A First Course in Physics · Ch. IX, §§ 227–237 · Chapter 9: Work and Heat Energy
26. Friction and efficiency
Goal: Your student can state the laws of sliding friction, find a coefficient of friction, and calculate the efficiency of a machine.
You'll need
- The book, open to these pages
- A brick or a block of wood with a hook or string, and a rubber band or luggage scale to pull it
- A few round pencils (rollers)
- Sandpaper, a smooth board, and a towel (different surfaces)
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Friction always wastes work; the laws of sliding friction; the coefficient of friction; rolling friction and ball bearings; fluid friction; internal friction; the definition of efficiency; the efficiencies of simple machines, water wheels and turbines. Two sets of problems follow.
The lesson, step by step
Hook question
SayWhy is it harder to get a heavy box moving across the floor than to keep it moving?
Read together
Read §§ 227–237 (the water-wheel paragraphs, §§ 235–237, can be skimmed). The first law of friction:
The friction between two solid surfaces is greater at starting than after the motion has begun.
Try it: test the laws
Pull the brick slowly across a table with the rubber band (or luggage scale) and measure the stretch: once to start it, once to keep it moving. Then test:
• double the load (put a book on top): about double the pull;
• turn the brick on its side: about the same pull (law 4);
• different surfaces: towel, board, sandpaper;
• set it on pencils as rollers: the pull drops a great deal (§ 230).
Explain the idea
Coefficient of friction = pulling force ÷ weight (§ 229). Efficiency = useful work out ÷ total work put in (§ 233). A lever is nearly 100% efficient; a jackscrew may be only about 25%, because most of the work goes into friction.
Say it back
Your student explains why ball bearings make a bicycle wheel spin so easily.
Problems
Work questions 1–6 on book page 170 and problems 1–5 on book page 174. For the water wheels, the work put in each second is the weight of water times the height it falls.
Afterwards
Notice friction helping and hindering this week: brakes, shoe soles, a sticking drawer, a sled.
Answers to the book's problems
Page 170: 1. Starting friction is greater than moving friction, and the load's inertia must be overcome. 2. Friction with the banks and bed slows the water there. 3. The same distance in all three cases, since friction does not depend on the area of contact. 4. 0.1. 5. 150 g. 6. Friction keeps the screw from running back down; but it wastes much of the work. Page 174: 1. About 67% (400 ft. lb. out for 600 ft. lb. in). 2. 6. 3. About 21.5 cu. ft. per second (taking the fall as the 72.5-ft. diameter). 4. About 22,900 cu. ft. per minute. 5. About 0.53 cu. ft. per second.
Worked out for this site from the scan. If a number in your copy differs, trust the book.