to determine the height of the stars. 4. Record the height of the stairs in the appropriate space on your student answer page. When using a ruler, meter stick, or tape measure, remember to make your measurements to the correct number of significant digits and estimate between marks. 5. Have your teacher or a student stand at the top of the stairs with a stopwatch to measure the time it takes you to climb the stairs from the bottom to the top. Timing should begin the moment your foot touches the first step. Use caution while climbing the steps, and be sure to step on each step as you travel up the stairs. 6. Record the time it takes for you to run from the bottom of the stairs to the top in the appropriate space on your student answer page. Record your measurement to the correct number of significant digits. Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. 2
Student Activity Running the Stairs Data and Observations Mass and weight conversion: 2.2 lbs = 1 kg Height of stairs, h = m Time to climb stairs, t = s Analysis Equations and constants: Remember to report the answers to all calculations to the proper number of significant figures. work = mgh work P t g = 9.81 m/s 2 1. In the space provided, show your calculation for the work you performed on your mass against gravity as you climbed the stairs. Be sure to indicate the units for the work done. 2. In the space provided, show your calculation for the power level at which you performed the work, and indicate the units for power. Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. 3
Conclusion Questions Student Activity Running the Stairs 1. If your p otential energy is taken to be zero when you are on the ground level, what is your potential energy when you reach the top of the stairs? 2. How would the work done against gravity change if you ran up the stairs in: a. Half the time? Justify your answer. b. Twice the time? Justify your answer. 3. How would your power level change if you ran up the stairs in: a. Half the time? Justify your answer. b. Twice the time? Justify your answer. Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. 4
Conclusion Questions (continued) Student Activity Running the Stairs 4. Brutus the football player has twice as much mass as you do and takes twice as much time as you to run to the top of the stairs. a. Calculate Brutus potential energy at the top of the stairs. b. How does Brutus power compare with yours? Justify your answer. 5. A calorie (cal) is a unit of energy that is commonly associated with heat. A kilocalorie (Cal) is 1000 calories, and is the common reference of calorie for the energy content of food. The conversion between kilocalories and joules is 1 kilocalorie = 4184 joules a. How many kilocalories did you burn in climbing the stairs? Show your work. b. If you ate an energy bar consisting of 50.0 kilocalories, what percentage of the energy bar did you use to climb the stairs? 6. Discuss two reasonable sources of error in determining your power in climbing the stairs, and explain how each error increased or decreased your value for the power. Copyright 2012 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. Visit us online at www.ltftraining.org. 5