A First Course in Physics · Ch. II, §§ 20–30 · Chapter 2: Force and Motion
3. Measuring force; adding and resolving forces
Goal: Your student can tell a gram of mass from a gram of force, draw forces as arrows, find a resultant with a parallelogram, and find the force needed to hold something on a ramp.
You'll need
- The book, open to these pages
- A rubber band or spring and a ruler (a homemade spring balance)
- Two luggage scales or spring scales if you have them (optional)
- A board for a ramp and a toy car
- Graph paper, ruler and protractor
- A notebook and pencil
What's in the book
The gram of force and the spring balance; forces drawn as lines; the resultant of two forces and the parallelogram law, tested with two spring balances; components of a force; the component of weight along an inclined plane; why a pendulum bob comes to rest under its support. Six problems follow.
The lesson, step by step
Hook question
SayIf you pull a wagon east and your friend pulls it north, which way does it go?
Read together
Read §§ 20–30. The book is careful to keep two ideas apart:
the amount of matter in a body is always the same, no matter where the body is in the universe, while the pull of the earth upon that amount of matter decreases as we recede from the earth's surface.
Explain the idea
A force has a size and a direction, so we draw it as an arrow of the right length. Two forces at an angle add up to the diagonal of the parallelogram they make (§ 25).
Going the other way, any force can be split into components (§§ 27–28). On a ramp, the part of the weight pulling down the slope is weight × height ÷ length (§ 29).
Try it: a homemade spring balance
Hang a rubber band from a hook and tape a ruler beside it. Hang a bag with 1, 2, 3 identical cans or water bottles and mark the stretch each time. That is the book's spring balance in § 21.
Then put a toy car on a ramp and pull it gently up the slope with the band. Raise the ramp and see the stretch grow, just as § 29 predicts.
Draw a parallelogram
On graph paper draw 10 squares east and 15 squares north from one point (the book's example in § 23). Complete the parallelogram and measure the diagonal. Check it with the Pythagorean theorem: √(10² + 15²) ≈ 18.0.
What we know now
The "gram of force" is no longer used. Today force is measured in newtons (N). The pull of the earth on 1 kilogram is about 9.8 N, so the book's "gram of force" is about 0.0098 N.
Say it back
Your student explains why a pendulum can only rest straight under its support, using the idea of components.
Problems
Work problems 1–6 on book page 20. Draw a diagram for each one.
Afterwards
Find inclined planes this week (a wheelchair ramp, a slide, a road up a hill). Estimate height ÷ length for each.
Tip
SE and SW are at right angles, so problem 1 is a right-triangle problem.
Answers to the book's problems
1. About 32 lb, a little west of due south (about 6° west of south). 2. 12 mi./hr = 17.6 ft./sec. Upstream: 12.6 ft./sec, about 8.6 mi./hr; downstream: 22.6 ft./sec, about 15.4 mi./hr. 3. About 19.2 mi., in a direction about 51° south of east. 4. 40 lb. 5. 5 lb. 6. 14 ft.
Worked out for this site from the scan. If a number in your copy differs, trust the book.