Throwing Things Off the Empire State Building Using Math
Рет қаралды 3,075
Ай бұрынYou probably already know that a penny thrown from the empire state building WON'T kill you. It's terminal velocity just isn't great enough. But what if it was really dense? Or falling in a vacuum? Or dropped from a greater height? And if a penny won't kill you what objects COULD kill you if dropped from a skyscraper? We explore all of these questions and more using math and physics in this video.
This is a re-upload of parts 2 and 3 combined into one video from a previous series on this penny problem. To watch part 1 click here: • Could a Penny KILL you...
Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?”
We use unique topics for algebra, trigonometry, calculus, and much more and go beyond context problems and use a technique called mathematical modeling to find solutions to real world questions and real world problems. These videos are great for students who plan to enter technical fields that require real world problem solving, and can be a great resource for teachers looking for ways to bring real world contexts into their classroom.
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Email: MathTheWorld@byu.edu
Created by Doug Corey
Script: Doug Corey and Jennifer Canizales
Audio: Doug Corey
Animation: Jennifer Canizales
Music: Coma Media
© 2023 BYU
@tar0nja 29 күн бұрын
Nice video! I really hate to be that guy, but i believe you made a mistake at 5:20. You are assuming that the gravity is constant, which in low altitudes can be considered true, but not when talking about 111km. Now, a way we could solve this is by assuming the conservation of the mechanical energy. We can do this since we are assuming we aren't loosing any energy due to friction with air. Thus, the initial gravitational potential energy is equal to the final kinetic energy and the potential energy at the earth's surface. We have, then, the two following formulas: F(impact) = m*v/t G*m*M/r = 0.5*m*v^2 + G*m*M/R F -> force of impact (3700 N) m -> mass of coin (0.0025 kg) v -> speed of coin at impact (? m/s) t -> time duration of impact (0.001 s) G -> gravitational constant (6.67*10^-11 N*m^2/kg^2) M -> mass of earth (5.97*10^24 kg) r -> distance needed (? m) R -> earth's radius (6371000 m = 6371 km) Reorganizing the previous formulas we get this: v = sqrt( 2*G*M*( 1/r - 1/R) ) = 1480 m/s = 5328 km/h = 3310 miles/h r = 2*G*M / ((t*F/m)^2 + = 6261285 m = 6261 km = 3890 miles I personally think that these results are more interesting than the 12 Everests. Mainly because these results are equivalent to: -> 708 Everests -> Approximately the Earth's radius -> The distance between NY & Madrid -> Approximately the overall distance of the Great Wall of China Otherwise, this video is excel·lent, keep it up! Sorry about my english, it isn't my first language.
@RubyPiec 29 күн бұрын
im gonna test this
@cinnamonaxis6256 29 күн бұрын
On me please
@JC-km5rd 29 күн бұрын
Who needs "Avada Kedavra" when you've got a taped shut version of the 7th Harry Potter book! 😂 Awesome video, thank you! You already know what I'm packing from now on
@MathTheWorld 29 күн бұрын
Yes, Harry Potter is deadly in so many ways!
@jnwahlgren 29 күн бұрын
At 1:26, when you solved for the mass of the penny they would be lethal, you did not account for how the heavier mass would also increase the terminal velocity. Terminal velocity is proportional to the square root of the mass, so the impact force is proportional to the mass to the 3/2 power. It still wouldn't be nearly enough to kill a person, but details matter!
@daniel_77. 29 күн бұрын
Great job! Shouldn't you also consider the surface area in the contact of the object with the head? (Pressure?)
@MathTheWorld 24 күн бұрын
Thank you for the positive feedback! We just focused on blunt force trauma. If you are hit with an object with very small area, you can take that into account, but it is a different equation, no longer blunt force.
@georgesos 29 күн бұрын
Very nice. Good work man.
@MathTheWorld 29 күн бұрын
Thanks! Although the credit really goes to our creative director, Jennifer, she actually wrote the script and did the visuals for this video, instead of just doing the visuals for a script that I wrote (which is typical). I don't deserve any credit.
@supalupallama 29 күн бұрын
Another great video thanks everything!! really means a lot!
@MathTheWorld 29 күн бұрын
You are welcome!
@lowellrindler9454 28 күн бұрын
Is the size of the impact relevant here? I would think the penny’s edge would be more dangerous because the force is concentrated in a smaller area.
@MathTheWorld 24 күн бұрын
We just focused on blunt force trauma. If you are hit with an object with very small area, you can take that into account, but it is a different equation, no longer blunt force
@Mowrioh 29 күн бұрын
1.3k views 12 hrs nah bro fell off 💀
@cadenbappy7408 14 күн бұрын
not every video is viral dude his other recent ones have lots of views
@Maanvik_ 29 күн бұрын
Show us a practical
@MathTheWorld 29 күн бұрын
@Maanvik_ Can you please tell me more about that kind of things that you would find practical? We tend to do practical problems in our videos, although the sauce cup optimization video is pretty over-the-top (kzfaq.info/get/bejne/gr6qgZiSyt6YZI0.html). I have also found that what one person finds as practical is not the same as what someone else finds out as practical. If you let me know what things you find as practical, maybe I can point you to which of our other videos you might enjoy, or make another that might be a good fit for you. We have videos on: How to invest better than the billionaire class. (kzfaq.info/get/bejne/gs15ZL1jypbVh2Q.html) How to strap down loads so they are actually secure. (kzfaq.info/get/bejne/asd4rNacqeDWlIU.html) How to earn a lot of money over the summer if you are a college student. (kzfaq.info/get/bejne/b719iNx13cu9kok.html) How much gas does a car burn when idling? And is it worth it to turn off an internal combustion car at a stop light? (kzfaq.info/get/bejne/ap-glrKBnK3aXYk.html) One thing we try to do is to use math to better understand math, science, and the world around us, and that can happen with problems that don't seem practical. For example, in this video about throwing things off the Empire State Building we were able to help people understand how contact time impacts the force in blunt force impacts, and how people have designed things (boxing gloves, car crumple zones, batting helmets, etc.) to make the world safer. Those are practical things, even though the problems we solved weren't very practical. Thanks for taking time to watch and to comment!
@Enderia2 29 күн бұрын
@@MathTheWorldreal quick, you put parentheses in your yt links, which would link to a completely different video or nothing at all. Put the parentheses a space away if you want it to be… well, practical.
@Maanvik_ 28 күн бұрын
@@MathTheWorld I was just kidding I meant throw the item on a person
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