Physics
Air Resistance
Air resistance is the force that opposes the motion of an object through the air. It is caused by the friction between the air molecules and the surface of the object. The amount of air resistance depends on the speed, size, and shape of the object.
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6 Key excerpts on "Air Resistance"
eBook - PDF- Ruth W. Chabay, Bruce A. Sherwood(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
In fact, measurements of a variety of ordinary-sized objects moving through air or other fluids show that Air Resistance is proportional to the density ρ of the air. 7.10 Energy Dissipation 309 For example, there is less Air Resistance at higher altitudes, where the air is less dense. Balls travel farther in Denver, Colorado, a mile above sea level, than they do in New York City. An Empirical Equation for Air Resistance An equation describing the Air Resistance force on a moving object must incorporate all the effects we have listed above: dependence on speed v, cross-sectional area A, shape of the object, and density of the air ρ. The shape effect is captured by a parameter denoted by the symbol C that reflects the sharpness or bluntness of the object. The parameter C is called the “drag coefficient,” and is typically determined empirically. Typically 0.3 ≤ C ≤ 1.0; blunter objects have higher values of C. The direction of the force is (-ˆ v), opposite to the velocity. APPROXIMATE Air Resistance FORCE (EMPIRICAL) F air ≈ - 1 2 CρAv 2 ˆ v for blunt objects at ordinary speeds. A is the cross-sectional area of the object; ρ is the density of the air; C reflects the bluntness of the object. How important is the effect of Air Resistance in the everyday world? In Chapter 2 we analyzed the motion of a ball thrown through the air. However, we neglected Air Resistance, which can have a sizable effect. In Problem P47 you are asked to include the Air Resistance force given above. You should find that a baseball thrown at high speed by a professional baseball pitcher goes only about half as far in air as it would go in a vacuum. However, even when we include Air Resistance in our predictions of the motion of a baseball, we still have ignored a force that can have a major effect on the trajectory.
eBook - ePub- Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler(Authors)
- 2019(Publication Date)
- Garland Science(Publisher)
Normally, in human motion we consider the effects of Air Resistance to be negligible (particularly on the human body as it travels as a projectile through the air). However, in certain applications the effects of Air Resistance will not be negligible and will be considered as an external force that affects motion (such as in extended free fall). For example, in the case of dropping objects vertically on Earth, we know from Newton’s law of gravitation that any object near to or on its surface, regardless of its mass, will accelerate towards the ground (or centre of the Earth) at a constant rate (as we saw previously, two objects of different masses when dropped at the same height will both hit the ground at the same time). However, if you take the case of dropping a piece of paper and a golf ball you will see that the golf ball may hit the ground first. In this case Air Resistance (an external force) could affect the piece of paper by a significant amount such that its descent towards the Earth will be slowed down as Air Resistance becomes an external force acting in the opposite direction (upwards) against gravity. Similarly, in sports such as javelin, hammer throwing and discus, and even to an extent in long jumping when there are “head and tail” winds, Air Resistance will and can have a significant effect. Often long jumps that are wind assisted (usually with a + 2 m/s or more wind) are not legitimate jumps that are used for record purposes (in this case the tail wind would be an external force of assistance). Hence, in certain sports and movements it may be the case that the Air Resistance effects should be considered to be more than negligible. TASK Experiment with dropping different objects from the same height to see if you can now demonstrate the effects of Air Resistance on the vertical downwards acceleration of objects. Key notes Newton’s law of gravitation This law states that any two objects that have mass exert an attractive force on each other
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Therefore, Air Resistance plays a major role in the motion of the ball, as evidenced by the variety of curve balls, floaters, sinkers, and the like thrown by baseball pitchers. Summary › Concepts and Principles A particle moving in uniform circular motion has a centripetal acceleration; this acceleration must be pro- vided by a net force directed toward the center of the circular path. An observer in a noninertial (accelerating) frame of refer- ence introduces fictitious forces when applying Newton’s second law in that frame. An object moving through a liquid or gas experiences a speed- dependent resistive force. This resistive force is in a direction opposite that of the velocity of the object relative to the medium and generally increases with speed. The magnitude of the resis- tive force depends on the object’s size and shape and on the properties of the medium through which the object is moving. In the limiting case for a falling object, when the magnitude of the resistive force equals the object’s weight, the object reaches its terminal speed. › Analysis Model for Problem Solving Particle in Uniform Circular Motion (Extension) With our new knowledge of forces, we can extend the model of a particle in uniform circular motion, first introduced in Chapter 4. Newton’s second law applied to a particle moving in uniform circular motion states that the net force causing the particle to undergo a centripetal acceleration (Eq. 4.21) is related to the acceleration according to o F 5 ma c 5 m v 2 r (6.1) r v S a c S F S Think–Pair–Share See the Preface for an explanation of the icons used in this problems set. For additional assessment items for this section, go to 1. You are working as a delivery person for a dairy store. In the back of your pickup truck is a crate of eggs. The dairy company has run out of bungee cords, so the crate is not tied down.
- Jay Wang(Author)
- 2016(Publication Date)
- Wiley(Publisher)
The position and the vertical velocity y are updated according to Eq. (3.1) by first-order Euler’s method. When the ball would fall below the floor, its velocity vector is reversed, so the ball moves back and forth perpetually. The path traces out the familiar parabolic shape, with front-back symmetry. Experiment with different parameters such as g, and initial x , y , and so on. What happens if only y is reversed on collision with the floor? 3.2 MODELING Air Resistance Anyone riding a bicycle can feel the rush of oncoming air and the resistive force that grows with increasing speed. As a fact of life, Air Resistance is easy to understand but hard to quantify because the underlying physics involves the interactions of a very large number of particles, and there is no exact form for that force. Nonetheless, we observe that, among other things, the force is dependent on the velocity of relative motion . In particular, it is zero if = 0. This leads us to describe the resistive force phenomenologically by a power series as F d = −b 1 − b 2 + · · · (3.3) Here F d is the force due to Air Resistance (or drag), is the velocity of the projectile relative to the medium (air), and = | | is the speed. The constants b 1 and b 2 are called linear and quadratic coefficients. The negative sign in front of b 1 and b 2 indicates that the drag force is opposite the direction of velocity. 3.2 Modeling Air Resistance 59 Linear Drag Physically, the first term in Eq. (3.3) comes from viscosity of the medium. The linear coefficient b 1 can be calculated from Stokes’ law applicable to laminar (smooth) flow. We can understand qualitatively how b 1 comes about from Newtonian physics. Let us consider a fluid between two large parallel plates shown in Figure 3.2. The top plate is moving with velocity to the right, and the bottom one is stationary. We assume is small, so the flow is smooth and separates into thin layers from top to bottom.
eBook - PDFBasic Aerodynamics
Incompressible Flow
- Gary A. Flandro, Howard M. McMahon, Robert L. Roach(Authors)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
15 Physics of Fluids 2 2.1 Aerodynamic Forces Because the objective of aerodynamics is the determination of forces acting on a flying object, it is necessary that we clearly identify their source. Lift and drag forces , for example, are the result of interactions between the airflow and vehicle surfaces. Part of the force must be a result of pressure variations from point to point along the surface; another part must be related to friction of gas particles as they scrub the surface. Clearly , the key to understanding these forces is found in details of the fluid motions. The application of simple molecular concepts provides considerable insight into these motions. Modeling of Gas Motion As a branch of fluid mechanics, aerodynamics is concerned with the motion of a continuously deformable medium. That is, when acted on by a constant shear force, a body of liquid or gas changes shape continuously until the force is removed. This is unlike a solid body , which only deforms until internal stresses come into equilibrium with the applied force; that is, a solid does not deform continuously . To understand the motion of a fluid, it is necessary to apply a set of basic physical laws, which consist of some or all of the following: • conservation of mass (the continuity equation) • Newton’s Second Law of Motion (the momentum equation) • First Law of Thermodynamics (the energy equation) • Second Law of Thermodynamics (the entropy equation) One skill that the student must develop is the effective application of approxi- mation and simplification methods. A proper set of approximations may make unnecessary the use of some laws to produce a practical yet accurate solution for a given problem. This approach is possible only if a clear understanding of the physics of a fluid motion is attained. It is, of course, possible to construct a mathematically correct solution to an incorrectly formulated problem or a solution that is based
eBook - PDF- Patrick Hamill(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
For objects moving at higher speeds (but less than the speed of sound) it is more realistic to assume the resistive force is proportional to the speed squared. That is, F = −Dv 2 . The equation of motion can then be written in the form m dv dt = −Dv 2 . The proportionality constant D depends on the size and shape of the body and the density of the fluid through which it is moving. A reasonable formula for calculating D is D = 1 2 C D Aρ, where the “drag coefficient” C D is a unitless parameter of the order unity which depends on the shape of the body. In practical applications the value C D = 0.2 is often used. A is the cross- sectional area of the object and ρ is the air density and depends on both the altitude and the temperature. (You can appreciate that Air Resistance problems can be very complicated, but here we are only going to concentrate on the method for solving them and assume D is a known constant.) If you apply this law to a body falling through air under the action of the force of gravity, the resistive force is upwards and the gravitational force is downwards, so the equation of motion becomes m dv dt = +Dv 2 − mg. In applying this last equation you will have to be very careful with the signs. If the body is rising, then both gravity and the force of Air Resistance are acting downwards. Worked Example 3.4 A body of mass m is acted upon by the gravitational force (−mg) and the retarding force of Air Resistance given by Dv 2 . It is dropped from rest at an initial height x 0 . Obtain expressions for its velocity and position as a function of time. Solution In problems such as this one, it is often convenient to express relations in terms of the “terminal velocity” which is the speed when the two forces are equal and opposite and the object is no longer accelerating. In this problem the net force is F = Dv 2 − mg. The terminal velocity is obtained by setting F = 0, so v T = mg/D.
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