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# 2D equilibrium -- balancing games

How does everything even out? Learn what 2D Equilibrium is and how it effects the balance of life. Created by MIT+K12.

## Want to join the conversation?

- Where can i get that tool in2:00?(11 votes)
- You can purchase that kind of tool online from somewhere like FLINN scientific.(16 votes)

- At0:38how do temperature and pressure change the equilibrium of an object?(6 votes)
- She is not saying that temperature and pressure change the 2D equilibrium, she is saying that those are other
*forms*of equilibrium.(14 votes)

- so the left side is 2D and it had 2W than the right side can be 1/2D and 5W?(3 votes)
- No, both sides have to equal out. 2D times 2W equals 4 DW because 2 x 2 = 4 and D times W equals DW. (Since they are letters, you show that they are multiplied times each other by just placing them next to each other.). If you have 1/2 D on the right side, you would need 8 W on the right side too for it to balance. 1/2 times (or, in other words, one-half of ) 8 equals 4. It might help you to understand it if you can make a similar balance at home and experiment with different weights and distances.(4 votes)

- Is there such thing as 3D equilibrium? This is only 2D equilibrium.(2 votes)
- The phenomena explained in the video is concerned with the statics branch of engineering mechanics. Furthermore, only the 2D equlibrium concerned with statics, or bodies in equilibrium. When analyzing structures in a 3D space with a 3D coordinate system, equilibrium is maintained not only in the presumed x and y axes but also z axis too. In aerodynamics, there are even more axes to be concerned about: yaw, pitch and roll.(3 votes)

- Where do I get all the tools in the video;((2 votes)
- ummm u can find the tools at walmart all for around 14:95(2 votes)

- This does not make sense a bit can you tell me more about it(2 votes)
- Have you watched any videos about basic algebra? It might help if you understood the concept of figuring out what to do to make both sides equal. I will try to find an appropriate video on the subject and post it here for you.(0 votes)

- Does distance matter in Equallibreium(1 vote)
- Isn't it a 3D equlibrium since it is equilibrium in 3D space and that everything that exists on this planet, even a sheet of paper is 3D?(1 vote)
- I agree that it is 3D equilibrium. But Since we are using just the front side of the wooden stick(part of the wooden stick) not the wooden stick as a whole it is 2D. A sheet of paper is 3D but when looked from one side it is 2D.(1 vote)

- What is the difference between
**Work done**and**Torque**,when`Work done=`

W=F x S

(where F is the force, S is the displacement and W is the work done)

?`Torque=F x D`

(where F is the force and D is the displacement)(1 vote)- The key difference is in both words' usage in various applications. For example, you wouldn't say that, "1000 Joules of "Toque" was done on a crate as it was lifted a specified distance h" instead you'd say, "1000 Joules of WORK was done on a crate as it was lifted a specified distance h." Compare that with: 1000 J Torque (or moment - interchangeable terms) was subjected about an arbitrary point A on the given lever"... and so forth.

So, in terms of equations, they're identical however in applications and terminology, not at all.(1 vote)

- So if we were on another plaint would our whole system of measurement need to change because things might weigh differently there?(1 vote)

## Video transcript

I got this to balance
by carefully measuring equal distances, and
hanging equal weights at those distances. This balance is
called equilibrium. Equilibrium is when the state
of the system isn't changing. In this case, the 2D equilibrium
case, the state of the system is the position of
these objects, which still isn't changing,
unless I throw a coin in to knock it out of equilibrium. In other types of equilibrium,
the state of a system could be its
temperature, or pressure, or something else entirely. But now, I'll focus
on 2D equilibrium, the balanced state where
the positions don't change. Some things balance
in the middle, and these things tend
to be symmetrical. Other things balance off to one
side, always the heavier side. What if I want to move this
cup a different distance away from the middle and still
keep it all balanced? One way of doing this
is moving the other cup to the new distance as well. Sure enough, it balances again. But there's another
way of doing this. I could've left the right
hand cup at the old position and just taken out
some of its weight. This also balances. So we found two different ways
of balancing the same thing. We can either change the
weight or change the distance. In equilibrium, where we have
forces F1 and F2 balancing each other at
distances D1 and D2, the counterclockwise
force times distance must equal the clockwise
force times distance. Force times distance has
a special name, torque, from the Latin word to twist. In 2D equilibrium, clockwise
and counterclockwise torques are balanced. Before I calculate
some torques, I need to check some
of the masses. The mass of five
coins is 13 grams. And the mass of the cup plus
the string is also 13 grams. And since we're on
Earth, this means that they both have
the same weight, which I'll call W. Start it off with
weights 2W one cup plus 5 coins hung on each side, distance
I'll call D from the middle. And I got it balanced, and
the torques 2 times W times D, are equal on both sides. And it balances. But when I moved
the distance to 1/2D and kept the weight at
2W, five coins plus a cup, there were two ways
that I could balance it. I could either move the
other cup closer to 1/2D, or I could keep
the other cup a D and just empty it
of the five coins. So now its weight
is only W. This leaves the counterclockwise
torque, 1/2D times 2W, equal to the clockwise
torque, D times W. But what if we
move the left hand cup farther from the middle to
2D, and leave its weight at 2W. One way of balancing it
is to move the right hand cup farther out as well. Or we can move the right
hand cup back to D, and increase its weight to 4W. Let's check that this would
make the torques work out. On the left hand side, we have
2D times 2W, which is 40W. And on the right
hand side, we have D times 4W, which is also 40W. How many coins will we
need in the cup for that? One cup is 1W, and so
we need three more W, So that's 15 coins. So four W is equal to
one cup plus three more W, which we get with 15 coins. I'll move the cup to a
distance D from the middle and add a total of 15 coins,
for a total weight of 4W. Sure enough, it balances,
because in equilibrium, the counterclockwise torque has
to equal the clockwise torque.