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Terminal Velocity

Hi guys,

As I mentioned certain scientific terms in my previous post, i would like to go in depth on those concepts,beginning with terminal velocity, it being the most fundamental concept in my post.

So what is terminal velocity?

Terminal velocity is the velocity of an object when the drag force (dependent on the fluid the object is travelling through) acting upon it is equal to the downward force of gravity acting upon it. Simply put, when the air resistance of a falling object cancels out the gravitational force which is pulling it downwards and accelerating it.

So how do these forces affect the motion of the object? The forces cancelling each other out make the object remain at a constant rate of motion.

You may ask why does the object still move when the forces cancel each other out. This is due to the fact that in the beginning the force of gravity still manages to overcome the drag force, allowing the object to gain speed (accelerate) initially. But as the object increases in velocity, the drag force increases, this effect can also be seen in the case of friction (Drag and friction are pretty much the same thing). Lets assume that a boy is dragging a heavy box, full of files, across a distance of 100 meters, now we will imagine this scenario in two different ways, firstly in the case whereby the boy is walking slowly and in the second whereby the boy is running. So in the first case the boy walks, when he reaches the end, he feels the bottom of the box, where the box and the floor meet, it still feels the same as before, now in the second case, he runs, he once again feels the bottom of the box, this time it feels warmer than before. So what can we infer from this scenario? Before I reveal the answer, i would like to state a few properties of friction:

  1. Friction opposes motion
  2. Friction causes wear and tear
  3. Friction produces heat when kinetic energy is converted into thermal energy

So what can we infer? In the second scenario, there was more heat, therefore we can assume that there was more frictional force produced in the second case.

Now lets go back to what i mentioned previously, air resistance increases (Drag Force) as the object’s velocity increases. As seen in the example above, we can tell that this statement is true.

That’s essentially the definition of terminal velocity. Before we move on, lets do a recap:

  1. Terminal velocity is the velocity an object is at when the gravitational force acting upon it is equal to the drag force acting upon it in the opposite direction therefore cancelling out all forces therefore having a resultant force of 0
  2. The drag force acting upon the object increases as the object accelerates due to the downward force of gravity.

Ok so lets move on to the math behind terminal velocity and some examples of it.

The formula for terminal velocity is as follows: V_t= \sqrt{\frac{2mg}{\rho A C_d }}

Vt=Terminal Velocity

m=Mass of falling object

g= Acceleration of the object due to gravity

ρ= Density of fluid which the object is travelling through

A= Projected area of the object

Cd= Drag Coefficient

I went through everything in my previous post but lets do a recap on these terms:

mass= Amount of matter in an object (SI Unit : kg)

Acceleration = Rate of increase of speed (SI Unit: m/s^2)

Gravitational force= how much gravitational force does an object exert on another object (SI Unit: N/kg)

Density= Mass per unit volume of matter (SI Unit: kg/m^3)

Projected Area= Area of a falling object which is in contact of the air flowing through it. (SI Unit: m^2)- Same as Area

Drag coefficient= A value which depends on the shape of an object and can only be calculated by using the drag force of the object and other factors or by doing actual testing. This value has no units.

That’s all the terms. So now I shall be doing some examples.

So assuming I drop a metal cube which has a mass of 3 kg and has a projected area of 1 m^2 on Earth 90 degrees downward, through air at a temperature of 25 degrees Celsius, what would the Terminal velocity of the cube be?

All we have to do is input all the values into the formula. The acceleration due to gravity on earth is 9.81 m/s^2. The density of air at 25 degrees Celsius is 1.1839 kg/m^3 and the drag coefficient of a cube is 1.05 facing downward. The result is : 6.881101581m/s.

So there’s Terminal Velocity for you!

I would like to thank Mr Tan Ping Hock and Mr Yao Zhi Wei Adrian, My current and previous physics teachers respectively for clearing my doubts about certain concepts within this topic of terminal velocity!

Thanks for reading!

Clyde Lhui

References:

http://en.wikipedia.org/wiki/Drag_coefficient

http://en.wikipedia.org/wiki/Density_of_air

http://en.wikipedia.org/wiki/Terminal_velocity

 

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