(16)Newton and his Laws
Part of a high school course on astronomy,
Newtonian mechanics and spaceflight
by David P. Stern
From Stargazers to Starships home page and index:
Terms: Force, mass
Stories and extras: Why a bicycle cannot be balanced unless it moves and why a boat slides back when one jumps from it.
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. The world had a regularity and 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:
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 also: built the first telescope based on concave mirrors, discovered "Newton's rings" which were a clue to the wave nature of light, proved the "binomial theorem", introduced "Newton's approximation" in solving equations, studied the flow of heat, and 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?
(2) Mass, the amount of matter, which resisted motion.
True, weight also increased with mass: a big stone was pulled down with a greater force than a small one. But it fell no faster, because it also resisted motion more than a small stone.
-- What did Newton say about the role of forces in producing velocity and acceleration?
Acceleration required a force.
[All this is the modern formulation of Newton's laws. Newton himself based his laws on the concept of momentum p = mv , which requires the use of calculus: F = dp/dt. However, here we try to avoid calculus.]
-- What is the connection between a force and the acceleration it produced?
(2) Proportional to the force
(3) Inversely proportional to the mass being accelerated.
--What is the above statement called?
--Can you state it in a formula?
We can choose k=1 and that way define the units of F: the law then becomes a=F/m or F = ma.
[The teacher might also raise the question "how can you divide a vector by m"? Answer: you are not dividing by m but multiplying by 1/m. What it all amounts to is, dividing the magnitude by m.]
--What is Newton's first law?
--The fact that the Earth has moved in its orbit for many years without any change, and keeps doing so indefinitely--is that an illustration of Newton's first law?
--What is Newton's third law?
Forces are always produced in pairs, with opposite directions and equal magnitudes. If body #1 acts with a force F on body #2, then body #2 acts on body #1 with a force of equal strength and opposite direction.
--The fact that a cannon recoils when fired--is that a consequence of the third law?
--Around 1920, when Dr. Robert Goddard proposed that it would be possible to fly to space using rockets, some newspapers wrote that was impossible, because in space a rocket needed air to push against, otherwise it could not advance itself.
What was wrong with their argument?
--When you ride a bicycle and it leans to one side, do you balance it by shifting your weight to the other side?
--What turns rotating garden sprinklers?
Author and curator: David P. Stern