Engineering Mechanics Dynamics Engineering Mechanics Volume 2 Dynamics Seventh Edition J. L. Meriam L. G. Kraige Virginia Polytechnic Institute and State . Engineering Mechanics Dynamics by J.L. Meriam, L.G. Hassan Muhammad. Loading Preview. Sorry, preview is currently unavailable. You can. Sorry, this document isn't available for viewing at this time. In the meantime, you can download the document by clicking the 'Download' button above.

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(Meriam and Kraige, Ed.,). Chapter 1. Introduction. Engineering Mechanics. Statics. Dynamics. Strength of Materials. Vibration. Statics:distribution of. Engineering Mechanics Dynamics, 6th Edition Meriam Kraige - Ebook download as PDF File .pdf) or read book online. Engineering Mechanics Dynamics J. L. MERIAM (6th Edition) [Text Book].

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Khurmi, J. Introduction to Dynamics. Kinematics of Particles. Kinetics of Particles. Kinetics of Systems of Particles. Plane Kinematics of Rigid Bodies. Plane Kinetics of Rigid Bodies. Vibration and Time Response. Appendix A: Area Moments of Inertia. Appendix B: Mass Moments of Inertia.

Appendix C: Selected Topics of Mathematics. Appendix D: Useful Tables Index Problem Answers. Other Useful Links.

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The reason for the small difference is that the earth is not exactly ellipsoidal, as assumed in the formulation of the In- ternational Gravity Formula.

The formula is based on an ellipsoidal model of the earth and also ac- counts for the effect of the rotation of the earth. The absolute acceleration due to gravity as determined for a nonro- tating earth may be computed from the relative values to a close approxi- mation by adding 3. The variation of both the absolute and the relative values of g with latitude is shown in Fig.

The values of 9. Apparent Weight The gravitational attraction of the earth on a body of mass m may be calculated from the results of a simple gravitational experiment. The body is allowed to fall freely in a vacuum, and its absolute acceleration is measured. If the gravitational force of attraction or true weight of the body is W, then, because the body falls with an absolute acceleration g, Eq.

The difference is due to the rotation of the earth. The ratio of the apparent weight to the appar- ent or relative acceleration due to gravity still gives the correct value of mass. The apparent weight and the relative acceleration due to gravity are, of course, the quantities which are measured in experiments con- ducted on the surface of the earth.

Thus, a di- mension is different from a unit. The principle of dimensional homogene- ity states that all physical relations must be dimensionally homogeneous; that is, the dimensions of all terms in an equation must be the same.

It is customary to use the symbols L, M, T, and F to stand for length, mass, time, and force, respectively. In SI units force is a derived quantity and from Eq. We can derive the following expression for the velocity v of a body of mass m which is moved from rest a horizontal distance x by a force F: You should perform a dimensional check on the answer to every problem whose solution is carried out in symbolic form.

This description, which is largely mathematical, en- ables predictions of dynamical behavior to be made.

A dual thought process is necessary in formulating this description. It is necessary to think in terms of both the physical situation and the corresponding mathematical description. This repeated transition of thought between the physical and the mathematical is required in the analysis of every problem.

You should recognize that the mathematical formulation of a physical problem represents an ideal and limiting description, or model, which approximates but never quite matches the actual physical situation. In Art.

We assume therefore, that you are familiar with this approach, which we summarize here as applied to dynamics. Approximation in Mathematical Models Construction of an idealized mathematical model for a given engi- neering problem always requires approximations to be made. Some of these approximations may be mathematical, whereas others will be physical. For instance, it is often necessary to neglect small distances, angles, or forces compared with large distances, angles, or forces.

An interval of mo- tion which cannot be easily described in its entirety is often divided into small increments, each of which can be approximated.

As another example, the retarding effect of bearing friction on the motion of a machine may often be neglected if the friction forces are small compared with the other applied forces. Thus, the type of assumptions you make depends on what infor- mation is desired and on the accuracy required. You should be constantly alert to the various assumptions called for in the formulation of real problems.

The ability to understand and make use of the appropriate assumptions when formulating and solving engi- neering problems is certainly one of the most important characteristics of a successful engineer. Along with the development of the principles and analytical tools needed for modern dynamics, one of the major aims of this book is to provide many opportunities to develop the ability to formulate good mathematical models.

Strong emphasis is placed on a wide range of practical problems which not only require you to apply theory but also force you to make relevant assumptions. Application of Basic Principles The subject of dynamics is based on a surprisingly few fundamental concepts and principles which, however, can be extended and applied over a wide range of conditions.

The study of dynamics is valuable partly be- cause it provides experience in reasoning from fundamentals.

This experi- ence cannot be obtained merely by memorizing the kinematic and dynamic equations which describe various motions.

It must be obtained through ex- posure to a wide variety of problem situations which require the choice, use, and extension of basic principles to meet the given conditions. At times a single particle or a rigid body is the system to be isolated, whereas at other times two or more bodies taken together con- stitute the system. Development of good habits in formulating problems and in representing their solutions will be an invaluable asset.

[PDF] Engineering Mechanics Dynamics By James L. Meriam, L. G. Kraige Free Download

Each solution should proceed with a logical se- quence of steps from hypothesis to conclusion. The following sequence of steps is useful in the construction of problem solutions. Formulate the problem: Develop the solution: The arrangement of your work should be neat and orderly. This will help your thought process and enable others to understand your work. The discipline of doing orderly work will help you to develop skill in prob- lem formulation and analysis.

Meriam Kraige Engineering Mechanics Statics 7th Edition book

This diagram consists of a closed out- line of the external boundary of the system. All bodies which contact and exert forces on the system but are not a part of it are removed and replaced by vectors representing the forces they exert on the isolated system. In this way, we make a clear distinction between the action and reaction of each force, and all forces on and external to the system are accounted for.

We assume that you are familiar with the technique of drawing free-body diagrams from your prior work in statics. Numerical versus Symbolic Solutions In applying the laws of dynamics, we may use numerical values of the involved quantities, or we may use algebraic symbols and leave the answer as a formula.

When numerical values are used, the magnitudes of all quantities expressed in their particular units are evident at each stage of the calculation. This approach is useful when we need to know the magnitude of each term. The symbolic solution, however, has several advantages over the numerical solution: The use of symbols helps to focus attention on the connection between the physical situation and its related mathematical description.

A symbolic solution enables you to make a dimensional check at every step, whereas dimensional homogeneity cannot be checked when only numerical values are used.

We can use a symbolic solution repeatedly for obtaining answers to the same problem with different units or different numerical values. Thus, facility with both forms of solution is essential, and you should practice each in the problem work. In the case of numerical solutions, we repeat from Vol.

Solution Methods Solutions to the various equations of dynamics can be obtained in one of three ways. Obtain a direct mathematical solution by hand calculation, using ei- ther algebraic symbols or numerical values. We can solve the large majority of the problems this way. Obtain graphical solutions for certain problems, such as the deter- mination of velocities and accelerations of rigid bodies in two- dimensional relative motion. Solve the problem by computer.

A number of problems in Vol. They ap- pear at the end of the Review Problem sets and were selected to illustrate the type of problem for which solution by computer offers a distinct advantage. The choice of the most expedient method of solution is an important aspect of the experience to be gained from the problem work. We em- phasize, however, that the most important experience in learning me- chanics lies in the formulation of problems, as distinct from their solution per se.

Perform calculations using SI and U.

Express the law of gravitation and calculate the weight of an object. Discuss the effects of altitude and the rotation of the earth on the acceleration due to gravity. Apply the principle of dimensional homogeneity to a given physical relation. Describe the methodology used to formulate and solve dynamics problems.

Determine its weight under these conditions in both pounds and newtons. The shuttle is in a circular orbit at an altitude of miles above the surface of the earth. Determine the weight of the module in both pounds and newtons under these conditions.

Round off all answers using the rules of this textbook. Here we have used the acceleration of gravity relative to the rotating earth, be- cause that is the condition of the module in part a. From the table of conversion factors inside the front cover of the textbook, we see that 1 pound is equal to 4.

Thus, the weight of the module in newtons is Ans.

Engineering Mechanics Dynamics, 6th Edition Meriam Kraige

Finally, its mass in kilograms is Ans. As another route to the last result, we may convert from pounds mass to kilograms. Again using the table inside the front cover, we have We recall that 1 lbm is the amount of mass which under standard conditions has a weight of 1 lb of force.

We rarely refer to the U. The sole use of slug, rather than the unnecessary use of two units for mass, will prove to be powerful and simple.

Be sure that cancellation of the units leaves the units desired—here the units of lb cancel, leaving the desired units of N. We must be sure that when a calculated num- ber is needed in subsequent calcula- tions, it is obtained in the calculator to its full accuracy If necessary, numbers must be stored in a calculator storage register and then brought out of the register when needed.

We must not merely punch into our calculator and proceed to divide by 9. Some individuals like to place a small indication of the storage register used in the right margin of the work paper, directly beside the number stored.

The weight at an altitude of miles is then Ans. We now convert Wh to units of newtons. We will study the effects of this weight on the motion of the module in Chapter 3. Thus the answers for part c are the same as those in part b. This Sample Problem has served to eliminate certain commonly held and persistent misconceptions. First, just because a body is raised to a typical shuttle altitude, it does not become weightless. This is true whether the body is released with no velocity relative to the center of the earth, is inside the orbiting shuttle, or is in its own arbitrary trajectory.

And second, the acceleration of gravity is not zero at such altitudes. Determine the gravitational force which sphere A exerts on sphere B. The value of R is 50 mm. Assume a spherical earth of radius R and ex- press h in terms of R. Use Table of Appendix D as needed. Convert your weight to newtons and calculate the corresponding mass in kilograms.

Convert the given mass of the car to slugs and calculate the corresponding weight in pounds. Determine the average mass of one apple in both SI and U.

Consider the vectors to be nondimensional. The particle is restricted to the line through the centers of the earth and the moon. Justify the two solutions physically. Determine the ratio of the force which the earth exerts on the woman to the force which the sun exerts on her. Neglect the effects of the rotation and oblateness of the earth. Deter- mine the ratio of the force which the earth ex- erts on the woman to the force which the moon exerts on her.

Find the same ratio if we now move the woman to a corresponding position on the moon. Repeat for moon position B. Even if this car maintains a constant speed along the winding road, it accelerates laterally, and this acceleration must be considered in the design of the car, its tires, and the roadway itself. A thorough work- ing knowledge of kinematics is a prerequisite to kinetics, which is the study of the relationships between motion and the corresponding forces which cause or accompany the motion.

A particle is a body whose physical di- mensions are so small compared with the radius of curvature of its path that we may treat the motion of the particle as that of a point. We can describe the motion of a particle in a number of ways, and the choice of the most convenient or appropriate way depends a great deal on experience and on how the data are given. Let us obtain an overview of the several methods developed in this chapter by referring to Fig. If there are no physical guides, the motion is said to be unconstrained.

A small rock tied to the end of a string and whirled in a circle undergoes con- strained motion until the string breaks, after which instant its motion is unconstrained. The motion of P can also be de- scribed by measurements along the tangent t and normal n to the curve. The direction of n lies in the local plane of the curve. Both descriptions will be developed and applied in the articles which follow.

A large proportion of the motions of machines and structures in engineering can be represented as plane motion. Later, in Chapter 7, an introduction to three-dimensional mo- tion is presented.

We begin our discussion of plane motion with recti- linear motion, which is motion along a straight line, and follow it with a description of motion along a plane curve. The displacement would be negative if the particle moved in the negative s-direction.

The velocity is positive or negative depending on whether the corre- sponding displacement is positive or negative. Note that the acceleration would be positive if the particle had a negative velocity which was becoming less negative. If the particle is slowing down, the particle is said to be decelerating. Velocity and acceleration are actually vector quantities, as we will see for curvilinear motion beginning with Art.

For rectilinear mo- tion in the present article, where the direction of the motion is that of the given straight-line path, the sense of the vector along the path is de- scribed by a plus or minus sign.

In our treatment of curvilinear motion, we will account for the changes in direction of the velocity and accelera- tion vectors as well as their changes in magnitude. By eliminating the time dt between Eq. The position coordinate s, the velocity v, and the acceleration a are algebraic quantities, so that their signs, positive or negative, must be carefully observed. Note that the positive direc- tions for v and a are the same as the positive direction for s.

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Thus, the velocity can be determined at all points on the curve and plotted against the corresponding time as shown in Fig. We now see from Fig.

Consequently, the net displacement of the particle during the interval from t1 to t2 is the corresponding area under the curve, which is Similarly, from Fig. Thus, the net change in velocity between t1 and t2 is the corresponding area under the curve, which is Note two additional graphical relations.

When the acceleration a is plotted as a function of the position coordinate s, Fig. Thus, the net area under the curve between position co- ordinates s1 and s2 is When the velocity v is plotted as a function of the position coordinate s, Fig.Have a great day!

No notes for slide. With this arrangement, the attention of the stu- dent is focused more strongly on the three basic approaches to kinetics. In addition, this approach allows us to use the symbol lb to always mean pound force.

Students with interests in one or more of these and many other activities will constantly need to apply the fundamental principles of dynamics. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. Preface ix 9.

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