A First Course in Physics · Ch. II, §§ 31–37 · Chapter 2: Force and Motion
4. Gravitation, center of gravity and balance
Goal: Your student can state Newton's law of gravitation, find the center of gravity of a flat shape with a plumb line, and tell stable, unstable and neutral equilibrium apart.
You'll need
- The book, open to these pages
- A piece of stiff cardboard cut into an irregular shape
- A pushpin, string and a small weight (a washer or key) for a plumb line
- A pencil and two table forks or butter knives (for problem 4)
- An egg, a ball and a cone (an ice-cream cone or paper cone)
- A notebook and pencil
What's in the book
Newton's law of universal gravitation and how weight changes with height above the earth; the center of gravity and two ways to find it; stable, neutral and unstable equilibrium. Five questions follow.
The lesson, step by step
Hook question
SayWhy doesn't the Moon fall down? And why does a tall truck tip over more easily than a sports car?
Read together
Read §§ 31–37, including the short life of Newton under his portrait. Newton's law in the book's words:
Any two bodies in the universe attract each other with a force which is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
Explain the idea
"Inversely as the square" means: twice as far, one fourth the pull; three times as far, one ninth. The earth's radius is about 4000 miles, so 4000 miles up (twice as far from the center) you would weigh one fourth as much.
The center of gravity is the one point where the whole weight seems to act. A body is stable if tipping it raises its center of gravity.
Try it: find a center of gravity
Make the hole near the edge of the cardboard and hang it from the pushpin with the plumb line beside it. Draw a line along the string. Hang it from a second hole and draw again. The lines cross at the center of gravity. Check: does the cardboard balance on a pencil point there?
Try it: three kinds of equilibrium
Lay an egg on its side, then try to stand it on end. Roll a ball. Stand a cone on its base, its point and its side. For each, ask: does a little push raise, lower, or not change the center of gravity?
Say it back
Your student explains the three kinds of equilibrium using one example of each, without the book.
Questions
Work questions 1–5 on book page 25. For question 4, try it with a pencil and two forks stuck in at an angle so their handles hang below your fingertip.
Afterwards
Notice how people carry heavy loads: leaning away from a heavy suitcase, leaning forward up a hill. Where is their center of gravity?
Tip
Kids love the balancing-forks trick. Two forks pushed into a cork with a toothpick through it will balance on the rim of a glass.
Answers to the book's problems
1. 25 kg at 4000 mi. up (twice as far from the center); 64 kg at 1000 mi. up (100 × (4/5)²); about 99.85 kg at 3 mi. up. 2. Ballast lowers the ship's center of gravity so it is more stable. 3. The heavy weight is in the rounded bottom; tipping the toy over would raise its center of gravity, so it rolls back upright. The center of gravity does not rise; it falls as the toy rights itself. 4. The knives hang below the fingertip and bring the center of gravity below the point of support. 5. To keep the vertical line through his center of gravity over his feet.
Worked out for this site from the scan. If a number in your copy differs, trust the book.