ENGINEERING MECHANICS GATE PI PAPER TECHNICAL SECTION PART 2
CONCURRENT FORCES ON A PLANE: INTRODUCTION TO ENGINEERING MECHANICS Mechanics It is defined as that branch of science, which describes and predicts the conditions of rest or motion of bodies under the action of forces. Engineering mechanics applies the principle of mechanics to design, taking into account the effects of forces. Statics Statics deal with the condition of equilibrium of bodies acted upon by forces.
. Force Force may be defined as any action that tends to change the state of rest or motion of a body to which it is applied. The three quantities required to completely define force are called its specification or characteristics. So the characteristics of a force are: 1. Magnitude 2. Point of application 3. Direction of application
COMPOSITION OF FORCES NUMERICAL PROBLEMS Composition of two forces . The reduction of a given system of forces to the simplest system that will be its equivalent is called the problem of composition of forces. Resolution of a force . The replacement of a single force by a several components which will be equivalent in action to the given force is called resolution of a force.
METHOD OF MOMENTS Moment of a force with respect to a point >Considering wrench subjected to two forces P and Q of equal magnitude. It is evident that force P will be more effective compared to Q, though they are of equal magnitude. The effectiveness of the force as regards it is the tendency to produce rotation of a body about a fixed point is called the moment of the force with respect to that point. Moment Magnitude of the force x Perpendicular distance of the line of action of force. Point O is called moment centre and the perpendicular distance (i.e. OD) is called moment arm >Unit is N.m
FRICTION Frictional force The force which opposes the movement or the tendency of movement is called Frictional force or simply friction. It is due to the resistance to motion offered by minutely projecting particles at the contact surfaces. However, there is a limit beyond which the magnitude of this force cannot increase. Limiting Friction: If the applied force is more than this limit, there will be movement of one body over the other. This limiting value of frictional force when the motion is impending, it is known as Limiting Friction
PARALLEL FORCES ON A PLANE Like parallel forces: Coplanar parallel forces when act in the same direction. | Unlike parallel forces Coplanar parallel forces when act in different direction. Resultant of like parallel forces: Let P and Q are two like parallel forces act at points A and B. R=P+Q
CENTRE OF GRAVITY Centre of gravity: . It is that point through which the resultant of the distributed gravity force passes regardless of the orientation of the body in space. . As the point through which resultant of force of gravity (weight) of the body acts. Centroid: Centeroid of an area lies on the axis of symmetry if it exits Centre of gravity is applied to bodies with mass and weight and centroid is applied to plane areas.