Physics
Force and Pressure
Force is a push or pull acting on an object, causing it to accelerate or deform. Pressure is the force applied per unit area. Force is measured in newtons (N), while pressure is measured in pascals (Pa). The relationship between force and pressure is that pressure is the result of a force distributed over an area.
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10 Key excerpts on "Force and Pressure"
eBook - PDFPhysics of Continuous Matter
Exotic and Everyday Phenomena in the Macroscopic World
- B. Lautrup(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
The component acting tangentially to the surface is called a shear force or a traction force . Fluids in motion, and solids at rest or in motion, are able to sustain shear forces, whereas fluids at rest cannot. Should shear forces arise in a fluid at rest, it will begin to flow until it again reaches mechanical equilibrium without shear forces. In this chapter we shall first investigate the basic properties of pressure, and afterward develop the mathematical formalism that permits us to analyze hydrostatic equilibrium in the sea and the atmosphere. Along the way we shall recapitulate some basic rules of thermody-namics. In the following chapters we shall continue to study the implications of hydrostatic equilibrium for balloons and ships, and the shapes of large fluid bodies subject only to gravity and small fluid bodies subject mainly to surface tension. 2.1 What is pressure? Pressure is defined as normal force per unit of area . The SI–unit for pressure is accordingly newton per square meter, but was in 1971 given the name pascal and the special symbol Pa D N m 2 . Earlier units for pressure were the bar ( 1 bar D 10 5 Pa) and the standard atmosphere ( 1 atm D 101; 325 Pa), which is close to the average air pressure at sea level. Modern television weather forecasters are now abandoning the older units and tend to quote air pressure in hectopascals rather than in millibars, even if they are exactly the same ( 1 hPa D 100 Pa D 10 3 bar D 1 millibar). 22 PHYSICS OF CONTINUOUS MATTER Case: The incompressible sea A p 0 p h 6 pA ? p 0 A r ? Mg 0 A column of sea water. The pres-sure difference between bottom and top must carry the weight of the water in the box. Notice that the sum of the forces vanishes. Before presenting a formal definition of the pressure field, we use simple arguments to cal-culate it in the sea. In the first approximation, water is incompressible and has everywhere the same mass density 0 .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Forces which do not act uniformly on all parts of a body will also cause mechanical stresses, a technical term for influences which cause deformation of matter. While mechanical stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid determines changes in its pressure and volume. Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Sir Isaac Newton; with his mathematical insight, he formulated laws of motion that remained unchanged for nearly three hundred years. By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia. With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational. High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.
eBook - PDF- John Ward-Smith(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Now although the force has direction, the pressure does not. The direction of the force also specifies the direction of the imaginary plane surface, since the latter is defined by the direction of a line perpendicular to, or normal to, the surface. Here, then, the force and the surface have the same direction and so in the equation ---→ Force = Pressure × Area -----→ of plane surface pressure must be a scalar quantity. Pressure is a property of the fluid at the point in question. Similarly, temperature and density are properties of the fluid and it is just as illogical to speak of ‘downward pressure’, for example, as of ‘downward temperature’ or ‘downward density’. To say that pressure 14 Fundamental concepts acts in any direction, or even in all directions, is meaningless; pressure is a scalar quantity. The SI unit of pressure is N · m -2 , now termed pascal , with the abbrevi-ation Pa. Pressures of large magnitude are often expressed in atmospheres (abbreviated to atm). For precise definition, one atmosphere is taken as 1.01325 × 10 5 Pa. A pressure of 10 5 Pa is called 1 bar . The thousandth part of this unit, called a millibar (abbreviated to mbar), is commonly used by meteorologists. It should be noted that, although they are widely used, neither the atmosphere nor the bar are accepted for use with SI units. For pressures less than that of the atmosphere the units normally used are millimetres of mercury vacuum. These units refer to the difference between the height of a vertical column of mercury supported by the pressure considered, and the height of one supported by the atmosphere. In the absence of shear forces, the direction of the plane over which the force due to the pressure acts has no effect on the magnitude of the pressure at a point. The fluid may even be accelerating in a particular direction, provided that shear forces are absent – a condition that requires no relative motion between different particles of fluid.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
4.1 | The Concepts of Force and Mass In common usage, a force is a push or a pull, as the examples in Figure 4.1 illustrate. In football, an offensive lineman pushes against his opponent. The tow bar attached to a speed- ing boat pulls a water skier. Forces such as those that push against the football player or pull the skier are called contact forces, because they arise from the physical contact between two objects. There are circumstances, however, in which two objects exert forces on one another even though they are not touching. Such forces are referred to as noncontact forces or action-at-a-distance forces. One example of such a noncontact force occurs when a diver is pulled toward the earth because of the force of gravity. The earth exerts this force even when it is not in direct contact with the diver. In Figure 4.1, arrows are used to rep- resent the forces. It is appropriate to use arrows, because a force is a vector quantity and has both a magnitude and a direction. The direction of the arrow gives the direction of the force, and the length is proportional to its strength or magnitude. The word mass is just as familiar as the word force. A massive supertanker, for instance, is one that contains an enormous amount of mass. As we will see in the next section, it is difficult to set such a massive object into motion and difficult to bring it to a halt once it is moving. In comparison, a penny does not contain much mass. The emphasis here is on the amount of mass, and the idea of direction is of no concern. Therefore, mass is a scalar quantity. During the seventeenth century, Isaac Newton, building on the work of Galileo, developed three important laws that deal with force and mass. Collectively they are called “Newton’s laws of motion” and provide the basis for understanding the effect that forces have on an object. Because of the importance of these laws, a separate section will be devoted to each one.
- Ravi Doddannavar, Andries Barnard, Jayaraman Ganesh(Authors)
- 2005(Publication Date)
- Newnes(Publisher)
2 Pressure and flow 2.1 Objectives On reading this chapter, the student will be able to: • Explain and understand the various terms and definitions used in hydraulics • Understand the significance of Pascal’s law and its applications • Understand the importance of flow and pressure in hydraulics. 2.2 Pressure Pressure along with flow is one of the key parameters involved in the study of hydraulics. Pressure in a hydraulic system comes from resistance to flow. This can be best understood from Figure 2.1. Figure 2.1 Pressure buildup in a hydraulic system Consider the flow from a hydraulic pump as shown. Here the pump produces only flow and not pressure. However any restriction in the flow from the pump results in the formation of pressure. This restriction or resistance to flow normally results from the load induced in the actuator. The various conductors and components of the hydraulic system Pressure and flow 17 such as pipes and elbows also act as points of resistance and contribute to the generation of pressure in the system. Pressure ( P ) is defined as the force ( F ) acting normally per unit area ( A ) of the surface and is given by the equation: F P A = Pressure in the SI unit is measured in terms of N/m 2 also known as a Pascal. Pressure can also be expressed in terms of bar, where 5 2 1 bar = 10 N/m Pressure in the US unit is measured in terms of lb/in. 2 or psi, where 2 1 psi = 0.0703 kg/cm 2.2.1 Pressure in fluids Fluids are composed of molecules, which are in continuous random motion. These molecules move throughout the volume of the fluid colliding with each other and with the walls of the container as a result of which the molecules undergo a change in momentum. Now, let us consider a surface within the fluid which is impacted by a large number of molecules. This results in a transfer in momentum from the molecules to the surface.
eBook - PDF- Fatih Gozuacik, Denise Pattison, Catherine Tabor(Authors)
- 2020(Publication Date)
- Openstax(Publisher)
surface with which the object is in contact system one or more objects of interest for which only the forces acting on them from the outside are considered, but not the forces acting between them or inside them tension a pulling force that acts along a connecting medium, especially a stretched flexible connector, such as a rope or cable; when a rope supports the weight of an object, the force exerted on the object by the rope is called tension thrust a force that pushes an object forward in response to the backward ejection of mass by the object; rockets and airplanes are pushed forward by a thrust reaction force in response to ejecting gases backward weight the force of gravity, W, acting on an object of mass m; defined mathematically as W = mg, where g is the magnitude and direction of the acceleration due to gravity SECTION SUMMARY 4.1 Force • Dynamics is the study of how forces affect the motion of objects and systems. • Force is a push or pull that can be defined in terms of various standards. It is a vector and so has both magnitude and direction. • External forces are any forces outside of a body that act on the body. A free-body diagram is a drawing of all external forces acting on a body. 4.2 Newton's First Law of Motion: Inertia • Newton’s first law states that a body at rest remains at rest or, if moving, remains in motion in a straight line at a constant speed, unless acted on by a net external force. This law is also known as the law of inertia. • Inertia is the tendency of an object at rest to remain at rest or, if moving, to remain in motion at constant velocity. Inertia is related to an object’s mass. • Friction is a force that opposes motion and causes an object or system to slow down. • Mass is the quantity of matter in a substance. 4.3 Newton's Second Law of Motion • Acceleration is a change in velocity, meaning a change in speed, direction, or both.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our container down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface. ________________________ WORLD TECHNOLOGIES ________________________ A closely related quantity is the stress tensor σ , which relates the vector force F to the vector area A via This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term pressure will refer only to the scalar pressure. Types Explosion or deflagration pressures Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces. Negative pressures While pressures are generally positive, there are several situations in which negative pressures may be encountered: • When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of -21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). • When attractive forces (e.g., van der Waals forces) between the particles of a fluid exceed repulsive forces. Such scenarios are generally unstable since the particles will move closer together until repulsive forces balance attractive forces.
eBook - PDF- Philip Dyke, Roger Whitworth(Authors)
- 2017(Publication Date)
- Red Globe Press(Publisher)
CHAPTER 2 Forces 2.1 Force as a vector We now introduce the concept of force. When forces are studied alone, the study is called statics . When they are studies in conjunction with kinematics, then the area of study is called dynamics . If a body changes its velocity, we conclude that a force acts upon it. Consider the motion of parachutists falling from an airplane: 1 At first, they fall vertically downwards as a result of the force acting on them in that direction (Figure 2.1(a)). Their speed increases as they move downwards. The vertical force involved is principally the weight , which is the force of the Earth's attraction acting on the parachutist. In addition, there are resistance forces . Resistance forces will always oppose motion when they occur. 2 After the parachute opens (Figure 2.1(b)), the parachutist's speed will eventually reach a stage when it stops increasing. In this case, the velocity is no longer changing and all the forces acting on the body must cancel out. In fact, the magnitude of the resistance force is then equal to the magnitude of the weight (see Chapter 5). In the case of a body in a state of equilibrium , that is, at rest, the total force acting on the body must also be zero. Consider the following cases of a body P in equilibrium: Resistance Resistance Weight Weight (b) (a) Figure 2.1 Parachutists 27 Tension Weight (a) Reaction Reaction Weight Weight (c) Thrust Weight (b) (d) (e) Normal reaction Friction Push Normal reaction Friction Weight Weight (f) Figure 2.2 Bodies in equilibrium 1 When the body is suspended by a string to hang freely (Figure 2.2(a)), the weight is supported by an upward force in the string, the tension . 2 When the body is supported on a spring from below (Figure 2.2(b)), the weight is supported by an upward force in the spring, the thrust . 3 When the body is resting on a horizontal surface, the weight is supported by an upward force supplied by the surface, the reaction or normal reaction (Figure 2.2(c)).
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
that pushes a body forward in response to a backward force; rockets, airplanes, and cars are pushed forward by a thrust reaction force the force w due to gravity acting on an object of mass m ; defined mathematically as: w = mg , where g is the magnitude and direction of the acceleration due to gravity Section Summary 4.1 Development of Force Concept • Dynamics is the study of how forces affect the motion of objects. • Force is a push or pull that can be defined in terms of various standards, and it is a vector having both magnitude and direction. • External forces are any outside forces that act on a body. A free-body diagram is a drawing of all external forces acting on a body. 4.2 Newton’s First Law of Motion: Inertia • Newton’s first law of motion states that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This is also known as the law of inertia. • Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object’s mass. • Mass is the quantity of matter in a substance. 4.3 Newton’s Second Law of Motion: Concept of a System • Acceleration, a , is defined as a change in velocity, meaning a change in its magnitude or direction, or both. • An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system. • Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. • In equation form, Newton’s second law of motion is a = F net m . • This is often written in the more familiar form: F net = ma . • The weight w of an object is defined as the force of gravity acting on an object of mass m .
- Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
40 2 In this chapter we will consider an important class of problems in which the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. In both instances there will be no shearing stresses in the fluid, and the only forces that develop on the surfaces of the particles will be due to the pressure. Thus, our principal concerns are to investigate pressure and its variation throughout a fluid and the force on submerged surfaces due to that pres-sure variation. The absence of shearing stresses greatly simplifies the analysis and, as we will see, allows us to obtain relatively simple solutions to many important practical problems. 2.1 Pressure at a Point As we briefly discussed in Chapter 1, the term pressure is used to indicate the normal force per unit area at a given point acting on a given plane within the fluid mass of interest. A question that imme-diately arises is how the pressure at a point varies with the orientation of the plane passing through the point. To answer this question, consider the free-body diagram, illustrated in Fig. 2.1, that rep-resents a small triangular wedge of fluid from some arbitrary location within a fluid mass. Since we are considering the situation in which there are no shearing stresses, the only external forces acting on the wedge are due to the pressure and gravity. For simplicity the forces in the x direction are not shown, and the z axis is taken as the vertical axis so the weight acts in the negative z direc-tion. Although we are primarily interested in fluids at rest, to make the analysis as general as pos-sible, we will allow the fluid element to have accelerated motion. The assumption of zero shearing stresses will still be valid as long as the fluid mass moves as a rigid body; that is, there is no relative motion between adjacent elements. After completing this chapter, you should be able to: ■ determine the pressure at various locations in a fluid at rest.
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