Figure 4.1: Force is a vector conceptHooke’s Law Figure 4.2: A sketch of a spring attached to a wall and an object.Figure 4.3: Plot of force vs. compression and extension of springGravitational Force near the Surface of the EarthNewton’s Third Law: Action-Reaction PairsFigure 4.4: Action-reaction pair of forcesFigure 4.5: Spring Scale Figure 4.6a Gravitational Force between two bodies. Figure 4.6b Coordinate system for the two-body problem. 4.4 Static Equilibrium 4.5 Contact Forces Figure 4.8: Normal and tangential components of the contact forceFigure 4.9: Total force on hand moving towards the left Figure 4.10: Object resting in handFigure 4.11: Force diagram on objectFigure 4.12: Force diagram on hand Figure 4.13: Gravitational forces on earth due to object and handFigure 4.15: Forces acting on block and ropeFigure 4.16: Force diagrams on block and ropeFigure 4.18: Force diagram for the left and right sections of ropeChapter 4: The Concept of Force Where was the chap I saw in the picture somewhere? Ah yes, in the dead sea floating on his back, reading a book with a parasol open. Couldn’t sink if you tried: so thick with salt. Because the weight of the water, no, the weight of the body in the water is equal to the weight of the what? Or is it the volume equal to the weight? It’s a law something like that. Vance in High school cracking his fingerjoints, teaching. The college curriculum. Cracking curriculum. What is weight really when you say weight? Thirtytwo feet per second per second. Law of falling bodies: per second per second. They all fall to the ground. The earth. It’s the force of gravity of the earth is the weight. James Joyce, Ullysses1 Introduction: In our daily experience, we can cause a body to move by either pushing or pulling that body. Ordinary language use describes this action as the effect of a person’s strength or force. However, bodies placed on inclined planes, or when released at rest and undergo free fall, will move without any push or pull. Galileo still referred to a force acting on these bodies, a description of which he published in 1623 in his Mechanics. In 1687, Isaac Newton published his three laws of motion in the Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), which extended Galileo’s observations. The First Law expresses the idea that when a no force acts on a body, it will remain at rest or maintain uniform motion; when a force is applied to a body, it will change its state of motion. Law 1: Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. Projectiles continue in their motions, so far as they are not retarded by the resistance of air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by air. The greater bodies of planets and comets, meeting with less resistance in freer spaces, preserve their motions both progressive and circular for a much longer time. The idea that force produces motion was recognized before Newton by many scientists, especially Galileo, but Newton extended the concept of force to any circumstance that produces acceleration. When the body is initially at rest, the direction of our push or pull corresponds to the direction of motion of the body. If the body is moving, the direction of the applied force may change both the direction of motion of the 1 James Joyce, Ulysses, The Corrected Text edited by Hans Walter Gabler with Wolfhard Steppe and Claus Melchior, Random House, New York. 8/14/2008 1body and how fast it is moving. This enables us to precisely define force in terms of acceleration. We shall define force first in terms of its effect on the standard body we introduced in Section 1.4, which by definition has a mass s1kgm=. We apply an action to the standard body that will induce the body to accelerate with a magnitude aG that can be measured by an accelerometer (any device that measures acceleration). Definition: Force Force is a vector quantity. The magnitude of the total force FG acting on the object is the product of the mass with the magnitude of the acceleration smaG. The direction of the total force on the standard body is defined to be the direction of the acceleration of the body. Thus sm≡FaGG (4.1.1) The SI units for force are 2[kg m s ]−⋅⋅ . This unit has been named the newton [N] and . 21N 1kg m s−=⋅⋅ In order to justify the statement that force is a vector quantity, we need to apply two forces and simultaneously to our standard body and show that the resultant force is the vector sum of the two forces when they are applied one at a time. 1FG2FGTFG Figure 4.1: Force is a vector concept When we apply the two forces simultaneously, we measure the acceleration , and define TaG sTm≡FTaGG. (4.1.2) We then apply each force separately and measure the accelerations 1aG and , noting that 2.aG 8/14/2008 21sm=F1aGG (4.1.3) 2sm=F2aGG. (4.1.4) We then compare the accelerations. The results of these three measurements, and for that matter any similar experiment, confirms that the accelerations add as vectors 1T2=+aaaGGG. (4.1.5) Therefore the forces add as vectors as well, 1T2=+FFFGGG. (4.1.6) This last statement is not a definition but a consequence of the experimental result described by Equation (4.1.5) and our definition of force. 4.2 Mass Our definition of force is based on proportionality between force and acceleration, ∝FaGG. (4.2.1) In order to define the magnitude of the force, we introduced a constant of proportionality, the inertial mass, which Newton called a “quantity of matter” and he was the first to clearly understand that inertial mass was a property of a body different from “weight” (see section 4.5). So far, we have only used the standard body to measure force. Instead of performing experiments on the standard body, we can calibrate the masses of all other bodies in terms of the standard mass by the following experimental procedure. We apply a force to the standard body and measure the acceleration . Then we apply the same force to a second body of unknown mass . We measure the acceleration of the unknown . Since the same force is applied to both bodies, saumua uu ssFma
View Full Document
Unlocking...