Title of Lesson: Can All Things Stretch?
RET Project Connection: Failure Modes of Lightweight Sandwich Structures
RET Teacher: Michael Wall
School: Andover High School
Town/District: Andover Public Schools
Subject(s) Taught: Physical Science, Environmental Science
Subjects Covered in Lesson: Physical Science, Physics
Grades Appropriate: 9, 10
Lesson Duration: Two 80-minute class periods
Goals/Objectives of Lesson: At the end of this lesson students should be able to: Use measurements of
force and length to calculate stress and strain of a material; Calculate Young’s modulus of various materials
from laboratory data; Qualify a material’s elasticity based on laboratory data and given values of Young’s
modulus.
Background Information: Students should have prior knowledge of forces, Newton’s laws of motion,
displacement, vectors, the SI system, graphing and basic algebra skills. Students should have basic
laboratory skills to measure mass, weight and length. Hooke’s law allows the elasticity of springs to be
calculated. The same concept in Hooke’s law can be extended to any material using Young’s modulus to
calculate elasticity. Using basic principles of forces, displacement, SI system, basic algebra and graphing,
students should be able to understand and calculate the elasticity of springs and other solid materials.
Essential Questions: Can rigid materials bend or change shape when a force is applied? What makes some
materials more elastic than other materials?
Links to Frameworks and Standards
*ational: Physical Science Standards, Levels 9 – 12, Motion and forces
State: Massachusetts Introductory Physics: 1. Motion and Forces, Broad Concept: Newton’s laws of
motion and gravitation describe and predict the motion of most objects. 1.1 – Compare and contrast
vector quantities (such as, displacement, velocity, acceleration, force, and linear momentum) and
scalar quantities (such as, distance, speed, energy, mass, and work). 1.2 – Distinguish between
displacement, distance, velocity, speed, and acceleration. Solve problems involving displacement,
distance, velocity, speed, and constant acceleration. 1.3 – Create and interpret graphs of 1-
dimensional motion, such as position vs. time, distance vs. time, speed vs. time, velocity vs. time,
and acceleration vs. time where acceleration is constant. 1.5 – Use a free-body force diagram to
show forces acting on a system consisting of a pair of interacting objects. For a diagram with only
co-linear forces, determine the net force acting on a system and between the objects.
Materials Required: Overhead projector, transparency slides, chalk or dry erase markers, springs, masses,
ring stands, graph paper, wooden blocks, marshmallows, plastic from beverage holders, computers with
internet access, TBD
Lesson Development: On day one the students will be introduced to Hooke’s law. The lesson will begin
with an inquiry based activity where the students will predict what happens when masses are added to
different springs of the same length. This will lead to a discussion about elasticity and notes about Hooke’s
law. The students will then work on an activity where they will test the elasticity of various springs and
graph the force versus displacement to find the spring constants. The first day ends with the students
practicing some sample problems about Hooke’s law. Day two reviews the material from the previous day
as well as the homework problems about Hooke’s law. The discussion will move from the elasticity of
springs to the elasticity of any solid material. An introduction to some engineering terms like load, shear
force, axial force, compression, tension and necessary before the discussion of stress, strain and Young’s
modulus. The students will then have an opportunity to find Young’s modulus for a marshmallow using
compression and Young’s modulus of the connective plastic connecting a bundle of beverages. Using the
data of force, area, initial and final lengths of the material, the students can calculate the elasticity of each
sample. Students can then graph their data for another method for obtaining Young’s modulus. Students
will strengthen their understanding with a homework assignment. On the third day the homework about
Young’s modulus will be reviewed and hopefully a short video will be shown. There is also an interactive
website about Young’s modulus that the students will complete so calculate the elasticity of virtual
materials. The lesson will end with an assessment that has yet to be determined. Please see attached lesson
plan and ancillary materials.
References: TBD
Lesson - Can All Things Stretch?
Day 1
Time Methods *otes to Me
10 min.
POE � “We have 2 springs of equal length. If we hang
the same mass on each spring, what do you expect to
observe? Write down your prediction in your notebook
and a diagram of this setup.”
• Give students a minute or two to write the information
in their notebooks.
• Solicit students’ responses about their predictions.
• “OK, so now we have to test our predictions. Make
sure you record any observations you see in your
notebooks.”
• Attach the first spring on the stand and hang the mass.
Measure how far the spring stretches. Repeat the same
procedure with the second spring.
• “Clearly there is something different between the two
springs. See if you can come up with an explanation
for what you just observed.”
• Solicit students’ responses about their explanations.
• “What seems to be different for the springs is their
elasticity, or their ability to stretch. We can assign a
number for each spring to indicate the elasticity, or
stretchiness, for all springs. As long as we don’t
overstretch a spring, this stretchiness number should
always hold true.”
Need springs, masses, ruler, ring
stand & clamps
Allow sufficient thinking and
writing time during each step of
the POE.
20 min.
*otes � Hooke’s Law
• “We can use the concepts of force and distance to find
out how stretchy a spring can be. The stretchiness of a
spring is determined by Hooke’s Law.”
• See Hooke’s Law overhead transparency.
Need Hooke’s Law overhead
transparency
35 min.
Activity � Hooke’s Law Lab Activity
• “.ow that we’ve discussed Hooke’s law, lets see if we
can put our knowledge to use. For this activity you will
be given some springs and it will be your job to find the
constants. Make sure you record all your data in your
notebooks. Be sure to include a diagram of your
experiment setup.”
• Students will work in groups for this activity.
• Students will be given 2 or 3 different springs. The
springs should be labeled.
• Begin by attaching your spring to the ring stand so that
it hangs freely. Measure the initial length of the spring.
• Add a mass to the spring and measure the new
displacement of the spring. Be sure to make sure that
the spring is no bouncing when you take your
Need materials for Hooke’s law –
springs, masses, ruler, ring stands
& clamps, Hooke’s Law lab
overhead transparency
Group size will depend on class
size and amount of materials.
measurement.
• Continue to add masses to the end of the spring and
record each new displacement.
• Use the data from your experiment to make a graph of
the force vs. displacement. Find the slope of the graph
to calculate the spring coefficient.
Finish activity and clean up with
15 minutes remaining in class.
10 min
Wrap Up � Discussion of what the data and graphs mean
in terms of Hooke’s Law.
• Questions to consider in class discussion:
o Which spring is the most elastic and most
inelastic?
o How does our data help to determine which
spring is most or least elastic?
o What does the slope of the Force vs.
Displacement tell us?
o Why is there a y-intercept value? What should
it be?
o Do you think that the Hooke’s Law, or the idea
that materials have some amount of elasticity,
only applies to springs? What else do you think
it would apply to?
5 min
Homework � Hooke’s Practice Problems Worksheet
• Write answers on the board.
• “I’ve put the answers on the board so that you can
check your work. Make sure you show all of your work
and follow all problem-solving steps.”
Need Hooke’s Law Practice
Problems Worksheet and answer
sheet
Day 2
Time Methods *otes to Me
10 min
RAP � Review of Hooke’s Law and introduces
Young’s Modulus.
• Students work on RAP questions.
• Review answers with class.
Need RAP overhead
transparency.
Check homework while students
work on RAP
10 min
Review Homework � Hooke’s Practice Problems
Worksheet
• Students compare their answers with the person
next to them.
• “After comparing your answers with your partner,
if you still want to review a problem, come up
and write that number on the board.”
• Review any problems that are put on the board.
Show all problem-solving steps.
Need Hooke’s Law Practice
Problems worksheet with
answers
2 min
Video � 2 short video clips
• “Yesterday we talked about Hooke’s Law and
how we can quantify how much elasticity a spring
has. Today we can use the same idea of Hooke’s
Law to show how other types of materials have
different amounts of elasticity. Even if you can’t
see it with your eyes, all materials exhibit some
amount of elasticity. We use a concept called
Young’s Modulus to quantify the elasticity of
materials Sometimes you can see the elasticity of
materials and the effects are dramatic.”
• Video clip of tensile steel rebar breaking
• Video clip of Tacoma Narrows Bridge
Need 2 short
25 min.
*otes � Young’s Modulus
• “Yesterday we talked about Hooke’s Law and
how we can quantify how much elasticity a spring
has. Today we can use the same idea of Hooke’s
Law to show how other types of materials have
different amounts of elasticity. Even if you can’t
see it with your eyes, all materials exhibit some
amount of elasticity. We use a concept called
Young’s Modulus to quantify the elasticity of
materials.”
• See Young’s Modulus overhead transparency.
Need Young’s Modulus overhead
transparency.
35 min.
Activity � Young’s Modulus Lab Activity –
Compression of a marshmallow.
• .ow that we have a better understanding of
elasticity let’s practice using Young’s modulus to
calculate elasticity of a familiar material. You
will be working in groups for this activity.
Need materials – wooden blocks,
masses, marshmallows, graph
paper, rulers.
• Students collect materials - four wooden blocks,
one marshmallow, graph paper, masses.
• Students set up three wooden blocks and attach
graph paper to one of the outermost blocks.
• All data should be recorded in the students’
notebooks.
• Calculate the area of the top of the marshmallow.
• Place the last wooden block on top of the
marshmallow and record the height of the block
on the graph paper. Place the first weight on top
of that wooden block and record the new height –
it will be less since the marshmallow is getting
compressed. Continue adding additional masses
on top of the wooden block to further compress
the marshmallow. As each mass is added be sure
to record the new block height.
• Calculate stress, strain and Young’s Modulus.
• Graph stress vs. strain and calculate the slope of
the graph.
• Answer questions.
Finish activity and clean up with
15 minutes remaining in class.
Homework � Finish the Young’s Modulus lab
graph and questions
Hooke’s Law
• Hooke’s Law � extension (or compression)
of a spring is directly proportional to the force applied
o Only if the spring is Not overstretched (inside elastic range) � returns to original length when force is removed. � Molecules return to original position
o Spring stretchiness is determined by a constant, k � harder to stretch = � constant
o Equation:
F = kd
F � applied force
k � spring constant (unique to each
spring) d � displacement spring is extended or
compressed
o Force and displacement are linear
� slope = spring constant, k
o Can also be used to find elastic potential energy (Ee) in a spring:
Ee = ½ kd
2
o Sample Problems:
1. What is the spring constant when a 45 N force stretches the spring 15 cm?
2. If it takes 50 N of force to stretch a spring 5 cm, how much will the spring stretch if 125 N are applied to the same spring?
3. What is the amount of elastic potential energy stored in the spring when it is stretched with 50 N and with 125 N?
Hooke’s Law Activity
Setup
Procedure
• Begin by attaching your spring to the ring stand so that it hangs freely. Measure the initial length of the spring.
• Add a mass to the spring and measure the new displacement of the spring. Be sure to make sure that the spring is no bouncing when you take your measurement.
• Continue to add masses to the end of the spring and record each new displacement.
• Use the data from your experiment to make a graph of the force vs. displacement. Find the slope of the graph to calculate the spring coefficient.
Data Table
Displacement Mass (kg) Force (N)
(mm) (m)
Graph Force vs. Displacement
• Force (N) � y-axis
• Displacement (m) � x-axis Questions
1. Which spring is the most elastic and most inelastic? 2. How does our data help to determine which spring is most or least elastic? 3. What does the slope of the Force vs. Displacement tell us? 4. Why is there a y-intercept value? What should it be? 5. Do you think that the Hooke’s Law, or the idea that materials have some amount of elasticity, only applies to springs? What else do you think it would apply to?
Name _______________________________ Date ________________
Physical Science Block _____
Hooke’s Law Practice Problems
Show ALL work and follow ALL problem-solving steps for the following problems.
1. What force is necessary to stretch an ideal spring whose force constant is 120 N/m by an amount of 30
cm? (36 N)
2. A spring with a constant of 600N/m is used on a scale for weighing fish. What is the mass of a fish that
would stretch the spring by 7.5 cm from its normal length? (4.6 kg)
3. A spring in a pogo stick is compressed 12 cm when a 40 kg girl stands on the stick. What is the spring
constant for the pogo stick spring? (3333 N/m)
4. An elastic cord is 80 cm long when it is supporting a mass of 10 kg hanging from it at rest at rest. When
an additional 4 kg is added, the cord is 82.5 cm long.
a) What is the spring constant of the cord? (1600 N/m)
b) What is the length of cord when no mass is hanging from it? (73.75 cm)
5. A mass of 5 kg is attached to the end of a spring causing it to stretch 0.98 m.
a) What is the spring constant?
b) How far would it stretch if 2.5 kg were suspended from the spring?
c) How far would it stretch if both masses were both hanging from the end of the spring?
Young’s Modulus
• Engineering Lingo: o Load (P) � same thing as force
� Units � N
o Shear force � a force, or component of
a force, that acts parallel to a plane � Can cause bending
o Axial force � force along the
longitudinal (or long) axis of a body � Tension � pulling away from
material, pulling force (load)
� Compression � pushing toward
material, pushing force (load)
• Material Characteristics o Some materials are stronger against tension, others compression
o Strain (ɛ) � change in length of a
material when an axial force is applied (ɛ is Greek epsilon)
� units � none, length units cancel
o stress (σ) � force per unit area (like
pressure) for solids (σ is Greek sigma)
� units � Pascal, Pa
∆L ɛ =
L Lf – Li ɛ = Li
F σ =
A
o Young’s Modulus (E) � shows the
relationship between stress and strain � Also known as Elastic Modulus � like Hooke’s law for solid materials � used by engineers to quantify elasticity of a material � important for designing and building structures
� unique property like boiling pt, specific heat capacity, etc.
� units = Pa or N/m2, psi,
� E > 0 always
� Equations:
F / A E =
∆L / L σ
E = ɛ
FL E =
A∆L FL
E = A(Lf – Li)
� Stress vs. Strain Graph
• Stress � y-axis
• Strain � x-axis
• Slope = E
• Yield Point � when slope stops being linear o material loses “strength” and is starting to fail
• Examples of Young’s Modulus
Material Young’s Modulus, E (GPa) Rubber 0.01 – 0.1 Nylon 2 – 4
Pine wood 9 Oak wood 11 Aluminum 69 Diamond 1220
Young’s Modulus Activity Set up the materials like the picture.
Data for the marshmallow:
• Diameter d = _______
• Radius
r = d/2
r = _______
• Area
A = πr2
A = _______
Mass
(kg)
Force
(*)
Area
(m2)
Stress, σ
(Pa)
Length
(m)
;Length
(m) Strain, ɛ
• Calculate Young’s Modulus, E:
• Graph stress vs. strain & find the slope of the graph.
• Questions
1. What does the slope of the graph indicate?
2. Is there a y-intercept for this graph? What
does this value mean? Do you think it should
be a particular value?
3. How does the marshmallow’s Young’s
modulus compare to some of the other
values? What does this tell you about the
marshmallow?
4. Where are some sources of error in this
experiment?