A First Course in Physics · Ch. VIII, §§ 202–207 · Chapter 8: Work and Mechanical Energy
22. Work, and the pulley
Goal: Your student can define work as force × distance, use the units (gram centimeter, erg, joule, foot pound), and show that a pulley system trades force for distance.
You'll need
- The book, open to these pages
- Two pulleys or two smooth curtain rings / spools on a pencil (or a broom handle over two chairs)
- Strong string, a bag with a known weight (a 1-liter water bottle is 1 kg)
- A luggage scale or spring scale if you have one
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
The definition of work and why holding a weight is not work in the scientific sense; units of work (gram centimeter, erg, joule, foot pound); the single fixed pulley, the single movable pulley and combinations; mechanical advantage. Two short sets of problems follow.
The lesson, step by step
Hook question
SayIf you hold a heavy bag of groceries still for five minutes, you get tired. Have you done any work?
Read together
Read §§ 202–207. The definition:
Whenever a force moves a body on which it acts, it is said to do work upon that body
Explain the units
Work = force × distance. Lifting 1 liter of water (1 kg) up 1 meter is 9.8 joules (§ 203). The joule is still the SI unit of work and energy; 1 joule = 1 newton × 1 meter = 10,000,000 ergs.
Try it: pulleys
Hang the bottle from a string over a single fixed support (a broom handle over two chairs). Pull it up 30 cm: your hand moves 30 cm, and the pull equals the weight.
Now make a movable pulley: tie one end of the string to the broom handle, loop it down under a spool or ring that the bottle hangs from, and back up over the handle. Pull: your hand moves twice as far, and (with a luggage scale) the pull is about half.
Mechanical advantage
Mechanical advantage = load ÷ effort. A single movable pulley has 2; with n strands holding the load it is n (§ 206). But the effort always moves n times as far: force × distance comes out the same (§ 207).
Say it back
Your student explains why a pulley system can lift a piano with a small force, but cannot reduce the work needed.
Problems
Work problems 1–3 on book page 147 and problems 1–3 on book page 151. For the drawing problems, count the strands holding the load.
Afterwards
Look for pulleys this week: a flagpole, window blinds, a crane, a clothesline.
Answers to the book's problems
Page 147: 1. 945,000 ft. lb. 2. 30,000 kg. m; 3,000,000,000 g. cm; about 2,940,000,000,000 ergs; about 294,000 joules. 3. 30,000,000 kg. m per day. Page 151: 1. The cage moves 4 times as far as the piston, so the piston force is 40,000 lb.; at 70 lb. per sq. in. the area is about 571 sq. in., a diameter of about 27 in. 2. Any arrangement with 4 strands supporting the load. 3. Any arrangement with 5 strands; mechanical advantage 5.
Worked out for this site from the scan. If a number in your copy differs, trust the book.