STATICS Chapter 2 CONCEPT OF FORCE AND EQUILIBRIUM

STATICS Chapter 2

CONCEPT OF FORCE AND EQUILIBRIUM • Statics – study on body that is at rest or in equilibrium • Force – a push or a pull exerted by our muscles (primitive concept) - an interaction that causes changes in the motion of bodies - action of one body on another

CONCEPT OF FORCE AND EQUILIBRIUM • If the interaction between bodies does not produce motion, it means that the forces neutralize each other. • If forces are not neutralized, a change in motion of the body or system will result.

CLASSIFICATIONS OF FORCES • Concurrent – forces that act at a point or whose line of action converges or intersects at a common point • Nonconcurrent – forces whose line of action does not converge at a common point

CLASSIFICATIONS OF FORCES • External force – force that a body exerts on another body • Internal force – forces exerted by one part of a body on other parts of same body

CLASSIFICATIONS OF FORCES • Co-planar – forces acting on one plane • Non-coplanar – forces acting in more than one plane

UNITS OF FORCE • (MKS) Newton = force that will give a mass of 1 kg an acceleration of 1 m/s 2 • (CGS) dyne = force that will give a mass of 1 g an acceleration of 1 cm/s 2 • (FPS) poundal = force that will give a mass of 1 slug an acceleration of 1 ft/s 2

UNITS OF FORCE • • 1 kg force = 9. 8 N 1 g force = 980 dynes 1 lb force = 32 poundal 1 slug mass = 32 lb

RESULTANT AND COMPONENT OF FORCES • Forces are vector quantities • Composition of forces = process of finding a single force which will produce an effect the same as the effect produced by the given forces • Resolution of forces = a single force is broken into separate forces called the component of the force.

EQUILIBRIUM OF PARTICLES • A particle which has no net force acting to it is said to be in equilibrium. • Equilibrant – single force that holds two or more forces in equilibrium. It prevents the motion of the body which is equal to the resultant but in opposite direction.

EQUILIBRIUM OF PARTICLES • Equilibrium – state in which there is no change in the motion of the body – Static equilibrium – resultant of all the forces is zero and the body is at rest – Dynamic equilibrium – resultant of all forces is zero, velocity of body is constant thus body moves in uniform motion

FIRST CONDITION FOR EQUILIBRIUM •

FIRST CONDITION FOR EQUILIBRIUM • The sum of all upward force components is equal to the sum of all downward force components. • The sum of all force components to the right is equal to the sum of all force components to the left.

EXAMPLE A pendulum bob with a weight of 20 N hangs from a cord. A horizontal force sufficient to bring the cord to an angle of 25° with the vertical is applied to the bob. Find the horizontal force and the tension in the cord.

SECONDITION FOR EQUILIBRIUM • When vector sum of concurrent forces acting on a body is zero, then there is no change in its translational motion but when there are several non-concurrent forces acting on a body, there is in general a change in the state of rotational motion.

SECONDITION FOR EQUILIBRIUM • In order that the rotational motion of a body will not change, the sum of the torques about any axis acting on the body must be equal to zero.

SECONDITION FOR EQUILIBRIUM •

TORQUE OR MOMENT OF FORCE • Measures the effectiveness of the force in changing rotation about the chosen axis. • Turning effect of the force.

TORQUE OR MOMENT OF FORCE • The effect of a force on a rotational motion of a body depends on: – Magnitude of the force – Torque arm or moment arm • Perpendicular distance from the axis of rotation (fulcrum) to the line of action of the force

TORQUE OR MOMENT OF FORCE • To change the state of rotational motion of a body, the point of application of the force is taken into consideration. • The effect of a given force upon the rotational motion of a body is greater, the further the line of action is from the axis of rotation.

TORQUE OR MOMENT OF FORCE • If the line of action of the applied force passes through the axis of rotation, then this force will not produce any change in the rotational motion of the body.

CENTER OF GRAVITY • Point about which the sum of gravitational torques is equal to zero • Point of application of the resultant of the attraction that the earth exerts upon all the particles of a body • A point in which the total weight of the body is concentrated • A point where object balances

CENTER OF GRAVITY • The center of gravity of a body may be situated outside of the body. • Center of gravity determines the stability of the body.

CENTER OF GRAVITY • When a force whose line of action passes through the center of gravity, this force will affect only the translational motion of the body but when line of action does not pass through the center of gravity both translational and rotational motion of the body is affected.

TYPES OF EQUILIBRIUM • Stable – center of gravity at its lowest position, object displaced slightly will return to original position • Unstable – object when displaced slightly will change position completely • Neutral – object when displaced, location of center of gravity remains the same