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Highlights of Basics and Statics of Particles

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Mechanical Engineering is a branch of science dealing with designing, construction and usage of machinery. It is very important that before you end up this chapter, certain details are highlighted in a specific manner.

The important points to note are:

  • When a body is in rest, its study is known as statics, whereas when a body is in motion, it is called dynamic. The Engineering mechanics is specifically divided into dynamics and static formats.
  • It is stated that a particle is a body that has extremely small volume and remains concentrated at a particular space.
  • Vector quantity is that quantity which remains specific by direction and magnitude.
  • To add up to all these factors comes the law of parallelogram. As per the law, when two forces acting on a particular point is represented in direction and magnitude, by two adjacent sides of the concerned parallelogram, then their result is represented by help of a diagonal of parallelogram that passes through this point.

When two forces P and Q act on a specific point, and it is taken that angle between two forces are ex, you can find the resulting solution as:

R=√(P^2+Q^2+2PQ cosα ) where it is taken that angle that is made by resultant when direction of force P is stated as:  tanθ=(Q sin⁡α)/(P+Q cosα )

  • As per the Lami’s theory, when there are triple forces acting on a point are in equilibrium, each of the forces are to be proportional to sine of the angle in regards to other two forces that are present.
  • When 2 forces, P and Q are acting at a certain angle A between them, the result is stated by: R=2P cos⁡〖 α/2〗
  • Perpendicular distance of line of action of that force from a certain point x Force is known as Moment of force about a certain point.
  • It is to be noted that while force causes linear displacement, angular displacement is caused by moment. There are 2 conditions to note that a particular body would be in equilibrium. They are: Net moment of forces about any point is taken to be as zero. Also, resultant force in any direction is taken to be as zero.
  • It is taken that One newton = 10^5 dyne.
  • The gravitational law of attraction is stated as: F=G (m_1×m_2)/r^2In this case, m1, m2 is termed as mass of the concerned bodies.

    G is termed as the Universal gravitational constant.

    F is termed as the force of attraction that is available between 2 bodies.

    r is taken to be the distance that is present between 2 bodies.

    Thus, these can be taken as some of the most important factors in case of understanding the basic concept of Mechanical Engineering.

    Co Planar Parallel Forces:

    When parallel forces have their lines of action parallel to each other, it is called Co Planar parallel forces. Here certain points are to be noted:

    • In this case, clockwise moment is taken in a negative value, while anticlockwise moment is taken as a positive value.
    • According to Varignon’s principle, the moment of a force on any specific point can be equated with algebraic sums of moments or its associated products at that specific point.
    • While calculating moment of force on any point, perpendicular distance between line of action of force and its point is to be multiplied with product of force that is present at that point.
    • It can be found that the like parallel forces act in the same direction while being parallel to each other. Quite contrarily, unlike parallel forces act in opposite directions with each other.
    • The two like parallel forces have a result that can be stated as the sum of 2 forces. It acts on a point between the lines to ensure that ratio distance while dividing is inversely proportional to magnitudes of the acting forces.
    • When 2 bodies are kept at a certain distance and 2 opposite but equal parallel forces act on them, then a force couple is formed. This helps in rotation of the body and moment can be termed as either force being in a perpendicular distance with them.
    • It is taken that a particular force, F when it is applied on a body at a certain position taken to be A, there are chances that it can be replaced with another force at point B of equal magnitude and when placed in the same direction, a couple is formed.
    • While calculating the amount of force, it can be seen that if result of multiple parallel forces is not taken at zero, then this whole system can be reduced to a singular force which can be equated to sum of forces in terms of algebraic notations. There is a specific process for getting this force and it can be said to have obtained from equating sum of all forces in algebraic terms with a single point force at a certain point. Hence, it needs to be seen that all the forces move around the same point.

    If the result of a number of parallel forces is taken to be zero, then either cases as equilibrium or static resulting couple can be obtained. If it is found that algebraic additional value of forces at a certain point does not amount to zero, then there are chances of resultant couple being present in that summation.  however, if it is found that algebraic value amounts up to zero, in that case, it is taken that the whole system was in a state of equilibrium.

Coplanar Concurrent Forces:

When the concerned forces are acting on the same line, it is specifically known as coplanar concurrent forces. Since they have the same line of action, they are often found to be intersecting on the common point that is placed between them.

Given such a scenario, there are certain points that have to be remembered while dealing with this context.

  • There are both analytical and graphical modes to determine the resultant forces that are acting on this same line. So every detail is placed after double checking.
  • While polygon law of forces is used for determining the coplanar concurrent forces that are acting on a particular line, it is to be remembered that by making use of sides of polygon they can be represented. As an important segment, magnitude is to be taken into consideration and direction of the closing side of polygon is taken into counting.
  • When 3 collinear forces are taken into counting as given F1, F2,F3, then the resulting count will be taken as R = F1 + F2 + F3. At times certain occasions arise when F2 acts in an opposite direction, even then this basic equation will remain.
  • If you find an equation as R =√((ΣH)^2+(ΣV)^2 ), it is to be remembered that ƩH is the sum of horizontal components in algebraic mode, ƩV is the vertical sum of all factors in algebraic mode, and tan θ = ((ΣV))/((ΣH) ) as the angle made.

Questions based on Theory:

These are specifically that set of queries that are based on theories.

  1. Parallelogram of forces? Define the law and give details of its usage?
  2. What do you understand by vector quantity and scalar quantity?
  3. If it is taken that 2 forces P and Q are specifically acting on a plane and the angle between them adds up to be α, so prove that R is the resulting force?
  4. What is Lami’s Theorem and the Triangular law of forces?
  5. How to prove that a newton is equal to 10^5 dyne?
  6. Define the values of Newton, Dyne, Moment of force and Meganewton?
  7. How force affects the moment and moments of a body?
  8. What is the concept of transmissibility of forces?
  9. What do you understand by Lami’s Theorem as well as Force resolved in a given direction?
  10. What do you understand by force and its resolution?
  11. What is the difference between the clockwise and anti-clockwise differences and how it is useful for the correct notation of force?

Questions on Coplanar Concurrent Forces:

  1. What do you mean by parallel forces on a body, unlike parallel forces and coplanar parallel forces?
  2. What is a moment of force? Show the algebraic sum of resultant forces when two coplanar forces are equated?
  3. Prove the resultant force of two forces as F and F1? Also show with example how resultant divides the two forces that are there.
  4. How to find the resultant force of 2 unlike parallel forces which are in magnitude?
  5. If parallel forces are zero, what does the result of it imply?
  6. How is Varignon’s principle defined? What are the differences associated with concurrent and non-concurrent forces along with coplanar and non-coplanar forces?
  7. In a system of parallel forces how to find a line of action in a mathematical manner?

State whether it is True or False?

  1. Is the force of gravitation on a body called weight?
  2. Is force the agency that causes motion?
  3. Is center of gravity in a body that specific point which is kept at a stricture for allowing the parallel forces to pass?
  4. Do coplanar forces always follow the same direct ion and have the same magnitude?
  5. Does a couple concept in force have the same line of action and 2 parallel and unequal forces acting on it?
  6. What does a specific vector diagram represent? Does it depict the direction, magnitude, and point of application only?

Sums:

  1. If resulting of 2 forces when they come at right angles is 10N, and the result is √148 with 60°, what is the magnitude of both these aspects?
  2. What is the resulting force and magnitude associated with 2 forces as 9N and 12N, where angle between these given forces come down to 30°?

 With this detailed analysis and sums given your concept regarding this topic will be completely clarified.

 

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