A First Course in Physics · Ch. VIII, §§ 212–218 · Chapter 8: Work and Mechanical Energy
24. The principle of work: wheel and axle, ramp, screw and gears
Goal: Your student can state the principle of work and use it to find the mechanical advantage of the wheel and axle, inclined plane, screw, gear trains and worm wheel.
You'll need
- The book, open to these pages
- A screwdriver and a screw in a scrap of wood
- A bicycle (to look at the gears)
- A pencil sharpener with a crank or an egg beater (gears)
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
The principle of work stated (first given by Newton); the wheel and axle and capstan; the inclined plane by the work principle; the screw and jackscrew; trains of gear wheels; the worm wheel; the differential pulley. Eleven problems follow.
The lesson, step by step
Hook question
SayWhy is it easier to turn a screw with a fat-handled screwdriver than a thin one?
Read together
Read §§ 212–218. The great rule:
In all mechanical devices of whatever sort the work expended upon the machine is equal to the work accomplished by it.
Explain the method
To find any machine's mechanical advantage: move the effort a little, see how far the load moves, and divide. Wheel and axle: R ÷ r. Ramp: length ÷ height. Screw: the circle the handle travels ÷ the distance between threads (the pitch).
Try it: turn a screw
Drive a screw into soft wood with the screwdriver. Count turns for 1 cm. Each turn your hand goes around a circle; the screw moves only one thread. Now hold the narrow shaft instead of the handle and feel how much harder it is.
Look at gears
Turn the crank of an egg beater or a bicycle pedal slowly and count how many times the small wheel turns for each turn of the big one. Gears trade speed for force, or force for speed (Fig. 164).
Say it back
Your student explains why a long ramp makes it easier to load a heavy barrel, using the principle of work.
Problems
Work a selection of problems 1–11 on book pages 159–161: try 1, 2, 3, 6, 7, 8, 9, 10 and 11. Problems 4 and 5 need careful reading of the figures.
Afterwards
Ride a bike up a hill in a low gear and then a high gear. Which is easier on the legs, and which goes farther per pedal turn?
Answers to the book's problems
1. 96 (the crank end travels 48π in. while the load rises ½(6π − 5π) = π/2 in.). 2. 100 lb. 3. 30 ft. 6. About 50 lb. each (2000 lb. × 0.5 ft. ÷ 5 ft. = 200 lb. in all), taking the 5 ft. from the center. 7. 15 (24 ÷ 4 = 6 for the crank and barrel, × 50/20). 8. 1.4 m. 9. About 22 lb. 10. 400. 11. 100 (50 cm ÷ 10 cm = 5, × 48/12 × 60/12 = 20).
Worked out for this site from the scan. If a number in your copy differs, trust the book.