Note: This lesson uses vectors, and some way of denoting them on the board
and in the notebook must be agreed on by the class. In this lesson plan, all vector quantities will be underlined.
Goals The student will learn:
The list below is significant and deserves to be copied from the blackboard.
(A printed list is useful too, but students learn better if they write down the words in their own handwriting, and in their own notebooks. The lesson itself will go back to these points time and again. )
Terms: Force, mass
Stories and extras: Alexander Pope's couplet:
Nature and Nature's laws lay hid in night
How supertanker officers are taught to appreciate the enormous inertia of their ships.
God said: "Let Newton be!" and all was light.
Starting the lesson:
The story of astronomy and space, as we follow it, is essentially a story of discovery.
In the 1600s, the picture of our world seemed to come together.
Motions, at least those of isolated objects, seemed to follow certain laws: Copernicus made sense of the motion of the Earth and planets, Kepler made it possible to predict such motions, Galileo found a regularity in the falling of objects.
But that seemed just a beginning. Every observation, every solved problem, seemed to bring up new questions:
- When a cannon was fired, it recoiled back: why?
- A swinging pendulum had almost exactly the same period whether its swing was wide or narrow: why?
- Why did planets move according to Kepler's laws? Was there something universal behind this regularity, so that anything orbiting the Sun or a planet followed those laws?
- Why didn't big stones fall any faster than small ones, if the force pulling them down was so much larger?
Newton, born in 1642, guessed that there existed some basic laws which governed these and other motions. If we understood those laws, we could explain everything. He was right, and he discovered those laws, too--they are now known as Newton's three laws of motion.
It is easy enough to state them, to learn what they say, but that is not enough. To use them properly, one must understand their meaning and become familiar with them through examples. Today we begin the process, and we will proceed quite carefully.
Guiding questions and additional tidbits
(Suggested answers, brackets for comments by the teacher or "optional")
-- Who was Isaac Newton? What were his three main contributions to science?
He was perhaps the greatest scientist Britain ever produced, and his contributions included:
- the laws of motion
- the "theory of universal gravitation" and
- the theory of quantities which vary and change continuously ("differential and integral calculus," a co-discovery with Leibnitz in Germany)
--built the first telescope based on concave mirrors (which is how all big telescopes are now made),
--Discovered "Newton's rings" under a lens resting on flat glass, which gave a clue to the wave nature of light,
--Proved the "binomial theorem",
--Introduced "Newton's approximation," a method of solving equations,
--Studied the flow of heat,
.. .. .. and much, much more.]
[Possible project: have a student prepare 5-minutes presentations on Newton, based on web sites, encyclopaedia entries and other material.]
--What concepts did Newton introduce to the study of motions?
(1) Force, which was the cause of motion
(2) Inertia, which resisted motion.
(Today we also call inertia "mass," a concept discussed again in a later lesson. Mass is seen as measure of the amount of matter--the more there is of it, the greater the inertia.
True, weight also increases with mass: a big stone is pulled down with a greater force than a small one. But it falls no faster, because it also resists motion by its inertia more than a small stone.
At this point, introduce the formulation of the 3 laws, approximately as given on the web site, with brief discussions. It is best if the students copy them down.
--What did Newton mean by "Force?
Force is that which initiates or changes motion
-- Can you give examples?
--Gravity causes objects to fall
--Water resistance slows down the fall of a stone through water.
--Pressure of gas inside a gun makes a bullet fly.
--Pressure of hot gas inside a car engine pushes its pistons (which ultimately turn its wheels).
--The force of the jet from a rocket causes it to lift up.
--A magnet makes a nail move to it, or rotates a compass needle
--A compressed spring can pop out the refill in a ball-point pen.
.. .. .. .. .. and so on!
What a force actually does depends on the resistance it meets. Sometimes the resistance is large enough to stop any motion, as in this example:
You stand on the floor, and the force of gravity strongly pulls your body down, to the center of the Earth. Why doesn't it move?
Because the floor resists with an equal and opposite force! So the net force is zero.
(You can actually measure that opposite force by standing on bathroom scales. The scales contain a spring which your weight compresses, and the scale on them tells you the opposing force of that compression. If the scale say 160 pounds, or 70 kilograms--that is the opposing force of the spring, which stops you from moving further down.)
--Second case: Sometimes the force overcomes resistance. When you lift a brick from the floor, the force of your arm overcomes the pull of gravity.
It does not give the brick much speed (in this example) but it performs work and invests energy, which can perhaps be later recovered and converted to some other form. We have already mentioned energy, and will come back to work later again.
--Dragging a weight across the floor, against friction.
[Energy invested in pounding the nail is ultimately converted to heat. When a nail meets strong resistance, after you have pounded it in halfway, stop and touch it--it has become warm.]
.. ..(many other examples involving friction)
--Pulling a boat through water, against resistance, or an airplane through the air.
--Pulling a nail away from a magnet.
--Pounding a nail into a board of wood. The force of the moving hammer overcomes the resistance of the wood.
--Third case: Suppose you apply a force to an object, and only negligible forces oppose it. What happens?
It accelerates in the direction of the force--it moves faster and faster.
--Any falling object, of course.
--A rocket being launched.
--A bullet being fired. There exists resistance, but it is small compared to the push of the burning gunpowder.
--A ball rolling down an incline (although some of the force also goes to spin up the ball)
--A stone being shot by a slingshot
--A pitched baseball accelerates, although some of the force (generated by muscles) also goes to accelerating the pitcher's arm.
--By Newton's first law, does mere motion require a force?
Not necessarily. If an object is already moving at a constant speed in a straight line, and nothing opposes it, that motion will continue indefinitely, without requiring any force.
(Imagine an ideal hockey puck sliding on an unlimited flat sheet of ice, with no friction. By Newton's first law, it just keeps going.)
--Suppose your car stalls on a railroad track, and a freight train is coming. What should you do?
Get out and run! The train has far too much inertia to stop. The force of its brakes is much too weak for that job, and it may take up to a mile to stop it.
[The teacher may also tell the story of supertanker captains, training on heavy, underpowered boats.]