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Fundamentals of Physics, Student's Solutions Manual
Abstract
No other book on the market today can match the success of Halliday, Resnick and Walker's Fundamentals of Physics! In a breezy, easy-to-understand style the book offers a solid understanding of fundamental physics concepts, and helps readers apply this conceptual understanding to quantitative problem solving.
... The applied DC field and the frequency are kept constant throughout the AC magnetization phase. Hence, the applied AC magnetization field (H AC a ) can be expressed by the following equation, where f is the frequency of the AC magnetic field [46]. ...
A new active infrared thermography based technique is proposed for defect detection in ferromagnetic specimens using low frequency alternating magnetic field induced heating. The test specimens (four mild steel specimens with artificially made rectangular slots of 8.0, 5.0, 3.3 and 3.0 mm depths) are magnetized using the low frequency alternating magnetic field and using an infrared camera the surface temperature is remotely monitored in real time. The alternating magnetic field induces eddy current in the specimens which increases the specimen temperature due to Joule’s heating. The experimental results show a thermal contrast in the defective region that decays exponentially with defect depth. The observed thermal contrast is attributed to the reduction in induction heating due to the leakage of magnetic flux caused by magnetic permeability gradient in the defective region. The proposed technique is suitable for rapid non-contact wide area inspection of ferromagnetic materials and offers several advantages over the conventional active thermography techniques like fast direct heating, no frequency optimization, no dependence on the surface absorption coefficient and penetration depth.
An experimental setup using a polarized optical microscope fitted with a detection module capable of measuring the cross-polarized transmitted light intensity and the transmitted light intensity of the polymer sample being analyzed, together with an accompanying calculation procedure, is proposed in order to characterize in real-time thermal transitions and degree of crystallinity, as well as birefringence (which is a measure of orientation) and turbidity. The experimental assessment of the technique was carried out studying commercial poly(ethylene terephthalate) multifilaments with different crystallinity and stretching levels and by direct comparison with the features of conventional DSC curves obtained under similar experimental conditions. While an excellent correlation was found between the type and temperature ranges of thermal events as detected by thermal and optical techniques, the measured birefringence was shown to be sensitive to distinct filament stretching levels, but unaffected by geometrical factors. Contrarily, turbidity is influenced by the latter.
We present evidence that although students' mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin's symbolic forms. We find that students use notions of ``dependence'' and ``parts-of-a-whole'' to successfully guide their work, even in novel situations. We also present evidence that students' naive conceptions of the limit may prevent them from viewing integrals as sums.
In this paper active vibration control of functionally graded material (FGM) plates using piezoelectric sensor/actuator patches is studied. A simply supported FGM rectangular plate which is bonded with a piezoelectric rectangular patch (patches) on the top and/or bottom surface(s) as actuators/sensors is considered. When a constant electric charge is imposed, the governing differential equations of the motion are derived using classical laminated plate theory (CLPT). The solution for the motion equation is obtained using a Fourier series method and the effect of feedback gain and FGM volume fraction on the plate frequency and displacement (w) are studied. It is noticed that increasing the feedback gain leads to the reduction of frequency and displacement and therefore a better control of the plate's vibration. Moreover, by increasing the value of the FGM volume fraction the resonant frequency decreases.
Some physicists have pointed out that we do not know what energy is. Many studies have shown that the concept of energy is
a problem for teaching. A study of the history of the concept shows that the discoverers of energy did not find anything which
is indestructible and transformable but rather that the concept of energy underwent a change of meaning and energy was considered
a substance towards the end of the nineteenth century. In distinguishing between the treatment of phenomena and the theories
carried out by Mayer and Joule, it can be concluded that they established equivalences between different domains, such as
motion and heat, motion and electricity or position and motion. This complies with the interpretation presented in textbooks
published about a century ago and enables us to overcome some difficulties with the concept of energy.
Electromagnetic force is an important driving force for convection in the weld pool during arc welding. Accurate calculation of the electromagnetic force field requires complex numerical calculations of three-dimensional current density and magnetic flux fields. Several simplifying assumptions have been suggested to avoid the complex calculations. The resulting analytical expressions for the electromagnetic force field have been widely used without any critical evaluation of their intrinsic merit, since accurate numerical calculations were difficult in the past because of lack of fast computers. A numerical model has been developed to accurately calculate the current density and magnetic flux fields and the resulting electromagnetic force field in three dimensions in the entire weldment. The model can take into account any current distribution on the work piece surface and evaluate the effects of different arc locations and work piece geometry on the electromagnetic force field. Contributions of the electrode current, arc plasma, and current distribution inside the three-dimensional work piece to the magnetic field and the electromagnetic force field are determined. The electromagnetic force field computed from the model is compared with those obtained from the commonly used simplified expressions of electromagnetic force to examine the accuracy of the commonly used simplifying assumptions. The accuracy of the computed electromagnetic force field can be significantly improved by using the proposed numerical model. © 2003 American Institute of Physics.
We'll be presenting an approach to solve the equation of simple harmonic motion (SHM) which is non-standard as compared with the usual way of solution presented in textbooks. In addition to help students avoid the unnecessary memorization of formulas to solve physics problems, this approach could help instructors to present the subject in a teaching framework which integrates conceptual and mathematical reasoning, in a systemic way of thinking that will help students to reinforce their quantitative reasoning skills by using mathematical knowledge already familiar to students in a first calculus-based introductory physics course, such as the chain rule for derivatives, inverse trigonometric functions, and integration methods.
The amount of published research in Physics Education Research (PER) shows, on one hand, an increasing interest in the design and development of high performance physics teaching strategies, and, on the other hand, it tries to understand plausible ways on which the brain processes scientific information so that scientific thinking skills could be taught more effectively. As physics is a subject in which mathematical and conceptual reasoning can not be separated, instructors of physics face the problem of finding suitable advise on the most effective methods of teaching physics (i.e. how much time should be spent on intuitive conceptual reasoning and how much time in developing quantitative reasoning, and how to teach both in a unitary way). In spite the important efforts made by the PER community, the published results are overwhelming and confusing for the physics instructors in the sense that the conclusions that have arisen in those articles are in some instances controversial and far from being conclusive in pointing out a particular strategy to overcome the afore mentioned problem. Accordingly, based on the analysis of published PER work, we'll be arguing that one of the major difficulties to overcome in the teaching of physics could be associated to the lack of a consistent and coherent methodological framework for teaching which integrates both aspects, conceptual and mathematical reasoning, in a systemic way of thinking. We will be presenting a set of plausible steps that could be applied to tackle the aforementioned difficulty.
A new simply constructed, easy-to-make demonstration of Hero's fountain is presented. The apparatus doesn't have a vessel above a fountain nozzle or a pump and can be considered as one of the best demonstration of Pascal and Bernoulli's principles. Its action is discussed on the basis of Pascal and Bernoulli's principles.
We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial-mass planets of all compositions we considered follow a generic functional form that is not a simple power law: for up to , where and are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form . We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found that: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with ~5% uncertainty water ice planets with water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super Earths'' based on the clear distinction in radii between planets with significant gas envelopes and those without. Comment: ApJ, in press, 33 pages including 16 figures
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