Recent Updates

Thursday, 16 January 2020

January 16, 2020

APPARENT WEIGHT OF A MAN IN A LIFT

We were discussing the projectile motion - trajectory equation, definition and formulas and we have also seen the concept of Terminal velocity with the help of our previous posts.  

Now, we will be interested further to understand a very important topic in engineering mechanics i.e. apparent weight of a man in a lift. 

Today we will first understand the basics of apparent weight and true weight and further we will find out the apparent weight of a man in a lift for various situations. 

Apparent weight and true weight 

True weight of a body is basically defined as the force exerted by the earth on it. 

Let us think that a person whose mass is m and he is located at or near the earth surface, true weight or simply weight of the person will be mg. Where g is the acceleration due to gravity. 

Weight of the body will be measured with the help of weighing machine. When a body will be placed over the surface of weighing machine platform, there will be acting basically two types of forces.
  1. Force due to gravity of weight of the body i.e. W = mg 
  2. Upward normal contact force i.e. N exerted by the platform of weighing machine on the body 

APPARENT WEIGHT OF A MAN IN A LIFT

The upward normal contact force (N) exerted on the body will be termed as the apparent weight of the body. Value of the upward normal contact force will be dependent over the state of motion of the body. 

Apparent weight of a man in a lift 

Now let us see the apparent weight of a man in a lift for the various state of motion of the lift. Please note that we are going to use here the Newton’s law of motion in order to secure the expression for the apparent weight of a man in a lift for the various state of motion of the lift. 

I hope all of you are well aware with the lifts or elevators used in various multi-storey buildings or towers. If you have an opportunity to travel in a lift that travels longer distance such as lift of a 50 storey or 70 storey buildings, you will surely feel that there is acceleration, deceleration and steady state motion too. 

So, we will analyse and find out the apparent weight of a man for each state of motion of the lift and we will also see here a case of snap of lift or elevator with the help of this post. 

Case 1: Apparent weight of a man in a lift when lift is moving up and accelerating 

Let us consider that a man is standing inside a lift over the spring scale as displayed here in following figure. 

Let us think that lift is moving up with an acceleration a.  

APPARENT WEIGHT OF A MAN IN A LIFT

Let us draw the free body diagram, as displayed above, considering the man as a particle. I will determine the apparent weight of man by using the newton’s law of motion and please note that I am not standing inside the lift. I am standing outside of the lift on ground and analysing the apparent weight of man in the lift. 

∑ Fy = m x ay
R – mg = ma
R = m (g + a) 

As we have already seen here that apparent weight is basically the reaction force exerted on the body and hence apparent weight will be higher as compared to the actual weight of the man. 

Spring scale will display the weight of man equivalent to the reaction force exerted on the man by the surface of spring scale. 

Therefore, apparent weight of a man in a lift, going upward with an acceleration, will be higher than his actual weight or true weight. 

Case 2: Apparent weight of a man in a lift when lift is moving with a constant velocity i.e. acceleration is zero 

Let us consider that a man is standing inside a lift over the spring scale as displayed here in following figure. 

Let us think that lift is moving with a constant velocity V. We will see here the apparent weight of man and we will find out here that what will be the reading of spring scale.  


Let us draw the free body diagram, as displayed above, considering the man as a particle. I will determine the apparent weight of man by using the newton’s law of motion and please note that as lift is moving with a constant velocity and hence acceleration will be zero.   

∑ Fy = m x ay
R – mg = 0
R = mg   

As we have already seen here that apparent weight is basically the reaction force exerted on the body and hence apparent weight will be same as the actual weight of the man. 

Spring scale will display the weight of man equivalent to the reaction force exerted on the man by the surface of spring scale. 

Therefore, apparent weight of a man in a lift, going with a constant velocity, will be equal to his actual weight or true weight. 

Case 3: Apparent weight of a man in a lift when lift is moving down and accelerating 

Let us consider that a man is standing inside a lift over the spring scale as displayed here in following figure. 

Let us think that lift is moving down with an acceleration a.  


Let us draw the free body diagram, as displayed above, considering the man as a particle. I will determine the apparent weight of man by using the newton’s law of motion and please note that I am not standing inside the lift. I am standing outside of the lift on ground and analyzing the apparent weight of man in the lift. 

∑ Fy = m x ay
R – mg = - ma
R = m (g - a) 

As we have already seen here that apparent weight is basically the reaction force exerted on the body and hence apparent weight will be lower as compared to the actual weight of the man. 

Spring scale will display the weight of man equivalent to the reaction force exerted on the man by the surface of spring scale. 

Therefore, apparent weight of a man in a lift, going downward with an acceleration, will be lower than his actual weight or true weight. 

Case 4: Apparent weight of a man in a lift when lift cable is snapped 

Let us consider that a man is standing inside a lift over the spring scale as displayed here in following figure. 

Let us think that lift cable is snapped and lift is free falling. Lift will free fall with an acceleration g i.e. acceleration due to gravity.  

APPARENT WEIGHT OF A MAN IN A LIFT

Let us draw the free body diagram, as displayed above, considering the man as a particle. I will determine the apparent weight of man by using the newton’s law of motion and please note that I am not standing inside the lift. I am standing outside of the lift on ground and analyzing the apparent weight of man in the lift. 

∑ Fy = m x ay
R – mg = - mg
R = 0 

As we have already seen here that apparent weight is basically the reaction force exerted on the body and hence apparent weight will be zero.   

Spring scale will display zero as the apparent weight of man. 

Therefore, we have seen here the basics of apparent weight and true weight of a body with the help of this post. We have also secured here the apparent weight of a man in a lift for various situations. 

Further we will find out another concept in engineering mechanics with the help of our next 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.   

We will find out now the in our next post.   

Reference:  

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

Also read   

Tuesday, 14 January 2020

January 14, 2020

TERMINAL VELOCITY AND ITS EXPRESSION

We were discussing the projectile motion - trajectory equation, definition and formulas with the help of previous post.  

Now, we will be interested further to understand a very important topic in engineering mechanics i.e. Terminal velocity with the help of this post. We will find out here the basics of terminal velocity and we will also find out the expression for terminal velocity here in this post. 

So, what is terminal velocity? 

When an object starts to fall from initial zero velocity, object will move towards downward direction. Velocity of object will be increasing as the object will move towards downward direction under the constant acceleration i.e. acceleration due to gravity. 

Object will be subjected here to two external forces. First one is the weight of the object and second one is the drag force due to the air resistance. 

Now we will understand here the effect of air resistance on the object which is falling through the atmosphere. Drag force will be developed due to the effect of air resistance. 

Following expression, as mentioned below, provides the drag force due to air resistance.  

Where,
Fd = Drag force
Cd = Drag co-efficient
A = Projected Area
V= Velocity 

We can conclude that the drag force will be increasing with increase in the velocity of the object as drag force is directly proportional to the square of the velocity as we can see from the expression of drag force. 

There will be a situation where this drag force will become equal to the weight of the object and object will come under equilibrium and there will be no net force over the object and the vertical acceleration will go to zero.  


According to Newton’s first laws of motion, object will fall with constant velocity when drag force will become equal to the weight of the object and object will come under equilibrium and there will be no net force over the object and the vertical acceleration will go to zero. 

This constant vertical velocity will be termed as terminal velocity and it will be given by the following expression. 

Following table, as displayed below, indicates the terminal velocity for various cases and also indicates the distance needed to secure the 95% of the terminal velocity.  


Therefore, we have seen here the basics of terminal velocity, expression of terminal velocity, and significance of drag force with the help of this post. We have also secured here the terminal velocity for various cases and also indicates the distance needed to secure the 95% of the terminal velocity. 

Further we will find out another concept in engineering mechanics i.e. apparent weight of a man in a lift with the help of our next 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.  

We will find out now the apparent weight of a man in a lift in our next post.   

Reference:  

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

Also read  

Saturday, 11 January 2020

January 11, 2020

PROJECTILE MOTION - TRAJECTORY EQUATION, DEFINITION AND FORMULAS

We were discussing the importance of friction i.e. positive and negative effects of frictionClassification of friction and Coulomb's law of dry friction with the help of our previous post.  

Now, we will be interested further to understand a very important topic in engineering mechanics i.e. projectile motion - trajectory equation, definition and formulas with the help of this post. We will find out here the basics of projectile motion, classification of projectile motion and various equations and formulas associated with the projectile motion. 

Let us first start here with the basic definition of projectile motion 

Projectile motion is basically defined as a motion where a particle moves in a vertical plane with some initial velocity but its acceleration will always be the free fall acceleration i.e. acceleration due to gravity which will be acting towards downward direction. 

When a particle will be thrown in to the space, it will have motion in x direction i.e. in horizontal direction and it will have motion in y direction too i.e. in vertical direction. 

The combination of motion of particle in x direction i.e. in horizontal direction and in y direction i.e. in vertical direction could be considered as the projectile motion. 

We must need to note it here that the horizontal motion and vertical motion of the particle in a projectile motion will be independent with each other. 

Let us consider that a particle is thrown in to the space with initial velocity u with an angle θ with the horizontal direction as displayed here in following figure. 


Following equations, as displayed below, will be used in order to determine the various desired formulas for a particle following the projectile trajectory. 


Where,
u = Initial velocity of the particle
V = Final velocity of the particle
a = Acceleration of the particle
t = Time of travel of the particle    

Above equations will be only valid for a particle which is under motion with constant acceleration.
In case of projectile motion, a i.e. acceleration of the particle will be basically acceleration due to gravity i.e. g and it will be acting towards downward direction. 

We will have following equations, as mentioned below, for particle motion in horizontal and in vertical direction. 


Projectile trajectory equation 

Above equation shows that it will be a parabolic equation and hence projectile motion trajectory will be parabolic. 

Time taken to reach the ground 

Time taken to reach the ground i.e. T will be determined with the help of following equation as mentioned below. 

Range or horizontal distance traveled by the particle

Range or horizontal distance traveled by the particle will be determined with the help of following equation as mentioned below. 

Maximum height or maximum vertical distance traveled by the particle

Maximum height or maximum vertical distance traveled by the particle will be determined with the help of following equation as mentioned below. 


Classification of projectile motion

Projectile motion will be basically classified in two types as mentioned here.
  1. Horizontal plane projectile motion
  2. Inclined plane projectile motion 

If we have a problem or a case of projectile motion where the point of projection and point of striking both are on inclined plane, we will say such projectile motion as inclined plane projectile motion.
Otherwise, we will say horizontal plane projectile motion. 

We must note it here very clearly that for inclined plane projectile motion, the point of projection and point of striking both must be on inclined plane. 

Therefore, we have studied here the basics of projectile motion, classification of projectile motion, equations associated with projectile motion, time of flight, range and maximum height traveled by the particle in a projectile motion with the help of this post. 

Further we will find out another concept in engineering mechanics i.e. terminal velocity and its expression with the help of our next 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.  

We will find out now the terminal velocity and its expression in our next post.  

Reference:  

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

Also read  

Sunday, 29 December 2019

December 29, 2019

DEFINE COULOMB'S LAW OF DRY FRICTION

We were discussing the importance of friction i.e. positive and negative effects of friction and classifications of friction with the help of our previous post.  

Now, we will be interested further to understand the coulomb's law of dry friction with the help of this post i.e. define coulomb's law of dry friction. We will find out here the coulomb's law of dry friction and we will also introduce here the co-efficient of friction.  

Define coulomb's law of dry friction 

Let us see here now the coulomb's law of dry friction. There will be basically three laws of coulomb's law of dry friction. The first two laws, as mentioned below, was given by another scientist whose name was Amonton. 

Even the following first two laws was given by scientist Amonton, but these laws also come under the coulomb’s law of dry friction. 

We must note it here that all the three coulomb’s law of dry friction are based on the experimental observations. 

So, let us first see here the first law 

According to the first law of coulomb’s law of dry friction, magnitude of the frictional force will be directly proportional to the normal load between the surfaces for a given pair of materials. 

Co-efficient of static friction and static frictional force

Where, 
µs is the co-efficient of static friction 
N is the normal load 

We must have to understand and note it here that the co-efficient of friction will be always given for a pair of material and it will never be given for a single material. 

Co-efficient of static friction will be dependent only on the two contacting surfaces. 

On the basis of observation of experiments, it was noted that co-efficient of static friction will be independent of normal load. 

We have also used here one term i.e. magnitude of frictional force in the first law of coulomb’s law of dry friction. Magnitude of frictional force represent here the maximum static frictional force. 

Let us see here now the second law 

According to the second law of coulomb’s law of dry friction, magnitude of the frictional force will be independent of the area of contacting surfaces i.e. apparent area for a given normal load.   

We have again used here term i.e. magnitude of frictional force and it represent here the maximum static frictional force. 

On the basis of observation of experiments, it was noted that co-efficient of static friction will be constant even when area of contacting surfaces i.e. apparent area will be varied by a factor of 250. 

If we assume two cases, let us think that there is larger surface contact in first case and smaller surface contact in second case. 
Static frictional force

We will be thinking that the resistance offered due to friction in these two cases will be different and resistance offered due to friction in first case where there is larger surface contact of object will be higher. 

But, will it be higher? 

No, co-efficient of static friction will be same in above mentioned two cases and it was concluded after analyzing the observation of experiments. 

We must note it here that the above two laws of coulomb’s law of dry friction are given for object which is in stationary condition or in static condition and that’s why we have used terms like co-efficient of static friction and maximum static frictional force. 

Now let us see the third law of coulomb’s law of dry friction 

Coulomb has given third law and according to the third law of coulomb’s law of dry friction, magnitude of the frictional force will be independent of the sliding velocity. 

Co-efficient of dynamic friction will be nearly independent of the sliding velocity. 

Therefore, we have studied here the three laws of coulomb’s law of dry friction. Further we will find out another concept in friction i.e. stick slip phenomenon in friction with the help of our next 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

We will find out now the stick slip phenomenon in friction in our next post.  

Reference:  

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

Also read  

Thursday, 26 December 2019

December 26, 2019

EXPLAIN THE DIFFERENT TYPES OF FRICTION IN DETAIL

We were discussing the importance of friction i.e. positive and negative effects of friction with the help of our previous post.  

Now, we will be interested further to understand the classifications of friction with the help of this post i.e. explain the different types of friction in detail. We will find out here the classifications of friction and will also brief here each type of friction in this post. 

Let us start here with the classifications of friction. 

Classifications of friction 

We will classify the friction as mentioned below.  
Friction classification

Fig: 1- Classification of friction 

External friction

External friction is basically defined as the friction due to the interaction between surfaces of two solid bodies in contact. 

External friction will be further classified in two types of friction as mentioned below.
  1. Static friction
  2. Dynamic friction 

Static friction

Static friction will come in to picture when surfaces of two solid bodies in contact are at rest but there is tendency for a relative motion. 

Dynamic friction

Dynamic friction will come in to picture when surfaces of two solid bodies in contact are in relative motion. 

Internal friction

Internal friction will be further classified in two types of friction as mentioned below.
  1. Fluid friction
  2. Solid friction 

Fluid friction

Fluid friction is also termed as viscous friction. 

Fluid friction is basically developed between fluid elements when adjacent fluid layers are moving with different velocities. 

Frictional force developed here will be proportional to the relative velocity between the fluid layers and the fluid viscosity. 

Fluid friction concept will be widely used in the problems based on flow through pipes and orifices, bodies immersed in fluids and lubricated surfaces. 

Solid friction

Solid friction will be found in all type of solid materials subjected to cyclic loading. Energy will be dissipated internally within the material. 

Frictional force due to solid friction will be proportional to the displacement. 

Let us see here one more type of friction i.e. Dry friction 

Dry friction 

Let us assume that a block, as mentioned in following figure, is subjected with a force F1.  
Friction
Fig: 2- Block stationary at the surface

Now we need to ask to our self that whether there will be frictional force over here or not. We can easily say that there will not be any friction and hence frictional force in above situation. 

Because, no frictional force will be developed in the absence of an external force to cause a tendency for relative motion. That means if there will not be any force acting on a body that causes the tendency for relative motion, there will be no frictional force. 

If we consider that only force F1 is acting on the body which is displayed above, there will be no frictional force as there will be no tendency for a relative motion between body and surface over which body is placed. 

If we consider the pushing force F is acting on the body, frictional force will be started to develop at the interface of the objects. 

Force F will be balanced by the frictional force and hence the object will remain in equilibrium and at the rest condition. 

When we will increase the pushing force F, frictional force will also be increasing to maintain the equilibrium condition of the body. When pushing force F will reach to the maximum frictional force, the object will be on the verge of sliding i.e. if force F will be increased even slightly more than the maximum value of frictional force, object will start to move or slide. 

We can see it in following figure left part, we can see the curve drawn between the applied force and the frictional force developed while body is in rest condition here. Frictional force fs (static frictional force) will be increasing linearly with the pushing force F. The body will remain in stationary condition up to a point where pushing force reaches to the maximum value of frictional force. 

Curve between applied force and frictional force
Fig 3- Frictional force Vs Applied force 

The first part of above figure shows the curve between the friction force and applied pushing force while body is in rest condition. 

The right part of the above figure shows the curve between the friction force and the applied force while body is in rest condition. When pushing force F will reach to the maximum frictional force, the object will be on the verge of sliding i.e. if force F will be increased even slightly more than the maximum value of frictional force, object will start to move or slide. 

We must have to note it here that the frictional force will be dropped when movement will be started and further it will be independent of relative velocity up to a limit and beyond that frictional force will be dropped again as displayed here in the right part of the above figure. 

Therefore, we have studied here the various types of friction and frictional force with the help of this post. We have also introduced here the term dry friction and we have also understood here the importance of static friction and dynamic friction with the curve drawn between the applied force and friction force. 

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.     

We will find out now the coulomb's law of dry friction in our next post.  

Reference:      

Engineering Mechanics, By Prof K. Ramesh 

Image courtesy: Google    

Also read