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. 35 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. 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 Hooke s Law overhead transparency 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 5 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? 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 25 min. 35 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 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. 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 2 short Need Young s Modulus overhead transparency. 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 (E e ) in a spring: E e = 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?
Setup Hooke s Law Activity
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 Mass (kg) Force (N) Displacement (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 Physical Science Date 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 ɛ = L L o stress (σ) force per unit area (like pressure) for solids (σ is Greek sigma) F σ = A units Pascal, Pa ɛ = L f L i L i
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/m 2, psi, E > 0 always Equations: E = σ ɛ F / A E = L / L FL E = A L FL E = A(Lf L i )
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 Radius r = d/2 Area A = πr 2 d = r = A = Mass (kg) Force ( ) Area (m 2 ) 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?