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1. Physical Entities in Engineering Mechanics Mass, Time, Space Length: It is a concept to measure linear distances. The diameter of a cylinder may be 300 mm, the height of a building may be 15 m. Actually, metre is the unit of length. Displacement Displacement is defined as the distance moved by a body/particle in the specified direction. Velocity: The rate of change of displacement with respect to time is defined as velocity. Acceleration: Acceleration is the rate of change of velocity with respect to time. Thus,𝑎=𝑑𝑣/𝑑𝑡 Momentum: The product of mass and velocity is called momentum. Thus,Momentum = Mass × Velocity

2. Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous medium (also called a continuum) rather than as discrete particles. A continuum model assumes that the substance of the object completely fills the space it occupies. Particle A body whose dimensions are negligible when compared with the distances or the length involved in the discussion of its motion is called a particle. For mathematical descriptions, a particle denotes a body in which all the materials are concentrated at a point. For example, while studying the motion of sun and earth, they are considered as particles since their dimensions are small when compared with the distance between them.

3. DIMENSIONAL ANALYSIS Any physical variable can be described using qualitative and quantitative approaches. The qualitative description is known as dimension and quantitative description is known as unit. The dimensions of basic quantities are selected as basic dimensions and dimensions of other variables are derived. Dimensions are classified as 1. Absolute system (MLT system) 2.Gravitational System (FLT System) Dimensional Homogeneity

4. Two particles of mass m1 and m2 are attracted towards each other along the line connecting them with a force whose magnitude ‘F’ is proportional to the product of their masses and inversely proportional to the square of the distance (r) between them. Attraction between two particles

5. Thus, the weight of the particle is It is sufficiently accurate to assume in most engineering computations

6. Two forces acting on a particle may be replaced by a single force, called their resultant which can be obtained by drawing diagonal of the parallelogram, which has the sides equal to the given forces. F2= 3 units F1= 4 units 4 units 4 units 3 units 3 units

7. F1 F2 O F1 F2 O F3