What is Applied Mechanics?
The fundamental concepts of mechanics, such as space, time, mass, and force, are units of measurement.
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| What is Applied Mechanics? |
That is, the measurement of a physical quantity relative to a standard measure is called a unit.
Method of Units:
The method by which the quantity of a commodity is determined is called the method or unit of measurement.
The methods or units of measurement are-
(1) Metric system or C, G, S, System
(2) British Method or F, P, S, Method
(3) M, K, S, Method
(4) S, I, Method.
Basic, SI and Composite Units:
Basic Unit: The units which do not depend on any other unit are called basic units. such as length, mass and time.
Compound Unit: All those units which are dependent on the base unit i.e. the unit whose value changes due to the effect of the base unit are called compound units. For example, force, work, area, volume etc.
SI units: c, g, s and f, p, s To eliminate the difficulty of the system, in 1968, scientists from all over the world met in Paris, France, and developed a single unit system for all countries. start up. , This system of units of measurement is called the International System or the S, I, system.
Zodiac:
The method by which it is possible to measure an object or object is called measurement of that object. Therefore, things that can be measured are called quantities.
There are two types of Rasi. Namely: Scalar Ratios and Physical Ratios.
Scalar, Physical, Fundamental and Composite Equations:
Scalar Equation:
Those physical quantities which can be completely expressed by values alone without the need for any direction are called scalar or one-dimensional quantities. Such as length, mass, time, work, temperature etc.
Any rasi related to physical science i.e. energy or material is called natural or material rasi.
principal amount:
The quantities whose measurement does not depend on any other quantity are called fundamental quantities.
Compound Yoga:
The equation obtained from an elementary equation is called a compound equation.
Vector Sum:
The physical quantities which require both a value and a day to be expressed completely are called vector quantities or direction quantities. Such as displacement, velocity, acceleration, deceleration, force, weight etc.
Vector Equation:
The physical quantities which require both a value and a day to be expressed completely are called vector quantities or direction quantities. Such as displacement, velocity, acceleration, deceleration, force, weight etc.
Co-vectors and Independent Fields:
Co-vector: If two like vectors acting in the same direction have the same value, then they are called co-vectors or similar vectors. The similarity of two vectors does not depend on the position of their origins.
Independent Vector: If the base point of a vector can be determined arbitrarily, then that vector is said to be an independent vector.
The plane vector is the zero vector:
Plane vector: Two or more vectors, if they lie in the same plane, are called plane vectors.
Zero Vector: The vector whose value is zero is called zero or zero vector. The zero vector is obtained by adding a vector to its opposite vector or dividing two equal vectors. The zero vector has no definite direction and has the same foot and vertex.
unit vector:
If a vector quantity has a value of one, it is called a unit vector. If the value of a vector is not zero, then dividing such a vector quantity by its value gives a vector quantity in the direction of that quantity. A single vector expression is represented by a cap (^) symbol instead of an arrow symbol.
Vector Addition and Subtraction:
Vector addition: A new vector is formed by the addition of two or more equal vectors. This new vector is called the product of two or more vector quantities. And the sum of the vectors to get the gain vector is called the subset of the gain vector. Finding the sum of two or more vector quantities using the quotient is called vector sum.
In the case of the sum of two vectors, the length of the straight line obtained by substituting the base of the second vector from the base of the first vector to the vertex of the second vector is the sum of the two vectors.
By doing this the direction of gain is from the foot of the first vector to the top of the second vector.
Vector Multiplication: The result of dividing one vector quantity by another vector quantity is called multiplication or division of the vector quantity.
The work that a stationary object does to set it in motion or can change its motion by acting on a moving object is called a force.
Ball Features:
a) It has a value, i.e. Kg, N, Lb etc.
b) It has the direction of the line of action, ie- OX, oy etc.
c) Forces have a nature, i.e. tensile force, compressive force.
d) the point of its application is known.
Mechanics:
The branch of physics in which the forces and their effects on objects are studied is called mechanics.
Name the classification of mechanics. mechanics is divided into three parts
(a) mechanics of rigid bodies
(b) mechanics of deformed bodies
(c) mechanics of fluids
What is Engineering Mechanics?
Engineers are engaged in planning, designing and manufacturing of various types of structures and machinery. It is necessary to have knowledge of the principles of mechanics to do the job smoothly and efficiently. So the branch of mechanics which discusses the principles and formulas of mechanics and their application techniques to solve various problems related to engineering work is called engineering mechanics or applied mechanics.
What Types of Applied Mechanics?
Applied Mechanics or Engineering Mechanics is mainly divided into two parts. i.e
(a) Statics and
(b) mobility.
The dynamics are again of two types:
(i) Kinetics
(ii) Kinematics.
The basic concepts of mechanics :
(1) space
(2) mass and
(3) force.
The formula for the parallelism of the ball:
If the value and direction of two forces acting at the same point can be expressed by two adjacent sides of a parallelogram, then the value and direction of the force of those two forces can be expressed by the diagonal drawn from that point of the parallelogram. can be done.
Ball's triangle formula:
If the value and direction of two forces acting at a point are indicated by two sides taken in the same order as in a triangle, then the value and direction of their force will be indicated by the third side taken in the opposite order of that triangle .
Ball Aim:
By substituting the work of several balls in one ball, the resulting ball is called a ladle ball. In the figure, the forces P and Q are R.
Ball Balance:
The balls are said to be in equilibrium if the value of two or more balls is zero.
Equilibrium equation:
The exponential sum of the forces along the x axis is zero: 2F = 0
The algebraic sum of the forces along the Y axis is zero: SF, = 0
The algebraic sum of the moments of the forces is zero: 2M = 0
Type: There are three types of ball balances viz.
i) Fixed Equilibrium
ii) Temporary Equilibrium and
iii) Neutral equilibrium.
Eligibility Conditions:
i) Displacement can happen in any direction of the object.
ii) can rotate on its axis without displacement.
iii) Displacement can occur in any direction including rotation.
iv) The object can remain completely stationary.
Equality Principle:
Dual principle: equal and opposite on the same line and in the same plane.
ii) Three ball principle: Two balls in the same line and have equal and opposite direction of the third direction.
Ball Force:
A force system is a combination of two or more forces acting on an object or a group of objects adjacent to each other.
Classification: Force systems acting on objects are classified as follows
i) Coplanar parallel force system.
ii) Planar concurrent force system
iii) Planar non-concurrent force system
iv) Non-coplanar parallel force system
v) Non-coplanar concurrent force system
vi) Non-coplanar non-concurrent forces
Frictional force:
When an object moves or tries to move on another object, the force produced in the opposite direction of motion when two objects are in contact is called frictional force. Frictional force and reaction force are proportional to each other, F R or, F = Rμ
It is of two types, namely - kinetic friction and static friction.
Coefficient of Friction and Angle of Friction:
Coefficient of friction:
The ratio of the limiting friction force and the perpendicular reaction force between two objects is called the coefficient of friction. It is denoted by μ.
μ = f/r
Friction Angle:
When the relative motion of two touching surfaces is constant, the angle formed by the tangential reaction, tangential reaction and tangential reaction of the force of friction is called the angle of friction.
μ = f/r = tan
Required formula:
* tanθ = μ = f/r
For P(min) the frictional force F will act in the direction of P.
* For P(max) the frictional force F will act opposite to P.
* For sliding, HF = 0, VF = 0
* M = 0 to reverse
Note: Work that requires less force or energy will be done first. The action with the lower value will take place first.
Lamy's formula:
Lamy's Law: If three plane forces acting on an object at the same time strike an equilibrium, then the value of each force is proportional to the sine of the interior angles of the other two forces.
here is,
P/Sinα=Q/Sinß=R/SinY
According to proof and illustration,
OA = BC = P; ob = ac = q;
OC = OD = R
In AOC,
AOC = 180 -
BOC = ACO = 180 - α
CaO = 180 - {180 - + 180 - α}
= 180 - 180 + - 180 + α
= α + = 180
but α + + = 360
Or, α + + -180 =180
Or, α + + + 180 = 180 - Y
Or, CAO = 180 - Y
Applying a single rule to AOC, we get,
P / Sin∠ACO = Q / Sin∠AOC = R / Sin∠CAO
Or, p/sin(180 - α) = q/sin(180 - ) = r/sin(180 - y)
P /sinα = Q/sinß = R/sinY (Prove)
Important Notice:
i) The value of R is given but not specified, then R must be calculated by force.
ii) Ladbi is said and said 0 mark is fixed, then there is no need to reverse the Ladbi.
iii) If said to be in equilibrium, there is no need to reverse the pair.
iv) If we talk about equality, then the meaning should be reversed.
v) If nothing is said, only the word is said then the word should be reversed.
What is Work?
When a force is applied to an object, if the object moves from the place where the force is applied, it is called work. The force on the object is F and the object
If element S is a mathematical function, then W = F x S = FS
The absolute units of work are:
1. Same logic of work in CGS method,
2. The unit of work in FPS method is foot-pound,
3. The unit of work in the MKS system is kilogram-meter
4. The unit of work in SI system is joule.
Gravity Units of Work:
1. The unit of work in CGS method is gram-cm,
2. The unit of work in FPS method is foot-pound,
3. The unit of work in the MKS system is kilogram-meter.
4. The unit of work in the SI system is the Newton-meter.
Terms of Disclosure of Working:
work = force x displacement
or, w = f * l
= mass x acceleration x displacement [force = mass x acceleration]
= mass x (velocity/time) x acceleration [acceleration = velocity/time]
= mass x displacement/time^2 x displacement [velocity = displacement/time]
= mass x displacement^2/time^2
So, work, W = M * L^2/T^2 = ML-^2T-^2
What is Power?
The rate at which a force acts on an object is called power. That is, the work done at the same time is called power. If w quantity of work is done in t time, then power, P = W/t
Absolute units of power:
1. In CGS system, the unit of power is arg/s,
2. The unit of power in FPS system is foot-pound/second,
3. The unit of force in the MKS system is kilogram-meter/second,
The unit of power in the SI system is joule/second.
Gravitational units of power:
1. In CGS system, the unit of force is gram-cm/second,
2. The unit of power in FPS system is foot-pound/second,
3. The unit of force in the MKS system is kilogram-meter/second,
4. The unit of power in the SI system is the watt newton-meter/second.
Practical units of power:
1. Mechanical unit of power (horsepower)
2. The power unit of power is the watt (watt).
power level:
power = work / time
= (force x displacement)/time [work = force x displacement]
= (mass x acceleration x displacement) / time [force = mass x acceleration]
= {mass x (displacement/time^2) x displacement}/time [acceleration = velocity/time]
= mass x (speed)^2 / (time)^2
= ml^2t^2
75 kg-meter or 550 foot-pounds per second or 4500 kg-meter per minute is converted to one horsepower or one hp. is called. It is the practical mechanical unit of power. Mathematically one horsepower = 550 foot-pounds/second
= 3300 ft-meter/minute
= 75 kg-m/s
= 4500 kg-m/min.
Relationship Between Horse Power (HP) and Kilowatt:
we know
1 hp = 746 watts = 0.746 kW
Therefore, kW = HP/0.746
= 1.34 hp
Indicated horsepower or IHP:
The amount of actual power produced by the combustion of fuel in an engine cylinder is called idized horsepower. It is abbreviated as IHP.
Brake Horsepower or BHP:
No engine can make all the power it actually produces. This is because some amount of power is wasted due to friction between the different moving parts of the engine. After this the amount of electricity is wasted
It is called brake horsepower or break hour power as it is used for work. It is abbreviated as BHP.
Engine efficiency or performance:
The ratio of brake horsepower and rated horsepower is called the mechanical efficiency or performance of the engine.
Mechanical Efficiency or Performance = Brake Horsepower / Built Inefficiency
Or, Efficiency, = B.H.P/ I.H.P
Factors to be considered in determining engine horsepower:
1. Average working pressure of cylinder during stroke = P kg/sqcm
2. Area of cross section of piston = A sq cm
3. Stroke length = l m
4. Number of strokes per minute = N rpm (Revs per minute)
Thus, work done per stroke = PLAN
Hence, I.H.P = Scheme/4500
= plan/75
Energy is the ability to do work. Power is measured by work.
What is Mechanical Energy?
The energy used for human work with the help of machines is called mechanical energy. There are two types of mechanical energy. ie:
1. Kinetic Energy
2. Stability
kinetic energy:
The energy received by a moving object for its motion is called kinetic energy. That is, the total work done by a moving object before coming to rest is kinetic energy. Mathematically, Kinetic Energy, KE = 1/2
mv^2
Stability:
The energy received by an object for its current position or position is called the static energy of the object. That is, the energy stored due to its position in the object is called static energy. Static force is measured by the work done to move an object from one place to another. Mathematically,
Static Energy, PE = mgh = Wh
Factors to be considered in determining engine horsepower:
1. Average working pressure of cylinder during stroke = P kg/sqcm
2. Area of cross section of piston = A sq cm
3. Stroke length = l m
4. Number of strokes per minute = N rpm (Revs per minute)
Thus, work done per stroke = PLAN
Hence, I.H.P = Scheme/4500
= plan/75
Relationship between mechanical energy and thermal energy:
Heat is generated when mechanical energy overcomes frictional barriers. The unit of heat is called kilocalorie. To heat 1 kg of water to 1 degree Celsius, 1 kcal of heat is required.
641.1 kcal = 1 horsepower-hour (IHP-hr.)
Heat and work are interchangeable. That is, a certain amount of mechanical work is required to generate a certain amount of heat.
Therefore, W = amount of mechanical work
H = amount of heat produced by work
Hence, W = JH [Here, J = constant]
Relationship between electrical energy and mechanical energy:
Watt is a unit of electrical power
and Watts = Amps x Volts
1 kW = 100 watts
1 hp = 746 watts
Therefore, HP = Watts/746
Or, 1 kW = (1000/746)x4500x60
= 361930.3 kg-m.
Relationship between heat, electricity and mechanical energy:
1. Electricity is generated by moving turbines with water flowing from high places. In this case, mechanical energy, electrical energy
2. Trains run on steam engines with the help of heat. In this case, thermal energy is converted into mechanical energy.
3. The fabric is ironed with the help of heat from an electric iron. In this case, electrical energy is converted into thermal energy.
If a force of one newton is applied to an object and the object moves one meter in the direction of the force, the amount of work done is called a joule.
What is SI Units of Work and Power?
The SI unit of work is joule and the SI unit of power is joule/second or watt.
Problem 1. An elevator weighing 200 kg is moving upwards with a speed of 7.2 kmph. If the lift efficiency is 70%,
But calculate the amount of horsepower.
given,
Weight, W = 200 kg
Distance = 7.2 km/h
= (7.2 x 1000) / 60x60
= 2 m/s
Therefore, work per second = 200 x 2 = 400 kg-m
HP = Work done / 75
= 400/75
= 5.33 hp = bhp
Efficiency, = bhp/ihp
Therefore, IHP = BHP /
Or, IHP = 5.33/0.70 [η = 70% = 0.70]
= 1.20 hp
Moments:
The frictional action of an external force on an object is called moment.
moment = force x vertical distance
There are two types of moments, namely (i) positive moments (ii) negative moments:
Verignon's Maintenance Policy:
If more than one plane force acts simultaneously on an object, then the sum of the moments of the forces about a given axis is equal to the momentum of their sum on the same axis.
Torque:
Torque or torque refers to the tendency of an object to rotate around an axis, axis or axis. Just as force refers to push or pull, torque refers to the tendency of an object to rotate around its axis. Mathematically, torque is the vector product of the force acting on an object rotating relative to an axis and the object's velocity. Distance is distance. Axis.
To put it simply, torque refers to the measure of the tendency of an object to rotate around its axis. For example, when loosening a nut or bolt attached to a machine, a torque is generated in the handle of the wrench when a wrench is attached to it and is rotated.
definition:
The product of the position vector of that point and the force applied at the point where the force is acting on an object moving with respect to a letter is called rotational force or torque.
However, it is denoted by M when it is described as wedges or ball wedges.
The value of torque depends on three factors: the applied force (F), the radius vector (r) and the angle between the direction of the force and the radius vector (θ).
Musically:
= r * f
= Fsinθ
Force is the vector of moment or force, r is the distance or radius vector of the point of application of force from the axis of rotation, F is the force acting on the object, the vector is expressed by the multiplication ×, is the angle between F and r .
When two equal, parallel and opposite forces act at two points on an object, but their lines of action are different, they are called a couple.
What is Centroid and Center of Gravity?
Center: A geometric figure like triangle, rectangle, square, polygon, circle etc. which has only area but no mass, the center of such area is called centroid or centroid.
Center of Gravity: Due to the position of an object, the point from which the force of attraction of the earth i.e. gravitational force or the weight of the object acts on it is called the center of mass. It is denoted by Cg.
moment of inertia:
The sum of the product of each small area of a region and the square of its distance from a fixed axis is called the moment of inertia of that region.
It is denoted by 'I'. Its units are m^4, cm^4, mm^4 etc.
Paul's moment of inertia:
The moment of inertia about a perpendicular axis is called Pella's moment of inertia. It is usually denoted by J.
That is, Paul's moment of inertia, I_zz = I_xx + I_yy
Radius of Transport:
If the mass of a solid body is assumed to be centered at a point such that the moment of inertia of the particle of the body centered about a fixed axis is equal to the moment of inertia of the whole body about that fixed axis, then
The distance of the centered object from the fixed axis is called the radius of revolution.
Ixx
Radius of revolution = K_xx = I_xx/A, K_zz = I_xx/A, K_yy = Iyy/A
What are you doing?
The moment of inertia about a perpendicular axis is called Pella's moment of inertia. It is usually denoted by J.
That is, Paul's moment of inertia, I_zz = I_xx + I_yy
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