Engineering Mechanics

N.S.G.

Presented by Nilesh Gaddapawar

Classification of MechanicsN.S.G.

Relativistic Mechanics In physics, special relativity (SR, also known as the

special theory of relativity or STR) is the accepted physical theory regarding the relationship between space and time

General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916[1] and the current description of gravitation in modern physics.

In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light.

Quantum Mechanics Quantum mechanics (QM – also known as quantum

physics, or quantum theory) is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the Planck constant.

It departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales.

Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter.

Quantum mechanics provides a substantially useful framework for many features of the modern periodic table of elements including the behavior of atoms during chemical bonding and has played a significant role in the development of many modern technologies.

Mechanics of Deformable Bodies:

The mechanics of deformable bodies deals with how forces are distributed inside bodies, and with the deformations caused by these internal force distributions.  These internal force produce "stresses" in the body, which could ultimately result in the failure of the material itself.

Principles of rigid body mechanics often provide the beginning steps in analyzing these internal stresses, and resulting deformations.  These will be studied in courses called Strength of Materials or Mechanics of Materials.

Mechanics of Fluids: The mechanics of fluids is the branch of mechanics

that deals with liquids or gases.   Fluids are commonly used in engineering

applications.  They can be classified as incompressible, or compressible.  While all real fluids are compressible to some degree, most liquids can be analyzed as incompressible in many engineering applications.  

Applications of fluid mechanics abound, from hydraulics and general flow in pipes to air flow in ducts to advanced applications in turbines and aerospace.  

The study of the mechanics of fluids will be studied in courses called Fluid Mechanics, Compressible Flow, Hydraulics, and others

Mechanics of Rigid Bodies:A rigid body is a body which does

not deform under the influence of forces.  

In all real applications, there is always deformation, however, many stuctures exhibit very small deformations under normal loading conditions, and rigid body mechanics can be used with sufficient accuracy in those cases.  

Classifiaction of Mechanics of rigid bodies

Mechanics of rigid bodies

Statics Dynamics

Kinematics

Statics

Fundamental Length:  Length is the quantity used to describe the position of a

point in space relative to another point. The universally accepted standard unit for length is the meter.

Time:  Time is the interval between two events. The generally accepted standard unit for time is the second.

Mass:  Mass is a property of matter.  Mass can be considered to be the amount of matter contained in a body.  The mass of a body determines both the action of gravity on the body, and the resistance to changes in motion.  This resistance to changes in motion is referred to as inertia, which is a result of the mass of a body.  The internationally accepted unit of mass is the kilogram.

Mass vs. Weight:  As stated above, mass is a fundamental quantity of matter.  It is independent of location and surroundings.  The weight of a body is the force exerted on the body due to gravitational attraction of the Earth. (W=mg)

             

Comparison of Mass and Weight

Sr. no.

Mass Weight

01 Mass is a property of matter. The mass of an object is the same everywhere.

Weight depends on the effect of gravity. Weight varies according to location.

02 Mass can never be zero. Weight can be zero if no gravity acts upon an object, as in space.

03 Mass does not change according to location.

Weight increases or decreases with higher or lower gravity.

04 Mass is a scalar quantity. It has magnitude.

Weight is a vector quantity. It has magnitude and is directed toward the center of the Earth or other gravity well.

05 Mass may be measured using an ordinary balance.

Weight is measured using a spring balance.

06 Mass usually is measured in grams and kilograms.

Weight often is measured in newtons, a unit of force.

07 Unit : Kilogram (Kg) W= mgUnit : newton (N)

Differences between distance and displacement:

Sr. no.

Distance Displacement

01 Distance is the length of the path travelled by a body while moving from an initial position to a final position.

Displacement is the shortest distance between the initial position and the final position of the body.

02 Distance is a scalar quantity. Displacement is a vector quantity.

03 Distance measured is always positive.

Displacement can be positive or negative depending on the reference point.

04 The total distance covered is equal to the algebraic sum of all the distances travelled in different directions.

The net displacement is the vector sum of the individual displacements in different directions.

05 There is always a distance covered whenever there is a motion.

Displacement will be zero if the body comes back to its initial position.

06 Unit: metre (m) Unit: metre (m)

For example: Q. Suppose you are observing an ant on the table, as shown in the diagram below. The ant moves from one corner of the table to the other corner. The blue irregular line shows the path of the ant.

For figure (B) & (C), Find Distance ?Displacement?

Answer :•For Length of this blue line is the distance covered by the ant.•The straight green line, which is the minimum distance between the two corners of the table is the displacement of the ant. Called the displacement.

Figure (B)

Figure (A)Figure (C)

Sr. no Speed velocity01 Speed is refers to "how fast an

object is moving."Velocity refers to "the rate at which an object changes its position."

02 Speed is a scalar quantity. Velocity is a vector quantity.

03 Speed is the rate of motion, or the rate of change of position.

velocity is the rate of change of displacement.

04 Speed is thus the magnitude component of velocity.

Velocity contains both the magnitude and direction components.

05 Explanation :How fast my hand is moving to slapped on your face, this is speed

Explanation :When you get the slap and changes your face from right to left.. i.e the rate at which your face changes its position, this is Velocity....

06 speed= total distance/time taken

velocity= displacement(shortest root from initial to the final position) /time taken including direction.

07 Unit: km/hr like 60km/hr, Unit: 60km/hr in east direction

Units of Measure The force unit is called a newton (N), and is defined

as the force required to accelerate a mass of 1 kg at a rate of 1 meter/sec.  So, we can write:

1 N = (1 kg)(1 m/s2)  or 1 N = 1kg.m/s2         The weight of an object is the gravitational force

which is exerted on that object which causes it to accelerate downward at the acceleration due to gravity So, we can write for the weight of a 1 kg mass:

W = mgW = (1 kg)(9.807 m/s2)W = 9.807 N

SI prefixesMultiplier

Prefix

Symbol

109 giga G

106 mega M

103 kilo k

10-2 centi c

10-3 milli m

10-6 micro µ

10-9 nano n

10-12 pico p

Newton’s laws of motion:

Fundamental laws: 1. Newton's first law

"An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This law is often called the law of inertia.Objects tend to "keep on doing what they're doing." In fact, it is the natural tendency of objects to resist changes in their state of motion. This tendency to resist changes in their state of motion is described as inertia.

Example :The motion of a kite when the wind changes can also be described by the first law.

Explanation to first law

2. Newton's second law

“ The rate of change of momentum is directly proportional to impressed force and takes place in the direction of force”.

Fundamental laws:

3. Newton's third lawFor every action there is an equal and opposite reaction.

Fundamental laws:

Vectors and ScalarsAll physical quantities (e.g. speed and force) are described by a magnitude and a unit.

VECTORS – also need to have their direction specified examples: displacement, velocity, acceleration, force.

SCALARS – do not have a directionexamples: distance, speed, mass, work, energy.

Addition of vectorsWith two vectors acting at an angle to each other:Draw the first vector. Draw the second vector with its tail end on the arrow of the first vector. The resultant vector is the line drawn from the tail of the first vector to the arrow end of the second vector.This method also works with three or more vectors.

4N

3N

Resultant vector

= 5N

4N

3N

Resolution of vectorsIt is often convenient to split a single vector into two perpendicular components.

Consider force F being split into vertical and horizontal components, FV and FH.

In rectangle ABCD opposite:

sin θ = BC / DB = DA / DB = FV / F

Therefore: FV = F sin θ

cos θ = DC / DB = FH / F

Therefore: FH = F cos θ

FFV

FHθ

C

BA

D

FV = F sin θ

FH = F cos θ

QuestionCalculate the vertical and horizontal components if F = 4N and θ = 35o.

FV = F sin θ= 4 x sin 35o

= 4 x 0.5736FV = 2.29 N

FH = F cos θ= 4 x cos 35o

= 4 x 0.8192FH = 3.28 N

FFV

FHθ

The moment of a forceAlso known as the turning effect of a force.

The moment of a force about any point is defined as: force x perpendicular distance from the turning point to the line of action of the force

moment = F x d

Unit: Newton-metre (Nm)

Moments can be either CLOCKWISE or ANTICLOCKWISE

Force F exerting an ANTICLOCKWISE moment through the spanner on the nut

QuestionCalculate the moments of the 25N and 40N forces on the door in the diagram opposite.

moment = F x d

For the 25N force:

moment = 25N x 1.2m

= 30 Nm CLOCKWISE

For the 40N force:

moment = 40N x 0.70m

= 28 Nm ANTICLOCKWISE

hinge

door

40N

25N

0.70 m

1.2 m

Couples and TorqueA couple is a pair of equal and opposite forces acting on a body, but not along the same line.

In the diagram above:total moment of couple = F x + F(d - x) = F d= One of the forces x the distance between the forces

Torque is another name for the total moment of a couple.