Newton's Third Law

9 Key excerpts on "Newton's Third Law"

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  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  6 Many‐body interactions

  AIMS

  • to introduce Newton's Third Law of motion, the law which governs the interaction between two bodies
  • to derive the general principles of conservation of momentum, energy and angular momentum as applied to many‐body systems
  • to develop techniques for analysing particle decays and collisions between particles
  • to show how an appropriate choice of origin of a coordinate system makes some problems more amenable to easy solution, particularly when the CM coordinate system is used
  • to introduce the principle of conservation of angular momentum of a system of particles

  6.1 Newton's Third Law

  Newton's second law provides us with a method of determining the state of motion of a single body, provided we know the magnitudes and directions of all forces acting on that body. The full analysis of dynamical systems which comprise two or more interacting bodies (such as two masses connected by a taut string, gravitationally bound bodies such as the solar system, electrically bound systems such as atoms or molecules, etc.) cannot be treated using Newton's second law alone. To deal with such systems requires knowledge of an additional law of nature which Newton called the third law of motion.

  Consider the two bodies in Figure 6.1 which interact, that is a force is exerted on A by B (FB→A ) and a force is exerted on B due to A (FA→B ). Newton's Third Law states that the forces on each of these body due to the other are always equal in magnitude and opposite in direction, that is

  Figure 6.1

  Newton's Third Law: the force exerted on B by A (FB→A ) is equal and opposite to the force exerted on A by B (FA→B ). The interaction in (a) is attractive while in (b) it is repulsive.

  We now consider the applications of this law to a number of familiar situations.

  Case 1:

  A body resting on horizontal table

  As a simple example of the use of this law, recall (Section 4.5 ) the case of the book resting on a horizontal table (Figure 6.2 ). We showed in that section that the force exerted on the book by the table (the normal reaction, upwards — a constraint force

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  Concepts of Force

  • Max Jammer(Author)
  • 2012(Publication Date)
  • Dover Publications

    (Publisher)

  ultima ratio in his reasoning was, of course, the law of inertia. To make it quite clear, we do not suppose that Newton inferred his second law from the laws of impact; such an inference would have met with insuperable conceptual and mathematical difficulties. Ultimately, it was a stroke of genius, a “free creation of the human mind.”

  The first two laws of motion add little information on Newton’s concept of force that is not contained in the preceding definition. The third law, however, supplies an additional important characteristic of force not mentioned previously: force manifests itself invariably in a dual aspect; it is action and reaction simultaneously. Much as a business transaction can be regarded both as a purchase and as a sale of the same amount, force can be considered as action as well as reaction of the same magnitude. As far as attraction is concerned, Newton believes himself capable of demonstrating the validity of the third law as follows: Suppose the two bodies A and B attract each other; imagine, now, that A , for example, attracts B with greater intensity than B attracts A ; suppose also that an obstacle is interposed to prevent the meeting of these two bodies; our assumption would then lead to the conclusion that the whole system (A -obstacle-B ) would move in the direction from B to A , for the obstacle, as Newton puts it, “will be more strongly urged by the pressure”309 of the body B than by the pressure of the body A and consequently will not remain in equilibrium, but accelerate in infinitum.

  It is generally contended that Newton’s statement of the third law is “his most important achievement with respect to the principles”310 of mechanics. Without diminishing Newton’s outstanding merits in the foundation of classical mechanics in the least, it should be recalled that Kepler had already a clear conception of the reciprocity of force,311

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  eBook - ePub

  Newtonian Dynamics

  An Introduction

  • Richard Fitzpatrick(Author)
  • 2021(Publication Date)
  • CRC Press

    (Publisher)

  A corollary of the previous result is that we can use the calibrated spring system pictured in Figure 4.1 to measure the net force acting on a given body, irrespective of the nature of the force. We just need to apply an additional force to the body, by means of the spring, that is such as to reduce the body’s acceleration to zero. The net force acting on the body is then minus the force exerted by the spring. In this manner, it is possible to prove experimentally that all forces are vector quantities [i.e., their three Cartesian components transform under rotation of the coordinate axis according to Equations (3.20)–(3.22), and their generalizations].

  4.5 Newton’s Third Law of Motion

  Suppose, for the sake of argument, that there are only two bodies in the universe. Let us label these bodies a and b. Suppose that body b exerts a force,

  f

  a b

  , on body a. According to to Newton’s third law of motion, body a must exert an equal and opposite force,

  f

  b a

  = −

  f

  a b

  , on body b. See Figure 4.3 . This is true irrespective of the nature of the force acting between the two bodies. Thus, if we label

  f

  a b

  the “action” then, in Newton’s language,

  f

  b a

  is the equal and opposed “reaction”.

  Figure 4.3

  Newton’s third law

  Suppose, now, that there are many objects in the universe (as is, indeed, the case). According to Newton’s third law, if object j exerts a force,

  f

  i j

  , on object i then object i must exert an equal and opposite force,

  f

  j i

  = −

  f

  i j

  , on object j. It follows that all of the forces acting in the universe can ultimately be grouped into equal and opposite action-reaction pairs. Note, incidentally, that an action and its associated reaction always act on different bodies.

  Why do we need Newton’s third law? Actually, it is almost a matter of common sense. Suppose that bodies a and b constitute an isolated system. If

  f

  b a

  ≠ −

  f

  a b

  then this system exerts a non-zero net force,

  f =

  f

  a b

  +

  f

  b a

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  AP Physics C Premium, 2024: 4 Practice Tests + Comprehensive Review + Online Practice

  • Robert A. Pelcovits, Joshua Farkas(Authors)
  • 2023(Publication Date)
  • Barrons Educational Services

    (Publisher)

  3

  Newton’s Laws

  Learning Objectives

  In this chapter, you will learn:

  Newton’s three laws of motion

  Mass vs weight

  Application of Newton’s laws

  Newton’s first law:

  Stated in words: When the net force acting on a body is zero, its acceleration must be zero, meaning that the velocity remains constant. This corresponds to two physical situations: (1) the object can either remain at rest (v = 0) or (2) continue along a straight-line path at constant velocity (v ≠ 0).

  Superposition of Forces What do we mean by net force? What happens if we exert several forces on a body at the same time? We find experimentally that the body behaves as if a single force is acting on it equal to the vector sum of all the individual forces (we call this vector sum the net force, Fnet ).

  The superposition of forces also works the other way, letting us treat each force as the sum of its components:

  When problem solving, we often combine these two approaches to add various forces together component-wise, obtaining a set of one-dimensional equations such as the following (which can then be related to the one-dimensional equations for uniformly accelerated motion).

  Concept of Inertia Inertia refers to how much an object resists a change in its velocity and is measured by mass. For example, it is easy to drastically change the velocity of an object with little mass or inertia (e.g., flicking a paper clip), but it is harder to change the velocity of an object with lots of mass or inertia (e.g., throwing a bowling ball).

  Corollary to Newton’s first law:

  What this equation means is that if an object is at rest (static equilibrium) or in motion with a constant velocity (dynamic equilibrium), it must have zero acceleration and zero net force. This equation is the basis of solving all static equilibrium problems involving particles.

  Newton’s Laws Are Valid Only in Inertial Reference Frames

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  eBook - ePub

  Doing Physics with Scientific Notebook

  A Problem Solving Approach

  • Joseph Gallant(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  on the first object by the second.

  There are two important points here.

  1. Forces come in pairs that have equal magnitudes and opposite directions.

  2. The two forces act on different objects.

  There are no isolated forces. Forces come in pairs which together comprise the interaction between two objects. In every interaction, forces act on each interacting object. For every force exerted by an object there is a force of equal magnitude but opposite direction which acts back on that object. An object can experience a non-zero net force and acceleration only if it interacts with some other object.

  Example 5.15

  Cosmic litter bug

  While working in outer space, a 75 kg astronaut discards a 1 kg Illudium Q-36 explosive space modulator by literally throwing it away. During the throw, the astronaut exerts a constant force of 15 N for 0.5s on the modulator. What happens to the astronaut? How far apart are the astronaut and modulator 5 minutes after the throw? What planet is the astronaut from?

  Solution.

  By Newton’s 3rd Law, the net force on the astronaut is also 15 N but in the direction opposite the throw. The astronaut pushed the modulator, but the modulator pushed back and in frictionless space the astronaut moves too. The astronaut and modulator feel the same amount of force, but their accelerations have different magnitudes and opposite directions.

  Let’s use Newton’s 2nd Law and Evaluate Numerically to find the acceleration of the astronaut and modulator.

  At the end of the half-second constant acceleration, they are both moving. After the throw, there are no forces acting on either the astronaut or the modulator, so they move at a constant speed. Five minutes later, the astronaut’s displacement is only 30 m.

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  eBook - ePub

  Classical Mechanics

  • Hiqmet Kamberaj(Author)
  • 2021(Publication Date)
  • De Gruyter

    (Publisher)

  0 . If we assume that only these two forces act at the body with mass zero, then their sum is zero, and hence, they have the same magnitude and oppositely directed. This experiment is what is known as Newton’s third law.

  Newton’s third law

  If two objects interact, the force

  F 12

  exerted by object 1 on object 2 is equal in magnitude to and opposite in direction to the force

  F 21

  exerted by object 2 on object 1:

  (5.14)

  F 12

  = −

  F 21

  .

  This law, which is illustrated in Fig. 5.4 , states that a force that affects the motion of an object must come from a second, external object. An equal magnitude but oppositely directed force exerted on the second object, too.

  Therefore, the forces cannot exist isolated in nature. The force acting from object 1 on object 2 is called the action force, and the force acting from object 2 on object 1 is called the reaction force. Note that either force can be called the action or the reaction force, and always the action force equals in magnitude the reaction force, and they have the opposite direction. Thus, the action and reaction forces always act on different objects.

  Figure 5.4 Illustration of Newton’s third law.

  5.6  Mass and weight

  In fact, the terms mass and weight are often interchanged with one another. But, in physics, their meanings are quite distinct.

  The mass measures the inertia of an object. As such, the mass is the resistance of an object to deviate from uniform straight-line motion under the influence of external forces. According to Newton’s second law, see eq. (5.7

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  Reasoning About Luck

  • Vinay Ambegaokar(Author)
  • 2017(Publication Date)
  • Dover Publications

    (Publisher)

  Newton’s first law states that motion at constant speed in a straight line, or as a special case no motion at all, occurs when there are either no external influences, which he called forces, or a perfect balance between them. Thus, when an ice hockey puck skids along the ice, it does so at constant velocity (which means directed speed and will be defined more precisely soon) except to the extent that the small frictional effect of the surface slightly slows it down, and that collisions with other objects turn it right or left. When you or I sit in a chair we are at ‘rest,’ to use Newton’s word for the condition of no motion, because there is a balance of forces – our weight vs. the support of the chair.

  † In metric units volume is often measured in liters. One liter is one thousandth of a cubic meter. Since a centimeter is one hundredth part of a meter, a liter is the volume of a cube 10 centimeters on a side.

  Newton’s second law addresses the question of what happens when there is an imbalance of forces. For an object consisting of a fixed quantity of matter it states that ‘acceleration,’ or rate of change of velocity, is proportional to impressed force, the coefficient of proportionality being the mass. This sounds like a circular chain of definitions until one thinks about it. Imagine a device that produces a force of a certain amount, say a spring stretched a certain distance. This force applied to a given mass is found to produce a constant acceleration of a certain amount. The same force applied to twice the quantity of matter is found to produce half the acceleration. This is, thus, not definition but a summary of how nature works. To quantify the notion of force one must measure the other quantities in the units introduced above. Imagine one kilogram of matter being accelerated at one mks unit, a notion that will be made precise below. The force needed to do this is one unit of force. It is called, appropriately enough, one newton.

  Newton’s third law says that forces come in equal and opposite pairs: for every action there is an equal and opposite reaction, as he put it. It is instructive to think of examples of such action-reaction pairs. If I push against a wall, the wall exerts an equal and opposite force on me. What about a person sitting in a chair? Are the person’s weight and the force from the chair on the person action and reaction? The answer is no . It is only when the person is at rest that this pair of forces are equal and opposite. If the chair is in an amusement park roller-coaster† where the occupant is being accelerated then there will be a net force on the person coming from the imbalance between weight and the force from the chair. A correct action-reaction pair is the force exerted by the person on the seat and the always equal and opposite force exerted by the seat on the person. To clarify this point consider a person sitting on a chair in a stationary room. What happens if the chair is suddenly pulled away? At first sight it seems that there is now only a single force, weight, which acts on the unfortunate person and causes him or her to be accelerated towards the ground. What the ‘reaction’ is to an object’s weight will emerge in the section on Newton’s Law of Gravitation. Weight is in fact the gravitational force of attraction between the object and the earth. It is exactly balanced by a reaction force attracting the earth toward the object. Why does the earth then not accelerate towards a falling object? In fact, it does

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  Physics for Students of Science and Engineering

  • A. L. Stanford, J. M. Tanner(Authors)
  • 2014(Publication Date)
  • Academic Press

    (Publisher)

  Equation (3-5) points out that the pair of forces are oppositely directed. The subscripts emphasize that the forces under consideration are on different bodies.

  Two important physical ideas are embodied in the third law. First, you cannot exert a force on an object unless the object exerts a force of equal magnitude on you. This fact provides the physical reasoning for a boxer to “roll with a punch.” A boxing glove cannot exert more force on your chin than you permit your chin to exert on the glove. Second, it is important to remember that two third-law forces, which are equal in magnitude and oppositely directed, never act on the same body.

  E 3.4  

  For each of the following forces, Newton’s third law requires the existence of a second force. Describe that second force: (a) an upward force of 160 lb on a person’s feet by the floor, (b) an upward buoyant force of 600 N by the water on a person floating on the water’s surface, (c) the force of attraction on the moon by the earth, and (d) a downward gravitational force of 170 lb on a person by the earth.

  Answers: (a) 160 tb force downward on the floor by that person’s feet; (b) 600 N force downward on the water by the person; (c) an oppositely directed attractive force on the earth by the moon; (d) 170 lb upward force on the earth by the person

  3.4 Weight and Mass

  We saw in Chapter 2 that a body that is released in space near the surface of the earth accelerates downward with magnitude g . Newton’s second law, ∑F = m a , then requires that there must be a net downward force on the body. The second law further prescribes that the downward force has magnitude mg . This force is the gravitational pull of the earth on the body. The force of the gravitational attraction of the earth on a body is called the weight W of the body. Under these conditions |∑F | = m a becomes, for this body,

  W = m g

  or

  m =

  W g

  (3-6)

  (3-6)

  which relates the mass and weight of the body at or near the surface of the earth. Notice that weight is a force. Therefore, in the English system the unit of weight is the pound (lb); in the metric system the unit of weight is the newton (N).

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  The Handy Physics Answer Book

  • Charles Liu(Author)
  • 2020(Publication Date)
  • Visible Ink Press

    (Publisher)

  In 1595, some years after Kepler discovered the first two laws of orbital motion, he deduced the Third Law based on philosophical and mathematical arguments. It synthesizes two important properties of objects orbiting around a central massive object.

  Kepler’s Third Law is: The square of the orbital period of a planet is proportional to the cube of the radius of the orbit. The proportionality constant in this relation depends on the mass of the object about which the orbit occurs and the gravitational constant of the universe.

  How does Kepler’s Third Law relate to the motion of satellites around Earth?

  Kepler’s Third Law relates the period of a satellite to its distance to the center of Earth. The table below shows the mean radius of the orbit, the altitude above Earth’s surface, and the period for some typical satellites.

  Most weather satellites have polar orbits, so the view of their cameras will sweep across the entire surface of Earth many times each day. The moon’s orbit is aligned with Earth’s orbit around the sun, not Earth’s equator.

  Kepler’s Third Law is useful for satellites about other planets and for planets revolving around the sun. For very detailed calculations and descriptions of orbits, Newton’s Laws of Motion and Einstein’s General Theory of Relativity are useful as well.

  STATICS

  What is statics?

  Statics is a branch of physics that describes the behavior and properties of objects that have volume, shape, and structure.

  What does it mean to say an object is static?

  The word “static” means “not moving.” In the fields of engineering and physics, an object that is static is one that does not move. When static, all the forces acting on a body must sum to zero. That is, the net force on the body is zero, so the object does not move.

  What is the name of the supporting force exerted by a chair?

  Another term for a supporting force is “normal force.” The normal force is always directed perpendicularly out of the surface. The normal force of a chair is straight up if the chair is on a level surface, while the normal force of an incline is perpendicular to the surface of the incline and not perfectly vertical. The term “normal” was derived from the geometrical name for a 90 degrees angle and is not the opposite of “abnormal.”

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