Levers are amazing!

Hi,
today I want to shine light upon one of the simplest machines that there ever were. Those are levers, so intuitive that you will see even small kids use them.

SPOILER alert:

They are amazing in crushing your fingers.


I kind of connect this word with the game Neverwinter Nights where it was used for the handles on walls that opened doors and so on, I had to use translator to make sure it was right because it did not feel so.

With this “door thing” it could come up to your mind that levers are kind of long rods of wood or iron. It is quite useful to have them like that.

Take for example something very close, door handle is an amazing illustration of how levers should look like! It is long quite enough for you to open the door.. now try to take

Epic door handle

just the closest part to your door, the one perpendicular to the plane of door. Sure it is much harder, probably even impossible for you to open them. This is because the further away you are applying force from axis of rotation the easier it is to rotate the whole thing.


Lets assume you have one Czech locomotive of class 363.

V čele orient expresu.

This is old Czech locomotive… there is ENGLISH wiki page about it!

Lets say that you are able to stabilise it and you have unlimitely strong rod of something that is also weightless. Also you have something that works as axis of rotation and it is also undestructible.Levers are amazing!

Everything is put like above. Lets say that you weight 70 kilograms (if less than you have sack of sand with you, if more than you touch the ground with your feet).

How far away do you need to be if you were able to put the locomotive 1 centimeter from the axis?

Well, we have to calculate it precisely because if you sit too close you are going to be thrown across a long distance!

What you want for balance is that the final moment of force is equal to 0. Both you and the locomotive has this moment which means that:

M(locomotive)=M(You)

You calculate the moment here pretty easily, there have to be to things in the equation and those are very intuitive. If you push on door handle very hard (force) it is easier. If the door handle is longer it is also easier (r for distance).

M=F*r

This type of locomotive weights 87 tons. Now we can calculate the moment (F=m*g):

M=87 000*10*0.01=8 700 N*m

You moment of force must be the same and you know your weight (times gravity acceleration) so there is last thing the distance.

r=M/F
r=8 700/700
r=12.4285714286 meters

Wow, only if you are 12.5 meters from the train you can easily rest down! The problem here is that usually in this type of physics we consider that all of mass of one object is compressed on one place called center of mass. This is the problem because in reality whole locomotive simply wont be 1 centimeter away from the center. Cool anyway 😉


I mentioned at the start that levers are good in crushing fingers.. and they are. Take for example door that is 0.8 meter long and somebody pushes it with the force of 5 Newtons which is like lifting 500 grams. If your finger is 2 centimeters from the door it is literary going to be crushed with the force of 200 N which is like putting 20 kilogram thing on your pinkie.

Dragallur

 

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