UNIT 3
NEWTONS LAWS OF MOTION
Pre-text exercises
Exercise 1. a). The text you are going to read is headlined NEWTONS LAWS OF MOTION. Guess what it can run about.
b).Think of 5-7 questions the answers to which you hope to find in the text.
c) In pairs, ask and answer these questions
Exercise 2. Mind the pronunciation of the following words:
Empirical
Constrain
Govern
Accomplish
Momentum
Proportionality
Quantity
Remain
Quantitative
Equation
Procedure
Calculus
Surface
Analyze
Exercise 3. Guess what the following international words mean.
Empirical, planetary, constant, postulate, inertia, basically, gravitational, planets, orbits, conception, vectors, proportional, basic, dynamics, gravity, statics, complex,
electromagnetic.
Exercise 4. Below you will find a list of physical terms mentioned in the text. Choose their Russian equivalents in the right-hand column.
| Time rate of change of the velocity | |
| Weight | |
| Magnitude | |
| Resistance | |
| Calculus | |
| Law of inertia | |
| Velocity | |
| Direction of motion | |
| Law of motion | |
| Straight line | |
| Constant speed | |
| Momentum | |
| Inversely proportional | |
| Directly proportional | |
| Mass | |
| Resultant | |
| Motion | |
| Acceleration | |
| Force |
Exercise 5. The words in A are used in the text NEWTONS LAWS OF MOTION Choose their definitions from B and translate these words into Russian.
| A | B |
| Velocity | The process of continual change in the physical position of an object |
| Weight | The quantity of motion of a moving body, measured as a product of its mass and velocity |
| Inertia | The speed of something in a definite direction |
| Acceleration | The quantity of matter which a body contains, as measured by its acceleration under a given force exerted on it by a gravitational field |
| Gravity | An influence tending to change the motion of a body or produce motion or stress in a stationary body |
| Momentum | A property of matter by which it continues in its existing state of rest or uniform motion in a straight line unless that state is changed by an external force |
| Reaction | Remaining the same in all cases and at all times, unchanging in form or character |
| Magnitude | The rate of change of velocity per unit of time |
| Mass | A numerical quantity or value |
| Uniform | A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another |
| Vector | The force that attracts a body towards the centre of the earth or towards any other physical body having mass |
| Force | A force exerted in opposition to an applied force |
| Motion | The force exerted on the mass of a body by a gravitational field |
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Exercise 6. Match nouns and verbs to form collocations. Use each verb and each noun once only.
| To define or constrain | Planetary motion |
| To change | The underlying physical processes |
| To keep | Three laws of motion |
| To formulate | Rest into motion or motion into rest |
| To describe | On a body |
| To define | The planets moving |
| To act | Force in terms of its effect on moving objects |
Exercise 7. There are some words given in bold type in the text. Choose their synonyms from the table below. Pay attention that the forms of the words in the text may differ from those in the table.
| To convert,to transform to replace, to modify, to vary | Fundamentally, mainly | To influence |
| To stay | To rule, to guide, to control | Axiom |
| To characterize, to specify | Try | Objects |
| To reach, to realize | To state, to devise | To accomplish, to understand |
| Idea, notion | Velocity, pace, rate | To get, to gain, to obtain |
| To evolve | To allow, to let |
Read the text and fulfill the tasks given in Comprehension check
NEWTONS 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.
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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.
1. Kepler
a) didnt try to define the physical processes governing the motion.
b) tried to define the physical processes governing the motion.
c) didnt try to define or constrain the physical processes governing the motion.
2. Newtons 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. Newtons 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.
1. What did Newton define before formulating the laws of motion?
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2. What does Newtons first law state?
3. What postulate is known as the law of inertia? What does it mean?
4. What does Newtons second law state?
5. How can the second law be derived?
6. What does Newtons third law state?
7. Why is the third law important in statics?
8. 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 NEWTONS LAWS OF MOTION.
1. This postulate is known as the law of inertia.
2. 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.
3. The empirical laws of Kepler describe planetary motion.
4.. 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.
5. Newton then defined in terms of its effect on moving objects and in the process formulated his three laws of motion.
6. Newton's second law is a quantitative description of the changes that a force can produce in the motion of a body.
7. 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.
8. 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.
9. Newton defined that momentum was proportional to velocity, the constant of proportionality being defined as mass.
10. 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.
1. When Newton (to be) twenty-two years old he (to begin) to study the theory of gravitation.
2. First he (to examine) the general problem of attraction of one mass by another.
3. This attraction (to apply) to every object everywhere, no matter where it (to locate).
4. 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.
5. The Sun (to attract) and (to attract) by the planets.
6. The Earth (to attract) and (to attract) by the Moon.
7. If you (to kick) a football, it (to react) with an equal force against your foot.
8. When you (to press) a stone with your finger, your finger (to press) back by the stone.
9. When the temperature of the body (to change), the magnitudes of almost all its properties also (to change).
10. When a body (to become) warmer we say that it (to receive) the heat.
11. 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.
1. .
2. , .. .
3. , , , .
4. .
5. .
6. - .
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7. , .
8. .
Follow-up activities
Exercise 1. Choose from the text and read sentences in which the author formulates Newtons 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 NEWTONS 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.
Additional texts
Read the texts and translate them in written form.
MOTION
Motion is the change of position of a body relative to another body or with respect to a frame of reference or a coordinate system. All motions take place on definite paths, and the nature of these paths determines the character of the motions. If all points in a body have similar but not necessarily straight paths relative to another body, the first body has motion of translation relative to the second body. If the paths are straight, it is called rectilinear translation. In both cases all points in the body have the same velocity (directed speed) and the same acceleration (time rate of change of velocity).
If all points in a body have different paths on another body, the motion of the first body relative to the second is a combination of translation and rotation. Rotation occurs when any line on a body changes its orientation relative to a line on another body. For example, on a reciprocating engine, one end of the connecting rod is attached by a hinge-type joint (the wrist pin) to the piston and moves with it on a straight path relative to the cylinder block, while the other end of the rod is attached by a hinge-type joint (the crankpin) to the crankshaft and moves with it on a circular path relative to the block.
Bodies connected by hinges can only rotate relative to one another. Consequently, the motion of the connecting rod relative to the piston and relative to the crankshaft is pure rotation. Relative to the block, the motion is a combination of translation and rotation, which is the most general type of plane motion--i.e., motion in parallel planes relative to the block.
All motions are relative, but the term relative motion is usually reserved for motion relative to a moving body--i.e., motion on a moving path. Strictly speaking, Newton's laws of motion are valid only for motions on paths that are fixed to the centre of the solar system. These are known as absolute paths, and, because the Earth rotates and moves around the Sun, motion relative to the Earth is not absolute motion. In most cases, however, the effects of the Earth's motion on calculations involving Newton's laws are small and can be neglected. Motions relative to the Earth or to any body that is fixed to the Earth are assumed to be absolute.
In addition to rotating about moving axes, like the connecting rod, or about a fixed axis, like the crankshaft, a body can also rotate about a fixed point. This is the type of motion that a spinning top executes.
VELOCITY
Velocity is a quantity that designates how fast and in what direction a point is moving. As it has direction as well as magnitude, velocity is known as a vector quantity and cannot be specified completely by a number, as can be done with time or length, which are scalar quantities. Like all vectors, velocity is represented graphically by a directed line segment (arrow) the length of which is proportional to its magnitude.
A point always moves in a direction that is tangent to its path; for a circular path, for example, its direction at any instant is perpendicular to a line from the point to the centre of the circle (a radius). The magnitude of the velocity (i.e., the speed) is the time rate at which the point is moving along its path.
If a point moves a certain distance along its path in a given time interval, its average speed during the interval is equal to the distance moved divided by the time taken. A train that travels 100 km in 2 hours, for example, has an average speed of 50 km per hour.
During the two-hour interval, the speed of the train in the previous example may have varied considerably around the average. The speed of a point at any instant may be approximated by finding the average speed for a short time interval including the instant in question. The differential calculus, which was invented by Isaac Newton for this specific purpose, provides means for determining exact values of the instantaneous velocity.
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MASS
Mass is a quantitative measure of inertia, a fundamental property of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force. Although mass is defined in terms of inertia, it is conventionally expressed as weight. By international agreement the standard unit of mass, with which the masses of all other objects are compared, is a platinum-iridium cylinder of one kilogram.
Weight, though related to mass, nonetheless differs from the latter. Weight essentially constitutes the force exerted on matter by the gravitational attraction of the Earth, and so it varies from place to place. In contrast, mass remains constant regardless of its location under ordinary circumstances. A satellite launched into space, for example, weighs increasingly less the further it travels away from the Earth. Its mass, however, stays the same.
For years it was assumed that the mass of a body always remained invariable. This notion, expressed as the theory of conservation of mass, held that the mass of an object or collection of objects never changes, no matter how the constituent parts rearrange themselves. If a body split into pieces, it was thought that the mass divided with the pieces, so that the sum of the masses of the individual pieces would be equal to the original mass. Or, if particles were joined together, it was thought that the mass of the composite would be equal to the sum of the masses of the constituent particles. But this is not true.
With the advent of the special theory of relativity by Einstein in 1905, the notion of mass underwent a radical revision. Mass lost its absoluteness. The mass of an object was considered equivalent to energy, interconvertible with energy, and it increased significantly at exceedingly high speeds near that of light (about 3 10 metres per second, or 186,000 miles per second). The total energy of an object was understood to comprise its rest mass as well as its increase of mass caused by high speed. It was discovered that the mass of an atomic nucleus was measurably smaller than the sum of the masses of its constituent neutrons and protons. Mass was no longer considered constant, or unchangeable. The new conservation principle is the conservation of mass-energy.
ACCELERATION
Acceleration is a time rate at which a velocity is changing. As velocity has both magnitude and direction, it is called a vector quantity; acceleration is also a vector quantity and must account for changes in both the magnitude and direction of a velocity. The velocity of a point or an object moving on a straight path can change in magnitude only; on a curved path, it may or may not change in magnitude, but it will always change in direction. This condition means that the acceleration of a point moving on a curved path can never be zero.
If the velocity of a point moving on a straight path is increasing (i.e., if the speed, which is the magnitude of the velocity, is increasing), the acceleration vector will have the same direction as the velocity vector. If the velocity is decreasing (that is, the point or object is decelerating), the acceleration vector will point in the opposite direction. The average acceleration during a time interval is equal to the total change in the velocity during the interval divided by the time interval. The acceleration at any instant is equal to the limit of the ratio of the velocity change to the length of the time interval, as the time interval approaches zero.
When a point moves on a curved path, the component of the acceleration that results from the change in the direction of the velocity vector is perpendicular to the velocity vector and is directed inward, to the concave side of the path; its magnitude is given by the square of the velocity divided by the radius of curvature r of the path: v /r. The change in the magnitude of v may be represented by another vector (that is, a second component of the acceleration) collinear with v and in the same direction if v is increasing and the opposite direction if v is decreasing. If velocity is stated in metres per second, acceleration will be stated in metres per second per second.
MOMENTUM
Momentum is a product of the mass of a particle and its velocity. Isaac Newton's second law of motion states that the time rate of change of momentum is proportional to the force acting on the particle. Albert Einstein showed that the mass of a particle increases as its velocity approaches the speed of light. At the speeds treated in classical mechanics, the effect of speed on the mass can be neglected, and changes in momentum are the result of changes in velocity only.
From Newton's second law it follows that, if a constant force acts on a particle for a given time, the product of force and the time interval (the impulse) is equal to the change in the momentum. Conversely, the momentum of a particle is a measure of the time required for a constant force to bring it to rest.
The momentum of a rigid body is the sum of the momenta of each particle in the body. Being proportional to velocity, momentum has direction; consequently, when a body in plane motion rotates, the momentum of each particle has a moment about any point in the plane. The sum of these moments of momenta is called the angular momentum of the body about the point and is equal to the product of the moment of inertia of the body about the point and the angular velocity of the body. The time rate of change of the angular momentum of a body about a point is equal to the moment of the applied forces about the point. Applied to elementary particles such as electrons, angular momentum is called spin.
