Middle Grades Science
OPEN LESSON
SAMPLE LESSONS FOR THE CLASSROOM FROM LAYING THE FOUNDATION
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
T E A C H E R
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.
Code
(Literacy)
RST.6-8.3
Standard
Follow precisely a multistep procedure
when carrying out experiments, taking
measurements, or performing technical tasks.
Level of
Thinking
Depth of
Knowledge
Apply
II
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Teacher Overview – Running the Stairs
Code
Standard
Level of
Thinking
Depth of
Knowledge
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 = s3 and A = 6 s2 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
Write arguments to support claims in an
analysis of substantive topics or texts, using
valid reasoning and relevant and sufficient
evidence.
Apply
II
(MATH)
6.RP.3d
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
II
T E A C H E R
(MATH)
6.EE.2C
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:
Additional teacher materials:
meter stick
stopwatch
string
washer, 2 in.
bathroom scale
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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.
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.
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
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iii
T E A C H E R
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.
Teacher Overview – Running the Stairs
Answer Key
Data and Observations
Mass and weight conversion: 2.2 lbs = 1 kg
Height of stairs, h
100 lbs×
1kg
= 45.5 kg
2.2 lbs
= 5.6 m
Time to climb stairs, t = 6.7 s
Analysis
1. work = mgh = (45.5 kg)(9.81 m/s2) (5.6 m) = 2497.0 J ≈ 2.50 × 103 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.
2. P 
work 2497.0 J

 372.7 W  370 W
t
6.7 s
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T E A C H E R
Round the value to two significant figures unless your stopwatch measures to the hundredth
of a second.
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Teacher Overview – Running the Stairs
Answer Key (continued)
Conclusion Questions
1. Potential energy = work done in climbing the stairs to the top = 2.50 × 103 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. P 
b. P 
work 2  work

, which yields twice the power
t
1 
t
 
2 
Work
, which yields half the power
 2t 
4. a. Potential energy = work done = mgh
2mgh = 2(45.5 kg)(9.81 m/s2)(5.6 m) = 4994.0 J ≈ 5.0 × 103 J (2 sig. figs.)
b. P 
T E A C H E R
work 4994.0 J

 372.7 W  370 W (2 sig. figs.)
t
2  6.7 s 
Thus, Brutus operates at the same power level as the student because he does twice the
work in twice the time.
5. a.
 2500 J  
1kilocalorie 
  0.60 kilocalories (2 sig. figs.)
 4184 J 
b. % of the energy bar used =
0.60 kilocalories
 100  1.2%
50.0 kilocalories
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.
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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/s2),
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,
P
work
t
(Eq. 2)
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.
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Student Activity – Running the Stairs
Procedure
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.
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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
P
work
t
g = 9.81 m/s2
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.
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Student Activity – Running the Stairs
Conclusion Questions
1. If your potential 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.
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Student Activity – Running the Stairs
Conclusion Questions (continued)
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.
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