Chapter 6 Equilibrium

STATICS Statics is the branch of mechanics which deals with the study of bodies at rest under a number of    forces, the equilibrium, conditions of equilibrium, types of equilibrium and torque etc.

Equilibrium    A body is said to be in equilibrium if it is at rest or moving with uniform velocity.    In other words if the linear and angular acceleration of a body are zero, the body is said to be in    equilibrium.     Or we can say that when two or more forces act on a body such that their resultant or combining effect    on the body is Zero and the body retains its state of rest or of uniform motion then the body is said to    be in equilibrium. Example    A book lying on the table, suspended bodies, all stationary bodies , jump by using parachute.

Types of equilibrium Static equilibrium    If the combined effect of all the forces acting on a body is zero and the body is in the state of rest then    its equilibrium is termed as static equilibrium.    For example: All stationary bodies Dynamic equilibrium    when a body is in state of uniform motion and the resultant of all the forces acting upon it is zero then it    is said to be in dynamic equilibrium.    For example: Jump by using parachute. Conditions of equilibrium    There are two conditions of equilibrium are as follows

First condition of equilibrium    To maintain the transitional equilibrium in a body the vector sum of all the forces acting on the body is    equal to zero    i.e.    In other words we can say that to maintain equilibrium the sum of all the forces acting along X-axis is    zero and the sum of all the forces acting along Y-axis is zero.    i.e.  

Second condition of equilibrium    The second condition of equilibrium stated as follow:    A body will be in rotational equilibrium when the algebraic sum of clock wise torque and anti clock wise    torque is zero.    In other words:    A body will be in rotational equilibrium if vector sum of all the torque acting on the body is zero.

STATES OF EQUILIBRIUM States of equilibrium    There are three states of equilibrium:     Stable equilibrium      Unstable equilibrium     Neutral equilibrium Stable equilibrium    When the center of gravity of a body lies below point of suspension or support, the body is said to be in    STABLE EQUILIBRIUM. For example a book lying on a table is in stable equilibrium. Explanation    A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from one edge    and then allowed to fall, it will come back to its original position.    Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc. Reason of stability    When the book is lifted its center of gravity is raised . The line of action of weight passes through the    base of the book. A torque due to weight of the book brings it back to the original position.

Unstable equilibrium Example    When the center of gravity of a body lies above the point of suspension or support, the body is said to    be in unstable equilibrium Example    pencil standing on its point or a stick in vertically standing position.    Explanation:    If thin rod standing vertically is slightly disturbed from its position it will not come back to its original    position. This type of equilibrium is called unstable equilibrium, other example of unstable equilibrium are    vertically standing cylinder and funnel etc. Reason of instability    when the rod is slightly disturbed its center of gravity is lowered . The line of action of its weight lies    outside the base of rod. The torque due to weight of the rod toppled it down.

Neutral equilibrium    When the center of gravity of a body lies at the point of suspension or support, the body is said to be in    neutral equilibrium. Example: rolling ball.    If a ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will    remain at rest. This type of equilibrium is called NEUTRAL EQUILIBRIUM.    If the ball is rolled, its center of gravity is neither raised nor lowered. This means that its center of gravity    is at the same height as before.

TORQUE - CENTER OF GRAVITY    The torque or moment of force can be define as “ The tendency of a force to produce rotation in a body  about an axis is called torque or moment of force."    The turning effect of a force depends upon two factors:     The magnitude of force (F)     Moment arm (r)    The torque about any axis is given by the product of force and moment arm  Torque = force x moment arm    Positive torque:    If a body rotates about its axis in anti clockwise direction, then the torque is taken positive .    Negative torque:    If the body rotates in the clockwise direction, then the torque is taken as negative .

Center of gravity The center of a body is that point in the body through which the resultant forces due to the earth’s    attraction posses and through which the whole weight of the body always acts.    OR    Center of gravity of a body is a point where total weight of the body is concentrated.    Every body posses a center of gravity and this is irrespective of the body. Its is not necessary that the    center of gravity should be within the body, but it may also be situated in space out side the body.    Example: center of gravity of a ring is at the center, which is in the space.    Center of gravity of different objects:     Rectangle    Center of gravity of a rectangular is at the point of intersection of its diagonals     Circle    Center of gravity of a circle is at its center.      Square    Center of gravity of square is at the point of intersection of its diagonals.     Regular bar    The center of gravity of a regular bar is at its geometrical center.      Triangle    The center of gravity of a triangle is at the point of intersection of its medians.      Cylinder    The center of gravity of a cylinder is at the axis of cylinder.