Newton’s laws of motion
The empirical laws of Kepler describe planetary motion, but Kepler made no attempt to define or constrain the underlying physical processes governing the motion. It was Isaac Newton who accomplished that feat in the late 17th century. Newton defined that momentum was proportional to velocity, the constant of proportionality being defined as mass. Newton then defined force (also a vector quantity) in terms of its effect on moving objects and in the process formulated his three laws of motion.
Newton's first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. This postulate is known as the law of inertia, and it is basically a description of one of the properties of a force: its ability to change rest into motion or motion into rest or one kind of motion into another kind. Before Galileo's time it was thought that bodies could move only as long as a force acted on them and that in the absence of forces they would remain at rest. Those who sought to find the forces that kept the planets moving failed to realize that no force was necessary to keep them moving at a practically uniform rate in their orbits; gravitational force, of which they had no conception, only changes the direction of motion.
Newton's second law is a quantitative description of the changes that a force can produce in the motion of a body. It states that the time rate of change of the velocity (directed speed), or acceleration, is directly proportional to the force F and inversely proportional to the mass m of the body; i.e., a = F / m or F = ma; the larger the force, the larger the acceleration (rate of change of velocity); the larger the mass, the smaller the acceleration. Both force and acceleration have direction as well as magnitude and are represented in calculations by vectors (arrows) having lengths proportional to their magnitudes. The acceleration produced by a force is in the same direction as the force; if several forces act on a body, it is their resultant (sum), obtained by adding the vectors tail-to-tip, that produces the acceleration.
The second law is the most important, and from it all of the basic equations of dynamics can be derived by procedures developed in the calculus. A simple case is a freely falling body. Neglecting air resistance, the only force acting on the body is its weight acting down, and it produces a downward acceleration equal to the acceleration of gravity, symbolized as g, which has an average value of 9.8 metres (32.2 feet) per second per near the surface of the Earth.
Newton's third law states that the actions of two bodies upon each other are always equal and directly opposite; i.e., reaction is always equal and opposite to action. The proposition seems obvious for two bodies in direct contact; the downward force of a book on a table is equal to the upward force of the table on the book. It is also true for gravitational forces; a flying airplane pulls up on the Earth with the same force that the Earth pulls down on the airplane. The third law is important in statics (bodies at rest) because it permits the separation of complex structures and machines into simple units that can be analyzed individually with the least number of unknown forces. At the connections between the units, the force in one member is equal and opposite to the force in the other member. The third law may not hold for electromagnetic forces when the bodies are far apart.
Comprehension check
Exercise 1. Choose the correct ending to the following sentences.
Kepler
didn’t try to define the physical processes governing the motion.
tried to define the physical processes governing the motion.
didn’t try to define or constrain the physical processes governing the motion.
Newton’s first law states that
a) if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed if it is acted upon by a force.
b) if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.
c) if a body is moving at a constant speed in a straight line, it will remain at rest unless it is acted upon by a force.
3. Newton’s second law states that
a) the time rate of change of the velocity (directed speed), or acceleration, is inversely proportional to the force F and directly proportional to the mass m of the body; i.e., a = F / m or F = ma; the larger the force, the larger the acceleration (rate of change of velocity); the larger the mass, the smaller the acceleration.
b) the time rate of change of the velocity (directed speed), or acceleration, is directly proportional to the force F and inversely proportional to the mass m of the body; i.e., a = F / m or F = ma; the larger the force, the smaller the acceleration (rate of change of velocity); the larger the mass, the larger the acceleration.
c) the time rate of change of the velocity (directed speed), or acceleration, is directly proportional to the force F and inversely proportional to the mass m of the body; i.e., a = F / m or F = ma; the larger the force, the larger the acceleration (rate of change of velocity); the larger the mass, the smaller the acceleration.
4. Newton's third law states that
a) the actions of two bodies upon each other are always equal and directly opposite; i.e., reaction is never equal and opposite to action.
b) the actions of two bodies upon each other are always opposite and directly equal; i.e., reaction is always equal and opposite to action.
c) the actions of two bodies upon each other are always equal and directly opposite; i.e., reaction is always equal and opposite to action.
Exercise 2. Find the answers to the following questions in the text.
What did Newton define before formulating the laws of motion?
What does Newton’s first law state?
What postulate is known as the law of inertia? What does it mean?
What does Newton’s second law state?
How can the second law be derived?
What does Newton’s third law state?
Why is the third law important in statics?
What scientists should be mentioned in discussing the laws of motion? What is their contribution?
Exercise 3. The sentences given below are jumbled. Arrange them in the logical order to sum up the contents of the text “NEWTON’S LAWS OF MOTION.
This postulate is known as the law of inertia.
Newton's first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.
The empirical laws of Kepler describe planetary motion.
. The proposition seems obvious for two bodies in direct contact; the downward force of a book on a table is equal to the upward force of the table on the book.
Newton then defined in terms of its effect on moving objects and in the process formulated his three laws of motion.
Newton's second law is a quantitative description of the changes that a force can produce in the motion of a body.
It states that the time rate of change of the velocity (directed speed), or acceleration, is directly proportional to the force F and inversely proportional to the mass m of the body.
Newton's third law states that the actions of two bodies upon each other are always equal and directly opposite; i.e., reaction is always equal and opposite to action.
Newton defined that momentum was proportional to velocity, the constant of proportionality being defined as mass.
The acceleration produced by a force is in the same direction as the force; if several forces act on a body, it is their resultant (sum).
Grammar exercises
Exercise 1. Open the brackets.
When Newton (to be) twenty-two years old he (to begin) to study the theory of gravitation.
First he (to examine) the general problem of attraction of one mass by another.
This attraction (to apply) to every object everywhere, no matter where it (to locate).
Newton (to show) that the attractive force of the Sun (to explain) some of the known perturbations of the Moon and actually (to calculate) some of those changes correctly.
The Sun (to attract) and (to attract) by the planets.
The Earth (to attract) and (to attract) by the Moon.
If you (to kick) a football, it (to react) with an equal force against your foot.
When you (to press) a stone with your finger, your finger (to press) back by the stone.
When the temperature of the body (to change), the magnitudes of almost all its properties also (to change).
When a body (to become) warmer we say that it (to receive) the heat.
The principle of the conservation of mechanical energy (to apply) to mechanical systems in which there is no friction.
Exercise 2. Translate from Russian into English.
Великий математик и физик Ньютон сформулировал общие законы движения тел.
Закон инерции часто называют первым законом Ньютона, т.е. он представляет собой просто повторение принципа инерции Галилея.
Второй закон гласит, что сила, действующая на тело, равна произведению массы на его ускорение.
Закон равенства действия и противодействия был открыт Ньютоном и назван третьим законом движения.
Наши опыты и наблюдения могут подтвердить справедливость закона равенства действия и противодействия.
Основные законы механики второй и третий законы Ньютона-дают возможность решения любой механической задачи.
Существуют простые случаи движения, которые можно решить числовыми методами.
Нам нужно найти и другие методы решения такой задачи.
Follow-up activities
Exercise 1. Choose from the text and read sentences in which the author formulates Newton’s laws of motion.
Exercise 2. Find the key sentence(s) in each paragraph and write them down.
Exercise 3. Use the chosen key sentences in making a short outline of the text.
Exercise4. Imagine you deliver a lecture on “NEWTON’S LAWS OF MOTION ”. Include all important facts from the text above and add additional information if necessary.
Exercise 5. Watch a video film and give its main ideas.