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JJ205 ENGINEERING MECHANICS COURSE LEARNING OUTCOMES : Upon completion of this course, students should be able to: CLO 1. apply the principles of statics and dynamics to solve engineering problems (C3) CLO 2. sketch related diagram to be used in problem solving (C3) CLO 3. study the theory of engineering mechanics to solve related engineering problems in group (A3) BASIC CONCEPTS ON STATICS CLO 1. apply the principles of statics and dynamics to solve engineering problems (C3) CLO 3. study the theory of engineering mechanics to solve related engineering problems in group (A3) INTODUCTION (CLO 1) MECHANICS - Body of Knowledge which Deals with the Study and Prediction of the State of Rest or Motion of Particles and Bodies under the action of Forces. STATICS - Statics Deals With the Equilibrium of Bodies, That Is Those That Are Either at Rest or Move With a Constant Velocity. DYNAMICS - Dynamics Is Concerned With the Accelerated Motion of Bodies BASIC CONCEPTS BUT VITAL TO THE STATICS (CLO 1) SPACE The geometric region in which study of body is involved is called space. At point in the space may be referred with respect to a predetermined point by a set of linear and angular measurements. The reference point is called the origin and set of measurements as ‘coordinates’. If coordinates involve only in mutually perpendicular directions they are known as Cartesian coordinates. If the coordinates involve angle and distances, it is termed as polar coordinate system. FORCE – Force is considered as a ‘push’ or ‘pull’ exerted by one body on another. This interaction can occur when there is direct contact between the bodies, such as a person pushing on a wall, or it can occur through a distance when the bodies are physically separated. MASS The quantity of the matter possessed by a body is called mass. The mass of a body will not change unless the body is damaged and part of it is physically separated. When a body is taken out in a space craft, the mass will not change but its weight may change due to change in gravitational force. Even the body may become weightless when gravitational force vanishes but the mass remain the same. Continue… TIME – Time is conceived as a succession of events. Although the principles of statics are time independent, this quantity does play an important role in the study of dynamics. LENGTH – Length is needed to locate the position of a point in space and thereby describe the size of a physical system. Once a standard unit of length is defined, one can then quantitatively define distances and geometric properties of a body as multiples of the unit length. BASIC CONCEPTS BUT VITAL TO THE STATICS (CLO 1) PARTICLES – A particle has a mass, but a size that can be neglected. For example, the size of the earth is insignificant compared to the size of its orbits, and therefore the earth can be modeled as a particle when studying its orbital motion. When a body is idealized as a particle, the principles of mechanics reduces to a rather simplified form since the geometry of the body will not be involved in the analysis of the problem RIGID BODY – A rigid body can be considered as a combination of a large number of particles in which all the particles remain at a fixed distance from one another both before and after applying a load. Concentrated force – ◦ Represents the effect of a loading which is assumed to act at a point on a body. ◦ We can represent a load by a concentrated force, provided the area over which the load is applied is very small compared to the overall size of the body. ◦ Example: contact force between a wheel and the ground. SCALARS AND VECTORS (CLO 1) SCALARS – A quantity characterized by a positive or negative number is called scalar. For example; mass, volume and length. VECTOR – A vector is quantity that has both a magnitude and the direction. For example; weight, force and moment. VECTORS (CLO 1) FREE VECTORS – One whose action is not confined to or associated with a unique line in space. For example, if a body moves without rotation, then the movement or displacement of any point in the body maybe taken as a vector, and this vector will be describe equally well the direction and magnitude of the displacement of every point in the body. Hence , we may represent the displacement of such a body by a free vector. VECTORS SLIDING VECTORS – Is one for which a unique line in space must be maintained along which the quantity acts. When we deal with the external action of a force on a rigid body, the force may be applied at any point along its line of action without changing its effect on the body as a whole and hence may be considered a sliding vector. VECTORS FIXED VECTORS – is one for which a unique point of application is specified, and therefore the vector occupies a particular position in space. The action of a force on a deformable or non rigid body must be specified by a fixed vector at the point of application of the force. In this problem the forces and deformations internal to the body will be dependent on the point of application of the force, as well as its magnitude and line of action. NEWTON’S LAWS OF MOTION (CLO 1) FIRST LAW – A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided the particle is not subjected to an unbalanced force. SECOND LAW – A particle acted upon by an unbalanced force ‘F’ experiences an acceleration ‘a’ that has the same direction as the force and a magnitude that is directly proportional to the force. If ‘F’ is applied to a particle of mass ‘m’, this law maybe expressed mathematically as ; F = ma. THIRD LAW – The mutual forces of action and reaction between two particles are equal, opposite, and collinear. SI SYSTEM AND UNIT (CLO 3) Mechanics deals with four fundamental quantities; length, mass, force, and time. SI UNITS QUANTITY DIMENSIONAL SYMBOL UNIT SYMBOL MASS M Kilogram kg LENGTH L Meter m TIME T second s FORCE F newton N * The unit of force, called a newton (N), is derived from F=ma. 1 newton is equal to a force required to give 1 kg of mass an acceleration of 1 m/s2. (N = kg. m/s2) PREFIXES (CLO 3) When a numerical quantity is either very large or very small, the units used to define its size maybe modified by using prefix. For example; Exponential form prefix SI symbol 1 000000000 109 giga G 1000 103 kilo k 0.001 10-3 mili m 0.000001 10-6 micro µ 0.000000001 10-9 nano n Example (CLO 3) : Evaluate each of the following and express with SI units having an appropriate prefix: a) (50 mN)(6 GN) b) (400 mm)(0.6 MN)2 c) 45 MN3/900 Gg Continue… First, convert each number to base units, perform the indicated operations, then, choose an appropriate prefix. a) Note carefully the convention kN2 = (kN)2 = 106 N2 Continue… b) We can also write: Continue… Exercises: