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Saturday, 16 November 2019

November 16, 2019

DIFFERENCE BETWEEN MOMENT OF FORCE AND MOMENT OF COUPLE

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force systemprinciple of transmissibility of forces and its limitations, classification of force systembody force and surface force in mechanics.  

Now, we will be interested to understand here the difference between moment of force and moment of couple in engineering mechanics  with the help of this post. first we will see here the basics of moment of force and after that we will find out the moment of couple in engineering mechanics. 

Further we will secure the basic difference between the moment of force and moment of couple with the help of this post. 

Moment of a force in mechanics 

As we have studied earlier that the effect of a force on a body or object will be the combination of translation motion i.e. linear motion and rotational motion. Only translation or only rotational motion will be in exceptional cases. 

Moment of force 

Moment of force is basically defined as the measure of the tendency of the force to rotate the body about the point of interest. 

Let us consider the following figure where a force F is acting at a point on the body. Let us think that we need to find out the moment of this force F about a point P which is an arbitrary point on the body as displayed here in following figure. 


Let us assume that r is the positional vector of the force F with respect to the arbitrary point P.
Therefore, we can write down the equation to find out the rotary or rotational effect of force F about the arbitrary point P as mentioned here. 


Above equation is representing the moment of force in vector form. Let us now find out the magnitude of the moment of force. 

Moment of force = Force x Perpendicular distance from the pivot point to the line of action of the force

Unit of moment of force = Unit of force x unit of distance 
Unit of moment of force = N x m  
Unit of moment of force will be N-m in SI system. 

Sign convention for moment of force 

We need to consider and visualize physically how the force is trying to rotate the object. In order to find out the sign of moment or moment of force i.e. positive or negative moment, we use the concept of right-hand thumb rule. 

If force is trying to rotate the object in anti-clock wise direction, moment of force will be taken as positive. 

Let us see here the following figure, when we will close the finger in anti-clock wise direction, thumb will be in upward direction and it will be the indication for positive moment of force in our sign-convention for moment of force.

Similarly, if force is trying to rotate the object in clock wise direction, moment of force will be taken as negative. 

Therefore, we need to take care the sign conventions for moment of force and we must note it here that moment of force will be always expressed with its magnitude, unit of measurement and sense of rotation i.e. positive or negative sign. 

Important notes 

There are few very important points that we need to keep in our mind while dealing with the moment of force. 
  1. Like force, Moment of force is also a vector quantity. 
  2. Moment of force and force are sliding vectors. 
  3. Anti-clock wise rotation or counter clock wise rotation about the pivot will be taken as positive. 
  4. Clock wise rotation about the pivot will be taken as negative. 
  5. Moment of force will be considered as the function of magnitude of the force and the moment arm. 
  6. Unit of moment of force will be N-m in SI system. 

Now, we will see the concept of moment of a couple here.   

Moment of a couple 

The force system consisting of two equal and parallel but non-collinear forces with opposite sense will be termed as couple. 

Let us consider the following figure where two equal and parallel forces are acting on a body in opposite direction. We will now understand here the moment of a couple for the given force system.
Let us consider an arbitrary point P and position vectors for these two forces are r1 and r2 as displayed here in above figure. 

Moment of these two forces about arbitrary point P could be determined with the help of following equation as mentioned below 

Where, a is the difference between position vectors r1 and r2.  

From above equation, we can conclude that there will be net moment M as mentioned above due to these two forces those are equal, parallel, non-collinear and with opposite sense. 

Where, d will be the perpendicular distance between the line of action of these two forces as shown in the above figure. 


Difference between moment of force and moment of  couple 

There is one very basic and important difference between two above. 

Let us think, what is the difference???

The value of moment of a couple will not be dependent over the location of point of interest. Moment of a couple will be a free vector. 


While in case of moment of force, moment of a force will be dependent over the point of interest.  

Therefore, we have seen here the basics of moment of force, moment of couple and also the difference between these two with the help of this post.  

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, varignon's theorem in engineering mechanics.  

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google 

Also read 

November 16, 2019

MOMENT OF COUPLE IN MECHANICS

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force systemprinciple of transmissibility of forces and its limitations, classification of force systembody force and surface force, moment of a force and Varignon’s theorem in mechanics. 

Now, we will be interested to understand here the concept of moment of a couple with the help of this post.  

Moment of a couple 

The force system consisting of two equal and parallel but non-collinear forces with opposite sense will be termed as couple. 

Let us consider the following figure where two equal and parallel forces are acting on a body in opposite direction. We will now understand here the moment of a couple for the given force system.
Let us consider an arbitrary point P and position vectors for these two forces are r1 and r2 as displayed here in above figure. 

Moment of these two forces about arbitrary point P could be determined with the help of following equation as mentioned below 

Where, a is the difference between position vectors r1 and r2.  

From above equation, we can conclude that there will be net moment M as mentioned above due to these two forces those are equal, parallel, non-collinear and with opposite sense. 

Where, d will be the perpendicular distance between the line of action of these two forces as shown in the above figure. 

There is one very important observation from above equation. The value of moment of a couple will not be dependent over the location of point of interest. Moment of a couple will be a free vector. 

Let us recall the concept of moment of a force, moment of a force will be dependent over the point of interest. 

Therefore, we have seen here the concept of moment of a couple with the help of this post. Further we will find out the difference between the moment of a force and moment of a couple.   

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com.   

Further we will find out, in our next post, difference between moment of a force and moment of a couple  in engineering mechanics. 

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google   

Also read  

Thursday, 14 November 2019

November 14, 2019

VARIGNON'S THEOREM STATEMENT AND PROOF

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force systemprinciple of transmissibility of forces and its limitations, classification of force system, body force and surface force and moment of a force in mechanics. 

Now, we will be interested to understand here a very important theorem i.e. Varignon’s theorem in mechanics with the help of this post. 

Varignon’s theorem in mechanics 

According to the varignon’s theorem, the moment of a force about a point will be equal to the algebraic sum of the moments of its component forces about that point. 

Let us consider the following figure where a force F is acting at a point P on a body as displayed here. 

Let us consider that the coordinate for point P is (x, y) as displayed in the figure. 

Force F could be written as mentioned below 

F = Fx i + Fy

Where, 
Fx = The component of force F in x direction 
Fy = The component of force F in y direction 
i and j are the unit vectors in x and y directions respectively. 

Let us assume that r is the positional vector and could be written as mentioned below 

r = x i + y

Let us find out and assume that the perpendicular distance of the line of action of force F from the point O is d. 

Moment of the force F about the point O will be given by following equation as mentioned below 

 

Where, k is the unit vector in z direction. 

We can also write down the equation for moment of force about the point O and it will be as mentioned here. 


From above equation, we can say that the magnitude of the moment of a force F about a point O will be equal to the algebraic sum of the magnitudes of the moments of its component forces about that point i.e. about point O. 

Therefore, we have seen here the concept and explanation of Varignon’s theorem with the help of this post.  

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com.  

Further we will find out, in our next post, moment of a couple in engineering mechanics.   

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google  

Also read  

Wednesday, 13 November 2019

November 13, 2019

MOMENT OF FORCE IN ENGINEERING MECHANICS

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force systemprinciple of transmissibility of forces and its limitations, classification of force system, body force and surface force in mechanics.  

Now, we will be interested to understand here the moment of force in engineering mechanics  with the help of this post. 

Moment of a force in mechanics 

As we have studied earlier that the effect of a force on a body or object will be the combination of translation motion i.e. linear motion and rotational motion. Only translation or only rotational motion will be in exceptional cases. 

Moment of force 

Moment of force is basically defined as the measure of the tendency of the force to rotate the body about the point of interest. 

Let us consider the following figure where a force F is acting at a point on the body. Let us think that we need to find out the moment of this force F about a point P which is an arbitrary point on the body as displayed here in following figure. 


Let us assume that r is the positional vector of the force F with respect to the arbitrary point P.
Therefore, we can write down the equation to find out the rotary or rotational effect of force F about the arbitrary point P as mentioned here. 


Above equation is representing the moment of force in vector form. Let us now find out the magnitude of the moment of force. 

Moment of force = Force x Perpendicular distance from the pivot point to the line of action of the force

Unit of moment of force = Unit of force x unit of distance 
Unit of moment of force = N x m  
Unit of moment of force will be N-m in SI system. 

Sign convention for moment of force 

We need to consider and visualize physically how the force is trying to rotate the object. In order to find out the sign of moment or moment of force i.e. positive or negative moment, we use the concept of right-hand thumb rule. 

If force is trying to rotate the object in anti-clock wise direction, moment of force will be taken as positive. 

Let us see here the following figure, when we will close the finger in anti-clock wise direction, thumb will be in upward direction and it will be the indication for positive moment of force in our sign-convention for moment of force.

Similarly, if force is trying to rotate the object in clock wise direction, moment of force will be taken as negative. 

Therefore, we need to take care the sign conventions for moment of force and we must note it here that moment of force will be always expressed with its magnitude, unit of measurement and sense of rotation i.e. positive or negative sign. 

Important notes 

There are few very important points that we need to keep in our mind while dealing with the moment of force. 
  1. Like force, Moment of force is also a vector quantity. 
  2. Moment of force and force are sliding vectors. 
  3. Anti-clock wise rotation or counter clock wise rotation about the pivot will be taken as positive. 
  4. Clock wise rotation about the pivot will be taken as negative. 
  5. Moment of force will be considered as the function of magnitude of the force and the moment arm. 
  6. Unit of moment of force will be N-m in SI system. 

Therefore, we have seen here the basics of moment of force, unit of moment of force, equation to determine the moment of force and finally we have also seen the sign conventions used to express the moment of force with the help of this post.  

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, varignon's theorem in engineering mechanics.  

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google 

Also read 


November 13, 2019

DIFFERENCE BETWEEN BODY FORCE AND SURFACE FORCE

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force systemprinciple of transmissibility of forces and its limitations, classification of force system and composition and resolution of forces in mechanics. 

Now, we will be interested to understand here the body force and surface force in mechanics with the help of this post. 

Body force and surface force 

As we have already seen that forces are acting between two bodies those are directly interacted with each other or might be at a distance away and not interacted directly. 

Therefore, we can classify the forces in two types on the basis of interaction between two bodies and these are as mentioned here. 
  1. Body forces
  2. Surface forces 

Let us first understand the body forces 

Body forces act on each volume element of the body and these are exerted when the body will be kept in a gravitational, centrifugal, electric or magnetic field. 

The best example of body force is the force due to gravitation and which is usually known as weight of the body. 

Let us consider the example of apple falling down from its tree due to force of gravitation.  


Gravitational force i.e. force of the earth on the body or object (here apple in the example) will be one good example of body force. 

Briefly, we can say that body forces are the forces acting on the volume of the body. 

Example of body forces 

Following are few examples for body forces which will help us to understand the basics of body forces. 
  1. Gravitational force 
  2. Centrifugal force 
  3. Electric field 
  4. Magnetic Field 
  5. Inertia force 

Surface forces

Surface forces act on each surface element of the body and these are exerted when the body will be kept in direct mechanical contact with another body. 

The best example of surface force is the pressure force, viscus force etc. 

Briefly, we can say that surface forces are the forces acting on the surface of the body. 

Let us consider the following figure where a person is pulling a load, such force will be one example for surface force as there is direct mechanical contact between two bodies. 

Example of body forces 

Following are few examples for surface forces which will help us to understand the basics of surface forces. 
  1. Pressure force 
  2. Viscus force 
  3. Frictional force 
  4. Normal force 

Therefore, we have seen here the basics of body force and surface force with the help of this post.  

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, moment of force in engineering mechanics.  

Reference:  

Engineering Mechanics, By Prof K. Ramesh 

Image courtesy: Google 

Also read 

Tuesday, 12 November 2019

November 12, 2019

EXPLAIN COMPOSITION AND RESOLUTION OF FORCES

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force system, principle of transmissibility of forces and its limitations and classification of force system in mechanics. 

As we have the basic information about the force system and its principle after reading the previous post. Now, we will be interested to understand here the composition and resolution of forces in mechanics with the help of this post. 

Composition and resolution of forces 

Composition and resolution of forces are very important tools in engineering mechanics to solve the problems where multiple forces are acting. Depending on the types of problem, we will apply the basics of composition and resolution of forces. 

Further, composition and resolution of forces will be used in various engineering mechanics problems. Therefore, we need to understand the both tools. 

First we will see here the composition of forces and after that we will find out the basics of resolution of forces. 

Composition of forces

Composition is basically defined as the process of reducing a force system to an equivalent and simplest force system, which will have the same external effect on the body as the original force system. 

Composition of forces are based on the principle of transmissibility of forces and law of parallelogram for vector addition. 

Let us consider the following case where two forces i.e. F1 and F2 are acting on the body as displayed here in following figure. Line of actions of these two forces are meeting with each other at point P. 


In order to determine the resultant of these two forces, we will use the principle of transmissibility of forces and law of parallelogram for vector addition. 

Let us first recall the principle of transmissibility of forces and move the forces F1 and F2 as displayed here in following figure. 


Now we will use the law of parallelogram for vector addition and the resultant of these two forces will be R as displayed here in following figure. 


We must note it here that the resultant R of these two forces i.e. F1 and F2 will have the same external effect on the body as that of the original forces F1 and F2

Resolution of forces 

Resolution of forces is basically defined as the process of determining two components of a force which will have the same external effect on the body as the force itself. 

Resolution of forces could be seen as the opposite of composition of forces. 

Let us consider the following case where a force F is acting on the body and its angle is θ. 


Now, there will be two components of this force F i.e. Fx and Fy and their value will be as mentioned here. 
Fx = F cos θ 
Fy = F Sin θ 
Tan θ = Fx/F
Magnitude of the force, F = Square root of {Fx2 + Fy2

Therefore, we have seen here the composition of forces and resolution of forces with the help of this post. 

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, body forces and surface forces, in engineering mechanics. 

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google 

Also read 

Basics of radial flow reaction turbines 
Difference between inward radial flow reaction turbine and outward radial flow reaction turbine 
Francis turbine 
Axial flow reaction turbine 
Specific speed of turbine 
Draft-tube 
Governing of turbines 
Governing of impulse turbine or Pelton turbine