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Tuesday, 14 January 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.   

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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   

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