STUDY4MECHANICAL for Mechanical Engineers

The thermodynamic system can be classifier in three ways open systems, closed systems, and isolated system. The main difference between open and closed system is that the matter can be exchanged with the surrounding in case of an open system, whereas matter cannot be exchanged with the surrounding in the closed system. Now let us check out some more difference between them in details below to know more about it.  What is an open system? The thermodynamic system where energy and matter can be exchanged with its surrounding.  What is a closed system? The thermodynamic system where only energy can be exchanged with its surrounding.  Difference between open and closed system: Mass of the system will change with time in an open system, whereas it is constant in case of a closed system.  An open system has boundaries which are not closed, and boundaries are completely closed in a closed system.  In an open system, difficult to control energy flow and other pa

What is a thermodynamic system? A thermodynamic system can be defined as a body of matter or radiation, bounded in space by walls, with defined permeabilities, which separates it from its surroundings. The surroundings may include other thermodynamic systems or physical systems that are not a thermodynamic system. You may arise question what is surroundings? The thermodynamic system has its boundaries, and anything outside the boundaries is called surroundings.  Thermodynamic system and types Types of the thermodynamic system: The thermodynamic system can be classified into three types such as a closed system, open system, an isolated system. There is a minor difference between an open and closed system . Let us discuss that in details one by one.  What is a closed system? A closed system is a physical system whose boundaries are determined by the space of the working substance occupied in it. This system does not allow certain types of transfers, through the

What is thermodynamics? Thermo means Energy and Dynamics means Pattern of Change In a basic and simple word, thermodynamics is the study of changes in energy associated with physical and chemical reaction. In another word, thermodynamics is the study of the effect of work, heat and energy on a system.  If the changes in energy are studied from a chemistry point of view, then it is called chemical thermodynamics.  The study of changes in energy and chemical reaction is based on the basis of a principle called as laws of thermodynamics that we discussed in brief. These are known as the Zeroth, First, Second and Third law of thermodynamics. 

What is speed? Speed is the rate of change of displacement with respect to its surrounding. It is a scalar quantity as the speed of the body is irrespective of its direction. SI Unit: m/s  Symbol: S What is the velocity? The rate of change of displacement with respect to its surrounding is called velocity, in a particular direction. It is a vector quantity as the velocity is always expressed in a particular direction.  Formula: v = S / t  Symbol: v = Velocity, S = Speed, t = Time Unit: m/s What are the acceleration and retardation? The rate of change of velocity of the body is called acceleration. It is positive when the velocity of a body increases with time and negative when the velocity of a body decreases with time. The negative acceleration is called retardation.  Formula: a = v / t  Symbol: a =  Acceleration, v = velocity, t = time Unit: m/s 2

The theorem of Lami is related to the system of forces such as the magnitude of three coplanar, concurrent and non-colinear forces which keep a body in static equilibrium.  Lami's Theorem Lami's theorem statement: Lami's theorem states that if three concurrent, coplanar, or non-colinear forces acting at a point which is in equilibrium, then each force is proportional to the sine angle between  the other two forces.  Now we consider the three forces A, B and C acting on a rigid body or particle and all forces making respective angles  α,  β  and γ with each other  as we have shown in the above figure. Now we can represent the Lami's theorem in mathematically : A / sin α    = C / sinγ  = B / sinβ

Newton's laws of motion-related with the motion of an object to the force acting on it. There are three laws of newton are together laid the foundation for classical mechanics. They all describe the relationship between the body and the force acting upon the body. Let us check it out one by one below.  Newton's first law of motion:  The first law of Newton states that an object continues to remain in the state of rest or uniform motion in a straight line unless acted upon by an external force. It is because of inertia, that object will remain in their state of motion unless a force acts to change the motion.  Example: Wearing a seat belt while driving a car. If any accident occurs, or if brakes are applied to the car suddenly, the body will tend to continue its inertia and move forward.  Newton's second law of motion:  The second law of Newton states that the rate of change of momentum or acceleration of a system is directly proportional to and

What is a free body diagram? In mechanics, a graphical, dematerialized, or symbolic representation used to visualize the applied forces, moments, and resulting reactions on a body in a given condition is called a free body diagram. A free body diagram used to draw a scaled drawing. It is a diagram that is modified as it solves the problem. There are flexibility and art to the process. The iconography of a free body diagram, not only how it is drawn but also how it is interpreted and depends upon how a body is modeled.  Features of free body diagram: The free-body diagram consists of the following. A coordinate system A simplified version of a body Force was shown as straight arrows pointing in the direction they act on the body The moment was shown as curved arrows pointing in the direction they act on the body In order to effectively use a free body diagram to analyze the motion of the body, you must know four skills.  Identify the force acting on the

The body is said to be in equilibrium if the resultant of all the force acting on a body is zero. There are mainly two types of equilibrium. One is translational and another one rotational equilibrium. Let us check out the equilibrium formulas for each type of force system following below.  Formulas of equilibrium of force system:  Concurrent force system:  ∑ F x = 0 ∑ F y = 0 Parallel force system: ∑ F = 0  ∑ M o = 0  Nonconcurrent nonparallel force system:  ∑ F x  = 0 ∑ F y  = 0 ∑ M o  = 0  Where  ∑ F x  is the sum of all forces in the x-direction ∑ F y  is the sum of all forces in the y-direction ∑ F is the sum of all forces ∑ M o  is the sum of the moment at any point O Important points on equilibrium force: Two forces are in equilibrium if they are equal and opposite direction.  Three coplanar forces in equilibrium are called concurrent forces.  Three or more concurrent forc

D-Alembert's principle is a statement of fundamental classical laws of motion. It is also known as Lagrange D-Alembert's principle. It is discovered by French physicist and mathematician Jean le Rond d'Alembert.  Principle of d'Alembert: D-Alembert's principle states that the resultant force acting on the body together with the inertia force or reversed effective force are in equilibrium.  Consider a rigid body that is acted upon by a system of force . The system may be reduced to a single resultant force on the body whose magnitude is given by the product of mass and linear acceleration of the body. According to newton's second law of motion,  F = ma   P - ma = 0  P + Fi = 0  Where Fi is called an inertia force. 

Moment and  torque are key concepts often encountered by students studying mechanics. These terms also confused students most often because of the similarity between them. There are some similarities between moment and torque but there are noticeable differences too. The difference between them will be explained in this article. Let us check out points on the difference between a moment and the torque discussed below. What is a couple OR moment?   In mechanics, a couple refers to two equal and opposite forces, whose line of action is different from a couple. The couple also called a force couple or pure moment. What is Torque? The twisting force that causes motion is known as torque refers to the turning effect. The point of the rotation of the object is called the axis of rotation. The concept of torque originated with the studies by Archimedes when ideas of the usage of the levers. Points on the difference between moment and torque: The moment used in

Definition of Torsion:  The action of twisting or the state of being a twist of the one end of an object related to another end. The torsion is the twisting of an object due to an applied torque.  Torsion Formula:  For shaft,  T = J T /  τ  × r =  J T  / l  ×  G ψ   Where, T = Applied torque τ =  Tau J T  = Torsional Constant r = Perpendicular distance between rotational axis and point in the section l = Length of an object ψ = Angle of twist  G = Shear modulus ( Modulus of rigidity) J T  G = Torsional rigidity  In noncircular cross-sections, twisting is applied by a distortion called warping, in which transverse sections don't remain plane. Torsion Units: SI Unit: N/m2 = Pascal (Pa) Other Unit: Pounds per square inch (psi) 

Torque and torsion are key concepts often encountered by students studying mechanics.  These terms also confused students most often because of the similarity between them. There are some similarities between torque and torsion but there are noticeable differences too. The difference between them will be explained in this article. Let us check out points on the difference between torque and torsion discussed below.  What is Torque? The twisting force that causes motion is known as torque refers to the turning effect. The point of the rotation of the object is called the axis of rotation. The concept of torque originated with the studies by Archimedes when ideas of the usage of the levers. What is Torsion? The action of twisting or the state of being a twist of the one end of an object related to another end. The torsion is the twisting of an object due to an applied torque.  Points on the difference between torque and torsion: Torque is twisting force we app

Definition of Torque:   The twisting force that causes motion is known as torque refers to the turning effect. The point of the rotation of the object is called the axis of rotation. The concept of torque originated with the studies by Archimedes when ideas of the usage of the levers. Force is what causes a body or object to accelerate in linear kinematics, likewise, torque is what causes an angular acceleration. Thus torque can be defined as the rotational equivalent of linear force.  Types of torque:  Torque can be classified into two types following below.  Static Torque The torque that does not produce an angular acceleration is called static torque. Example: A person pushing a closed-door is applying a static torque because the door is not rotated despite the force applied.  Dynamic Torque The torque that does produce an angular acceleration is called dynamic torque.  Example: The drive shaft in a racing car accelerating from the start line ex

Torque and couple are key concepts often encountered by students studying mechanics. These terms also confused students most often because of the similarity between them. There are some similarities between torque and couple but there are noticeable differences too. The difference between them will be explained in this article. Let us check out points on the difference between torque and the couple discussed below.  What is Torque? The twisting force that causes motion is known as torque refers to the turning effect. The point of the rotation of the object is called the axis of rotation. The concept of torque originated with the studies by Archimedes when ideas of the usage of the levers. What is a Couple? In mechanics, a couple refers to two equal and opposite forces, whose line of action is different from a couple. The couple also called a force couple or pure moment. Points on the difference between torque and couple:  The couple is two equal but opp

Definition of angle of repose:  The angle of repose is also called a critical angle of repose. The angle of repose is the steepest angle of dip or descent relative to the horizontal plane to which is possible to pile material without slumping.  The angle of repose can be range from 0 0 to 90 0 . Angle of repose The angle of inclination  α of the plane is equal to the limiting angle of the friction   ϕ. It is the angle of the plane to the horizontal, at which the body just begins to move down the plane.  The formula for confirming that is the following below.  W sin  α = F =  µ × R N = µ  W cos  α  tan  α =  µ = tan  ϕ  α =   ϕ  Uses of the angle of repose: The angle of repose is used in the design of equipment for the processing of particulate solids.  

Definition of limiting angle of friction:  The angle between resultant reaction R and normal reaction R N is known as limiting angle of friction. Let us check out the formula of the limiting angle of friction to know more about it.  Limiting Angle of friction Let us consider an object of weight W resisting on a horizontal plane B. A horizontal force P is applied to the body, no relative motion takes place until the force P applied is equal to the force of friction F, acting opposite to the normal direction. The magnitude of the force of friction is given by the formula below.  F =  µ W =  µ  R N   Where  R N  = Normal reaction  When the body just begins to move, it is in equilibrium under the action of a force which is following below, in the limiting case.  Weight of the body W A horizontal force applied P Reaction R between the body and the plane  The resultant reaction R which makes and angle  ϕ with the normal reaction  R N

Definition of friction:  A force that is acting in the opposite direction to the motion of the body is called friction. Friction is resistance to the motion of one object moving relative to another object.  Frictional force f = µ × N Where, f = frictional force µ = coefficient of friction  N = Normal force Types of friction:  Friction mainly classified into two types.  Static friction  Dynamic friction  The friction experienced by a body, when an object is at rest is known as static friction.  The friction experienced by a body, when the body is in motion is known as dynamic friction. It is also called kinetic friction. Kinetic friction also divided into two types which are the following below.  Sliding friction Rolling friction The friction experienced by a body, when the one body slides over another body is known as sliding friction.  The friction experienced by a body, when balls or rollers are plac

Definition of a moment of inertia:  The moment of inertia also called a mass moment of inertia, angular mass or rotational inertia. The moment of inertia is a quantity expressing a tendency of the body to resist angular acceleration about a rotational axis. It is similar to how mass determines the force needed for the desired acceleration.  Mathematically, the moment of inertia is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.  Units of a moment of inertia:  SI Unit: kg m 2 Other Unit: lbf ft s 2 Dimension: M L 2 Moment of inertia usually denoted by I. 

Definition of center of gravity: The center of gravity is the point that shows the average location of the weight of an object. The point through which the whole mass of body acts, irrespective of the position of the body is known as a center of gravity OR centroid.  The plain geometrical figures such as rectangle, triangle, circle all have only areas not mass. The center of an area of all such figures is known as a center of gravity of the area of the body. Every object has one and only one centroid.  Types of figure and its center of gravity: The center of gravity of a uniform rod is at a middle point of the rod.  The center of gravity of a rectangle or parallelogram lies at a point where its diagonal intersects.  The center of gravity of a triangle lies at a point where the three medians of the triangle intersect.   For a general shaped object, there is a simple mechanical way to determine the center of gravity which is the following below.  The point at