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?