Can a coin falling from the Empire State Building kill you?

In Physics by Mystifact

We know that when objects are dropped, they start picking up speed before they hit the ground; for example, you know that jumping off a bench is fine, but jumping off the second floor of a building may break a bone due to your increased speed. Consider a metal coin of your choice; would it kill someone if dropped from the Empire State Building?

Freefall

When objects begin falling, their velocity (which is speed) increases. This is when a certain law of Physics, comes into play; terminal velocity.

What is terminal velocity?

Terminal velocity is the maximum speed an object reaches in freefall [1]. Everything has a terminal velocity and it’s dependent on many factors – the main one being air resistance. If you went skydiving without a parachute you’d be certain there would be no happy ending. The reason parachutes are used, is to reduce your terminal velocity so you land on the floor at a slow enough speed to not hurt yourself!

How is terminal velocity reached?

Terminal velocity is achieved when there is no overall force acting on the falling object. This means that the force pulling the object down, is the same as the force of the air resisting the object from falling down faster. To feel this air resistance, just wave your hand down towards the floor – you should feel the air pushing up against your hand trying to slow it down.

This is why parachutes work. When they are opened, more air can push up on the falling object, which means the force of air resistance pushing up, increases – thus slowing the object down.

Figure 1: Image showing terminal velocity of object achieved when the force acting down (Fg) is equal to air resistance acting up (Fd)

Will a coin kill if dropped from the Empire State Building?

Considering a penny is about 2-3 grams and it has a flat-ish shape; the math shows us that the terminal speed of this penny equates to about 25 miles an hour. This is about the same speed as Usain Bolt! A penny travelling at that speed will not do you any harm. Worst comes to worst it might sting for a second or two [2].

What if there was no air?

Removing air from an empty room turns it into a vacuum. A vacuum is a space completely free of matter. From the top of the Empire State Building to the ground, all you have is air, so removing that air will make this space a vacuum, meaning there is no air resistance to slow the object down in freefall – so what happens in this case? Something amazing happens.

How are objects in freefall affected by a vacuum?

Objects in a vacuum; no matter how heavy, all fall at the exact same speed and acceleration, since the only force that acts on them is gravity. The acceleration of Gravity is roughly 10 metres every second; meaning the object travels an extra 10 metres every single second! Please read my article: A feather as HEAVY as a bowling ball! and watch the video which demonstrates this. It will baffle you!

Say our coin falls in a vacuum from the top of the Empire State Building; considering the height of the drop and the acceleration due to gravity (10 metres every second) – the coin would hit the floor at 208 miles per hour. That’s slightly faster than the top speed of a Ferrari 458! A coin of that speed would probably do damage to your skull but never penetrate it and would not kill you. Do you see the effect of air resistance?

What if a ball point pen was thrown?

Depending on how this object falls, it could very well kill you. If you’ve ever thrown a pen, you would know that it either spins around, flutters about or shoots through the air like a bullet. If this pen ends up falling through the air like a bullet – air resistance is decreased to a minimum. As a result, the pen could reach speeds up to 200 miles per hour – again, just like the top speed of a Ferrari 458!

Since the pen has a much smaller contact point – at such speeds it could very well penetrate the skull and kill. If you ever end up at the top of the Empire State Building, remember to behave yourself!

The video below shows you different experiments carried out with a penny on a material roughly the same strength as a skull. I recommend you watch it – it’s quite entertaining.

If you have any questions, leave them below and until next time, take care.

~ Mystifact


References:
[1]: http://study.com/academy/lesson/what-is-terminal-velocity
[2]: http://uk.businessinsider.com/drop-penny-off-empire-state-building

Please note; no copyright infringement is intended. All images used have been labelled for re-use on Google Images. If any artist or designer has any issues with any of the content used in this article, please don’t hesitate to contact me to correct the issue.

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