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- 1. 1 A Preparation for Interview - Engineering Mechanics Compiled by: Mr.B.Ramesh, Associate Professor/Mechanical, St.Joseph’s College of Engineering, Chennai‐119 Distinguish between Particle and Rigid Body. A Particle is a body of infinitely small volume and is considered to be concentrated at a point. Rigid body is which does not deform under the action of the loads or the external forces. In case of Rigid body, the distance between any two points of the body remains constant, when this body is subjected to loads. Define a force. It is defined as an agent that changes or tends to change the position of a body which is either at rest or in motion. A force can produce push, pull or twist. Force is a vector quantity which has both magnitude and direction. State Principle of Resolution. The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction. State and explain Lami's theorem of triangle law of equilibrium. If three forces acting on a particle are in equilibrium, then each force is proportional to the sine of the angle included between the other two forces. Define resultant of forces. Resultant of a system of forces is the single force that replaces the original forces without changing the external effect of the system on the body. Distinguish between the resultant and equilibrant. Resultant is the single equivalent force of a system (group) of forces. Equilibrant is a single force that balances other forces. Thus, equilibrant can be said to be a single force which is equal, collinear and opposite to the resultant.
- 2. 2 State the analytical conditions for equilibrium of a rigid body. 1. Algebraic sum of the horizontal component of all the forces (Σ H) must be zero 2. Algebraic sum of the vertical component of all the forces (Σ V) must be zero 3. The resultant moment of all the forces (Σ M) must be zero State the condition of equilibrium of a body acted upon by (a) two forces (b) three forces. Two forces : the two forces must be equal in magnitude collinear and opposite in sense. Three forces : the three forces must be concurrent. Distinguish between space diagram and free - body diagram. Diagram giving the physical representation of a body and the forces acting on it including the distances is known as space diagram. A free - body diagram is a pictorial representation of the significant, isolated body with all the forces acting on it and all the external forces applied to it. Explain the transmissibility of forces. The condition of equilibriums or of motion of a rigid body will remain unchanged if the point of application of force acting. in the rigid body is transmitted to act at any other point along its line of action. What is moment of a force about an axis ? Moment of force acting on a rigid body about an axis measures the tendency of the force to rotate the rigid body about that axis. State Varignon's theorem. The moment about a given point 'O' the resultant of several concurrent forces is equal to the sum of the moments of various forces about the same point O. Define couple. A pair of two equal and unlike parallel forces (forces equal in magnitude with lines of action parallel to each other and acting in opposite directions) is known as couple. List the different types of beams. (i) Simply supported beam (ii) cantilever beam (iii) fixed beam (iv) Continuous beam and (v) overhanging beam.
- 3. 3 State the different types of supports. (i) roller or rocker support (ii) hinged or pin-joint support (iii) fixed or built-in support (iv) smooth surface or frictionless surface support. What are the different types of loads ? (i) Point or concentrated load (ii) Uniformly Distributed Load (iii) Uniformly Varying Load. Differentiate between simply supported beam, cantilever and fixed beam. In simply supported beam, both the ends rest on simple supports without any fixity. In cantilever beam, one end is fixed and the other is free. Fixed beam has both its ends fixed. Differentiate between Centroid and Centre of gravity. The centre of figures which have only area but no mass is known as Centroid. Centre of gravity is a point where the entire mass or weight of the body is assumed to be concentrated. Under what conditions do the Centre of mass and Centre of gravity coincide? The material must be homogeneous and (ii) the gravitational force on a body of mass 'm' must also pass through its centre of mass. Define Moment of Inertia of an area. The first moment of a force about any point is the product of the force (P) and the perpendicular distance between the point and the line of action. If this first moment is again multiplied by the perpendicular distance, the resulting moment is the second moment of the force or moment of moment of the force. Instead of force, if the area is considered, it is called the second moment of the area or Moment of Inertia. Define Parallel axis theorem. Parallel axis theorem : Moment of inertia of an area any axis is equal to the sum of the moment of inertia about an axis passing through the centroid parallel, to the given axis and (b) the product of area and square of the distance between the two parallel axes. IAB = I CG + A h2 Where, IAB = Moment of inertia of an area about any given axis (say AB) ICG = Moment of inertia about an axis passing through the centroid A = area of the section given h = distance between the two parallel axes
- 4. State perpendicular Axis Theorem. Moment of inertia of plane Iamina about an axis perpendicular to the Iamina and passing through its centroid is equal to the sum of moment of inertia about two mutually perpendicular axes passing through the centroid and in the plane of the lamina. Izz = Ixx + Iyy Define polar moment of inertia of an area and state its application. Moment of inertia of an area about an axis perpendicular to the area through a pole point in the area is called polar moment of the inertia. Polar moment of inertia has application in problems relating to the torsion of cylindrical shafts and rotation of slabs. Define the term, radius of gyration. The radius of gyration 'k' of any lamina about a given axis is the distance from the given axis at which all the elemental parts of the lamina would have to be placed, so as not to alter the Moment of inertia about the given axis. Radius of gyration, k = √I/A Define Product of inertia. Product of inertia of an area with respect to x and y axes is denoted by Ixy = ∫xy dA where x and y are the coordinates of an element dA of the area A. NOTE : Ixy = 0, for a figure, which is symmetrical about either x or y axes. State the salient properties of product of inertia. (i) Product of inertia Ixy is zero when x axis or y axis or both the x and y axes are axes of symmetry for the given area. (ii) Product of inertia may be either positive or negative. (iii) Product of inertia of the given area with respect to its principal axes is zero. Define Principal Axis and Principal Moment of Inertia. The axes about which moments of inertia is ZERO are known as principal axes. The moment of inertia w.r. to the principal axes are called principal moments of inertia. State Pappus - Guldinus theorems. Theorem 1 : The area of surface of revolution obtained by revolving a line or curve is equal to the length of the generating line or curve multiplied by the distance travelled by the centroid of the generating line / curve when it is being rotated. Theorem 2: The volume of a body obtained by revolving an area is equal to the generating area multiplied by the distance traveled by the centroid of the generating area when it is being rotated. 4
- 5. 5 Define Moment of inertia of mass. Consider a body of mass m. The moment of the body with respect to the axes AA' is defined by the integral, l=∫r2 dm where, dm is the mass of an element of the body situated at a distance r from axes AA' and integration is extended over the entire volume of the body. State the relationship between the second moment of area and mass moment of Inertia for thin uniform plate. Mass moment of inertia of a thin plane about an axis x - x, (Ixx) mass = p t (Ixx) area Where, (Ixx) area is the second moment of the area of the plate about the axis xx, p is the mass density and t, thickness of the plate which is uniform. Define Friction. An opposing force, which acts in the opposite direction of the movement of the block is called force of friction or simply Friction. What is limiting friction ? It is the maximum value, up to which Static friction can rise and balance the externally applied force and beyond which it cannot raise. What is dry friction (or) Coulomb friction (or) solid friction ? Dry friction also called Coulomb friction or solid friction relates to rigid bodies which are in contact with each other along surfaces that are not lubricated. Dry friction assumes the name static friction when the surfaces of contact are stationary. Dry friction gets the name kinetic friction (also called dynamic friction) when there is motion of one body over another. Differentiate between Static friction and Dynamic friction. Static friction : It is the friction experienced by the body when it is at rest, or when the body tends to move. Dynamic friction : It is the friction experienced by the body when it is in motion. It is also called kinetic friction.
- 6. 6 State the Laws of friction. 1. The direction of the frictional force is always opposite to the direction in which a body resting over another has a tendency to move, under the action of external force. 2. Friction always acts along the common surface of contact between two bodies. 3. Magnitude of limiting friction is directly proportional to the normal reaction, F α R 4. Limiting friction is independent of the area and shape of the contact surfaces. 5. The limiting friction depends upon the roughness of the surface. Differentiate between angle of friction and coefficient of friction. Angle of friction : When the angle of inclination (α) of a plane is gradually increased, the angle at which the body on the plane just starts sliding down the plane, is called angle of friction. Coefficient of friction : It is the ration of limiting friction to the normal reaction between the two bodies, and is generally denoted by µ - F / R - tanφ φ = Angle of friction . F = Limiting friction. R = Normal reaction. Define angle of repose. Angle of repose is the maximum angle of inclination that an inclined plane may have with the horizontal before a body lying on the plane begins to slide down under the action of its own weight. What is a Wedge. A wedge is of a triangular or trapezoidal in cross section. It is generally used for slight adjustments in the position of a body. i.e., for tightening fits or keys shafts. It is also used for lifting heavy weights. State the relationship between tension in the belt on tight and slack sides. e µθ = T1/T2 Where ,T1 = Tension in the belt on the tight side. θ = Angle of contact in radians. T2 = Tension in the belt on the slack side. µ = Co efficient of friction. What is projectile motion? Any object that is given some initial velocity and during the subsequent motion the object is subjected to only the acceleration due to gravity is termed as a projectile. A projectile travels in the horizontal as well as in the vertical directions and traces a curvilinear path. For example: The motion of a bullet fired from a gun. State D' Alembert's principle. The force system consisting of external forces and inertia force can be considered to keep the particle in equilibrium. Since the resultant force externally acting on the particle is not zero, the particle is said to be in dynamic equilibrium. This principle is known as D' Alembert's principle.
- 7. 7 State the different forms of energy. (i) heat energy (ii) electrical energy (iii) mechanical energy (iv) chemical energy (v) nuclear energy (vi) sound energy and (vii) magnetic energy. State the work - energy principle. The work done by force acting on a particle during its displacement is equal to the change in the kinetic energy of the particle during that displacement. Work done = Final Kinetic energy - Initial Kinetic energy = 1/2 (mv2 2 -mv1 2 ) Define linear impulse or (impulse). Linear impulse or impulse is the product of force acting on a body and the time elapsed. What is impulsive force and impulsive motion? When a large force acts on a particle for a short period of time and produces a definite change in its momentum, then, such a force is called an impulsive force. The motion caused by such an impulsive force is known as impulsive motion. State impulse momentum principle Final momentum - Initial Momentum = Impulse of the Force. The equation expresses that the total change in momentum of a particle during a time interval is equal to the impulse of the force during the same interval of time. What is impact or collision? A collision between two bodies that lasts for a very short interval of time during which period, the two bodies large forces on each other is called an impact or collision. Define line of impact. A line perpendicular to the surfaces of contact during impact is known as the line of impact. What is the difference between central and eccentric impact ? If the mass centres of the two colliding bodies lie on the line of impact, then, the impact is said to be central impact otherwise it is eccentric.
- 8. Distinguish between direct impact and oblique impact. If the velocities of the two colliding bodies act along the line of impact, the impact is called direct impact. If the velocities of the two colliding bodies act along lines other than the line of impact , the impact is known as oblique impact. Distinguish between perfectly plastic impact and perfectly elastic impact. In the case of perfectly plastic impact, e = 0. This means that there is no period of restitution. The two colliding bodies join together and travel with the same velocity. In the case of perfectly elastic impact, e= 1. This means that the relative velocity before the impact is equal to the relative velocity after the impact. Define linear momentum. The linear momentum of a particle is the product of mass and velocity. Define co -efficient of restitution. The ratio of magnitudes of impulses corresponding to the period of restitution and to the period of deformation is called coefficient of restitution. It is also defined as the ration of velocity of separation to the velocity of approach. relative velocity of separation coefficient of restitution, e = relative velocity of approach What is Inertia force ? The inertia force can be defined as the resistance to the change in the condition of rest or of uniform motion of a body. The magnitude of the inertia force is equal to product of the mass and acceleration of the particle and it acts in a direction opposite to the direction of acceleration of the particle. The equation of motion of the particle P ΣF = ma, can be written in the form ΣF - ma = 0 What is translation ? The motion of a rigid body in which the velocity of each element in the rigid body remains equal and the acceleration of each element remains equal is called translation. What is meant by general plane motion ? General plane motion is neither a translation nor a rotation. It can be considered to be a sum of translation and rotation about an axis perpendicular to the plane of motion. 8
- 9. 9 Give two examples of general plane motion. (i) A cylinder rolling on a flat or a curved surface without slipping. (ii) A rod one end of which slides along a horizontal track and the other end along a vertical track. Explain Instantaneous centre of rotation. A rigid body in plane motion, at any given instant of time appears as it rotating about a certain point in the plane of the body. The point which is instantaneously at rest and has zero velocity is called as the instantaneous centre of rotation. The body may seem to be rotating about one point at one instant of time and about another point at the next instant. This instantaneous centre is changing every instant and is not a fixed point. The velocity of any point in the body can be determined by assuming that point to be rotating with some angular velocity ω, about the instantaneous centre at the instant. What is instantaneous centre of rotation in plane motion? A rigid body in plane motion can be considered to rotate about a point that remains at rest at a particular instant. This point having zero instantaneous velocity is called the instantaneous centre of rotation. If a circular cylinder rolls without slipping, where the instantaneous centre of rotation will be located? At the point of contact of the cylinder with the surface. State the principle of work and energy (work energy equation) for the general plane motion of rigid bodies. Principle of work and energy for the general plane motion of rigid bodies (or work energy equation is written as follows: 'Work done by a rigid body undergoing general plane motion = change in kinetic energy o the rigid body due to translation from one point to another point + change in kinetic energy of the rigid body due to rotary motion from one position to another position." State the principle of conservation of energy of a rigid body. Principle of conservation of energy states that the sum of potential energy and kinetic energy of a rigid body or the system of rigid bodies moving under the influence of conservative forces is always a constant.
- 10. 10 The friction experienced by a body, when in motion, is known as dynamic friction Two balls of equal mass and of perfectly elastic material are lying on the floor. One of the ball with velocity v is made to struck the second ball. Both the balls after impact will move with a velocity v/2 If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is 120° Coefficient of friction is the ratio of the limiting friction to the normal reaction between the two bodies. The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane equal to the angle of friction. The range of a projectile is maximum, when the angle of projection is 45° The mechanical advantage of a lifting machine is the ratio of load lifted to the effort applied Static friction is always greater than dynamic friction. A body will begin to move down an inclined plane if the angle of inclination of the plane is greater than the angle of friction. The angle between two forces when the resultant is maximum and minimum respectively are 0° and 180° The point, through which the whole weight of the body acts, irrespective of its position, is known as centre of gravity The force which acts along the radius of a circle and directed towards the centre of the circle is known as centripetal force. According to the law of moments, if a number of coplaner forces acting on a particle are in equilibrium, then the algebraic sum of their moments about any point in their plane is zero A machine having an efficiency less than 50%, is known as non-reversible machine Varingon's theorem of moments states that if a number of coplaner forces acting on a particle are in equilibrium, then the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point. The radius of gyration is the distance where the whole mass (or area) of a body is assumed to be concentrated.
- 11. 11 When the spring of a watch is wound, it will possess strain energy An irregular body may have more than one centre of gravity. Energy may be defined as the capacity of doing work. For a self locking machine, the efficiency must be less than 50% When a train is rounding a curve, the side thrust on the wheel flanges is prevented by raising the outer edge of the rail. The centre of gravity of a triangle lies at a point where its medians intersect each other. The force, by which the body is attracted, towards the centre of the earth, is called weight One joule means that work is done by a force of 1 N when it displaces a body through 1m Mass moment of inertia of a thin rod about its one end is four times the mass moment of inertia of the same rod about its mid-point The angle of inclination of the plane at which the body begins to move down the plane, is called angle of friction According to lami's theorem if the three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two A machine having an efficiency greater than 50%, is known as reversible machine The acceleration of a body sliding down an inclined surface is g sin θ The length of a second's pendulum is 99.4cm Coefficient of friction depends upon nature of surface only The motion of a wheel of a car is combined translation and rotational All the steel trusses of the bridges, have one of their end roller supported, and other end hinged. The main advantage of such a support is that the truss remains stable.