A First Course in Physics · Ch. VI, §§ 151–159 · Chapter 6: Molecular Forces
16. Molecular forces in solids: elasticity and Hooke's law
Goal: Your student can explain tensile strength and elasticity, discover Hooke's law with a rubber band or spring, and define hardness, brittleness, ductility and malleability.
You'll need
- The book, open to these pages
- A rubber band or a spring (a pen spring or toy Slinky)
- A paper cup with a string handle and a bag of identical coins or washers
- A ruler, tape
- Graph paper
- A notebook and pencil
What's in the book
How strongly solids hold together (a steel rod 1 cm across holds several tons); breaking weights of wires; elasticity and the elastic constant; the limit of perfect elasticity; Hooke's law; why solids neither collapse nor fly apart; cohesion and adhesion; hardness, brittleness, ductility and malleability. Five problems follow.
The lesson, step by step
Hook question
SayWhy does a spring come back to its shape, but a paper clip you bend stays bent?
Read together
Read §§ 151–159. Hooke's law in the book's words:
Within the limits of perfect elasticity elastic deformations of any sort, be they twists or bends or stretches, are directly proportional to the forces producing them.
Try it: discover Hooke's law
Hang the cup from the rubber band or spring and tape a ruler beside it. Add coins five at a time and write down the stretch each time. Plot coins (across) against stretch (up) on graph paper. While the band is not over-stretched, the points fall on a straight line. That is Hooke's law.
Find the elastic limit
Unbend a paper clip a little and let go: it springs back. Bend it a lot: it stays bent. It has passed its limit of perfect elasticity (§ 155).
Explain the idea
Molecules in a solid pull on each other (cohesion) but also jiggle, which pushes them apart. A solid's size is a balance between the two (§ 157). Glue sticking to wood is adhesion: unlike molecules attracting.
Note the book's careful meaning of "elastic": steel is more elastic than rubber, because it takes a much larger force to stretch it the same amount.
Test the properties
Use a scratch test on a few safe objects (a coin, a nail, glass, a fingernail) to rank hardness. Talk about which metals are ductile (copper wire) and malleable (aluminum foil).
Say it back
Your student explains the difference between cohesion and adhesion with two examples of each.
Problems
Work problems 1–5 on book page 113. Remember: strength and stiffness grow with the cross-section area, which grows with the square of the diameter.
Afterwards
Weigh things this week with your rubber-band balance after marking it with known weights.
Answers to the book's problems
Using the book's table (copper 51 kg, iron 77 kg per sq. mm): 1. About 1.23 mm (the area must be 77/51 times as large). 2. √5 ≈ 2.24 times. 3. 12 kg, reading the problem as 1 kg stretching the first wire 1 mm (4 times the area, 3 times the stretch). 4. 0.875 mm (7 kg ÷ 4 × 0.5 mm). 5. Yes, because by Hooke's law the stretch is proportional to the load.
Worked out for this site from the scan. If a number in your copy differs, trust the book.