Lesson Plan #25

(16)Newton and his Laws

A short lesson, introducing Newton's laws--what they state, and what the intuitive meaning is of the first and third laws

Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern

Material:Newton and his Laws, section #10

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    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

  • About Isaac Newton and his work.

  • About Newton's laws of motion.

  • The meaning of the first and third laws.

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:

  • 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:

    1. the laws of motion
    2. the "theory of universal gravitation" and
    3. the theory of quantities which vary and change continuously ("differential and integral calculus," co-discovery with Leibnitz in Germany)

    [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?

    (1) Force, which was the cause of motion

    (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?

    Motion with a constant velocity did not require any forces. Without anything opposing it (friction with the ground, air resistance), once such motion began, it could in principle continue indefinitely.

    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?

    The acceleration was
      (1) In the direction of the force
      (2) Proportional to the force
      (3) Inversely proportional to the mass being accelerated.

--What is the above statement called?

    Newton's second law.

--Can you state it in a formula?

    a = k F/m with a and F vectors, and k some constant number expressing proportionality.

    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?

    In the absence of forces, an object ("body") at rest will stay at rest, and a body moving at a constant velocity in a straight line continues doing so indefinitely.

--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?

    No. The Earth moves in an elliptic orbit, not in a straight line, and its motion is subject to forces, mainly the Sun's gravity.

--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?

    Rockets push themselves forward by pushing their exhaust gases in the opposite direction. Air is not needed.
[Still, Dr. Goddard went to the trouble of firing a rocket in a vacuum and showing--by springs that held it--that its thrust was unchanged.]

--When you ride a bicycle and it leans to one side, do you balance it by shifting your weight to the other side?

    No, doing so will only cause it to lean more, by the third law. You control the lean by turning the handlebars, which shifts rotational momentum; the details are not explained here.

--What turns rotating garden sprinklers?

    The recoil from pushing out the water.

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Author and curator: David P. Stern
Last updated 4 August 1999