Let’s Get Physics-l: Terminal Velocity

(Fear not, you are not going mad. This post has already been up but it wasn’t where it was meant to be (It was bugging me a fair bit). I am merely correcting this.)

In the last Forces and Motion post, we looked at Dynamics. One of the forces we came across was drag, a frictional force that occurs in fluids (liquids and gases). Objects that pass through fluids experience drag.

Drag

Any objects in contact with each other experience a frictional force. This is because, at microscopic level, material surfaces are covered in ridges, indentations and trenches that scrape against those of other materials when in contact with them. Though frictional forces act to slow objects down, those caused by two objects don’t depend on the velocities of the respective objects.

Drag, on the other hand, does depend on the velocity of objects. An absolutely delightful equation can help prove this:

F(d) = ½pC(d)Av²

Where:

  • F(d) – Force of Drag/ N
  • – Density of the fluid/ kgm^-3
  • C(d) – Coefficient of Drag/ No unit
  • A – Cross-sectional area of the moving object/ m²
  • v – Velocity/ ms^-1

In truth, that’s not a nice equation to work with. With that in mind, we can simplify it down to F(d) = kv² which effectively states that the force of drag is directly proportional to the velocity of the moving object squared.

Terminal Velocity

Before we establish what terminal velocity (Which sounds like an action film from the 90s in my opinion (As it happens, it is an action film from the 90s)) is, an experiment of my own (Apologies for the picture quality in some panels, I’ll put it down to poor skill):

IMG_4193
CAPTAIN AMERICA in DANGER AT 30,000 FEET!

If you’ve ever been skydiving or punched out of the sky by a robot that knows every punch you’ve ever thrown (I don’t encourage violence mind you) you may recall that as you first start to fall you do so at an accelerating rate. This is because the force due to gravity is greater than the force of drag. However, as you continue to fall drag increases until it is level with the force due to gravity. As the forces are equal and opposite the resultant force is 0N. It’s at this point that you are moving at a terminal velocity.

IMG_4192.JPG

If we consider the graph in conjunction with the example above, we can better visualise how Captain America, in this instance, reaches a terminal velocity. At Stage 1, Cap has just left the plane. His downward velocity is increasing as he is accelerating towards the ground. In this instance, the force due to gravity is greater than drag. At Stage 2, drag has increased, reducing acceleration until drag is equal to the force due to gravity. Here Cap has reached his first terminal velocity. Stage 3 represents Cap releasing his parachute which causes a rapid deceleration. The force of drag is greater than the force due to gravity. At Stage 4 the forces are again balanced, Cap reaching his second terminal velocity.


Summary:

  • Drag – Frictional Force that occurs in fluids
  • F(d) = kv²
    • Drag is directly proportional to velocity squared.
  • Terminal velocity – The velocity at which drag and the force due to gravity are equal resulting in no resultant force.

Terminal Velocity, an action film and a concept in physics. I can’t comment on how related they are but you are welcome to find out or, better yet, comment below if you know already (I feel like I should watch it myself). If you have any thoughts or questions feel free to leave them in the comments. Thank you.

(The Characters referenced are property of Marvel Comics. I in no way lay claim to them, they are simply being used to help convey a Physics concept)
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