Statics, Dynamics and Mechanical Engineering 1、 ntroduction Mechanics Science which describes and predicts the conditions of rest or motion of bodies under the action of forces The field of Classical Mechanics can be divided into three categories 1) Mechanics of Rigid Bodies 2) Mechanics of Deformable Bodies nIcs Rigid-body mechanics General mechanics Statics deals with bodies that are in equilibrium with applied forces. I Such bodies are either at rest or moving at a constant Dynamics deals with the relation between forces and the motion of bodies. I Bodies are accelerating Notes Rigid-body mechanics is based on the Newtons laws of motion These laws were postulated for a particle, which has a mass, but no size or shape Newton's laws may be extended to rigid bodies by considering the rigid body to be made up of a large numbers of particles whose relative positions from each other do not change Newton's laws of motion I st law. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. 2nd law. If the resultant force acting on a particle is not zero, the particle will experience an acceleration proportional to the magnitude of the force and in the direction of this resultant force 3rd law. The mutual forces of action and reaction between two particles are equal in magnitude, opposite in direction, and collinear 2.1 Vectors Scalar: Any quantity possessing magnitude(size)only, such as mass, volume, temperature 6 Vector: Any quantity possessing both magnitude and direction, such as force, velocity, momentum The calculation of a vector must be in a reference frame. A scalar is independent of reference frames Given two vectors, the vectors will only be equal if both the magnitude and direction of both vectors are equal In Cartesian coordinate system, an arbitrary vector can be written in terms of unit vectors Addition of two vectors Subtraction of two vectors Inner product of Two vectors Vector Product of Two vectors 2.2 Forces Force is a vector quantity, a force is completely described by: 1. Magnitude2 Direction 3. Point of Application External force: Forces caused by other bodies acting on the rigid body being studied. EX--weight, pushing pulling Internal force: Those forces that keep the rigid body together Force in 3D Aforce F in three-dimensional space can be resolved into components using the unit vectors The vectors i, j, k are unit vectors along the x, y and z axes respectively 2.3 Moments The moment of force About point O is defined as the vector product where r is the position vector drawn from point O to the point of application of the force F The right-hand rule is used to indicate a positive moment. torque)Statics, Dynamics and Mechanical Engineering 1、Introduction Mechanics: Science which describes and predicts the conditions of rest or motion of bodies under the action of forces. The field of Classical Mechanics can be divided into three categories : . 1) Mechanics of Rigid Bodies 2) Mechanics of Deformable Bodies 3) Mechanics of Fluids Rigid-body mechanics ( General mechanics ) Statics deals with bodies that are in equilibrium with applied forces. [ Such bodies are either at rest or moving at a constant velocity. ] . Dynamics deals with the relation between forces and the motion of bodies. [ Bodies are accelerating. ] Notes ➢ Rigid-body mechanics is based on the Newton’s laws of motion. . ➢ These laws were postulated for a particle, which has a mass, but no size or shape. . ➢ Newton’s laws may be extended to rigid bodies by considering the rigid body to be made up of a large numbers of particles whose relative positions from each other do not change. Newton’s Laws of Motion 1st law. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. 2nd law. If the resultant force acting on a particle is not zero, the particle will experience an acceleration proportional to the magnitude of the force and in the direction of this resultant force. 3rd law. The mutual forces of action and reaction between two particles are equal in magnitude, opposite in direction, and collinear. 2.1 Vectors ❖ Scalar : Any quantity possessing magnitude (size) only, such as mass, volume, temperature. ❖ Vector : Any quantity possessing both magnitude and direction, such as force, velocity, momentum. The calculation of a vector must be in a reference frame. A scalar is independent of reference frames. Given two vectors, the vectors will only be equal if both the magnitude and direction of both vectors are equal. In Cartesian coordinate system, an arbitrary vector can be written in terms of unit vectors as Addition of Two Vectors Subtraction of Two Vectors Inner Product of Two Vectors Vector Product of Two Vectors 2.2 Forces Force is a vector quantity, a force is completely described by:1.Magnitude2.Direction3.Point of Application External force : Forces caused by other bodies acting on the rigid body being studied. ( Ex.-- weight, pushing, pulling. ) Internal force : Those forces that keep the rigid body together. Force in 3D A force F in three-dimensional space can be resolved into components using the unit vectors : The vectors i, j, k are unit vectors along the x, y and z axes respectively. . 2.3 Moments The moment of force F about point O is defined as the vector product : where r is the position vector drawn from point O to the point of application of the force F. . The right-hand rule is used to indicate a positive moment. ( torque )