A First Course in Physics · Ch. VIII, §§ 219–226 · Chapter 8: Work and Mechanical Energy
25. Power and energy
Goal: Your student can define power and its units (horse power, watt, kilowatt), tell potential from kinetic energy, and calculate both.
You'll need
- The book, open to these pages
- A stopwatch and a flight of stairs
- A bathroom scale
- A pendulum: a string with a weight
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Power as the rate of doing work; Watt's horse power and the watt and kilowatt; energy as the capacity for doing work; potential and kinetic energy; their changes back and forth in a pendulum; the general law of frictionless machines; P.E. = Mgh and K.E. = ½Mv². Seven problems follow.
The lesson, step by step
Hook question
SayYou and a friend carry identical boxes up the same stairs. You run, they walk. Who did more work? Who used more power?
Read together
Read §§ 219–226. The definition:
The energy of a body is defined as its capacity for doing work.
Try it: your horse power
Weigh your student (in pounds). Measure the height of a flight of stairs (count steps × step height, in feet). Time a fast but safe climb. Power = weight × height ÷ seconds, in foot pounds per second. Divide by 550 to get horse power, or multiply ft·lb/s by 1.356 for watts. The book says an ordinary man is about 1/7 H.P.
Try it: energy in a pendulum
Pull the pendulum to one side and let go. At the ends it stops (all potential energy); at the bottom it is fastest (all kinetic). Without friction it would rise to the same height on the other side (§ 224). Let your student hold the bob at their nose and let it go: it swings back and stops just short of their nose.
The formulas
Potential energy = weight × height (or Mgh in ergs). Kinetic energy = ½Mv² ergs. In SI units, PE = mgh joules and KE = ½mv² joules, with m in kilograms and v in meters per second. A watt is a joule per second; 746 watts is a horse power.
Say it back
Your student explains the energy changes in a pile driver (problem 4).
Problems
Work problems 1–7 on book page 166.
Afterwards
Look at the power ratings (watts) on a few appliances: a light bulb, a hair dryer, a microwave. Which uses energy fastest?
Answers to the book's problems
1. About 347 kg. m per second, about 3.4 kW or 4.6 H.P. 2. About 13,150 H.P. (1,000,000 kg. m per second ÷ 76.05). 3. About 0.67 H.P. (220 lb. raised 100 ft. per minute). 4. Work lifting it becomes potential energy, then kinetic energy as it falls, then heat as it drives the pile; 60,000 ft. lb. ÷ ⅓ ft. = 180,000 lb. average resistance. 5. About 6,800,000 H.P. (taking a ton as 2000 lb.). 6. About 408,000 g. cm. 7. About 5,040,000 kg. m (about 4.9 × 10¹⁴ ergs).
Worked out for this site from the scan. If a number in your copy differs, trust the book.