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Harut

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I see Fadiushka will not answer my math puzzles anymore. :(

 

------

 

"After the long, miserable spring we had here in the great Montreal, we finally had a nice sunny, warm day. It happened to coincide with my 20 year old friend(Domino) being home from university on summer vacation. I asked him if he wanted to go for a ride, and he said, "Not really, dude."

 

Then I said those magic words: "ice cream." He quickly changed his mind.

 

As were riding over to the nearby creamery, he turned to me, and said, "I know that one and six is six. But, is two and five 10?"

 

"No", I replied, "two and five is twelve."

 

"Then what's 3 and 3?", he asked.

 

"Seventeen," I responded.

 

"Oh yeah", He said. "I think I've got it now."

 

The question is, what the heck are Azat and Domino talking about?

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Okay Harutik and Fadiushka and all others who know some basic physics and math. :)

 

My friend Sip has a seesaw. The board of the seesaw is a foot wide and eight-feet long. It weighs 36 pounds.

 

"What's odd is that the fulcrum is two feet from one end. Of course, there's six feet on the other end. On the short side, he's placed a solid concrete cube, which is one foot on each side, right at the end of the board. The cube weighs 48 pounds. He wants to balance the seesaw."

 

So, here's the question: What weight, also a solid cube one foot on a side, does he have to put all the way at the other end, for the seesaw to balance?

There is many way to interprate this thing Azat.

 

From what i understood and one interpretationg of the question.

 

The gravity center of the cube is in the middle, which result on the half distance of each sides.

 

Which means that the concrete center of gravity will be on 1.5 foot from the center in one side and 5.5 foot on the other side.

 

Be x the mass of the first concrete.

Be y the mass of the second concrete.

Be r1 the distance between the center of gravity of x and the center of the board.

Be r2 the distance between the center of gravity of y and the center of the board

 

(x * r1) = (y * r2)

 

(48 pounds * 1.5 foot) = (y * 5.5 foot)

 

y = (48 pounds * 1.5 foot) / 5.5 foot

y = 144/11 pounds.

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Maybe you should think about the weight of the board a bit as well. it is there for a reason

weight of the board does not play a relevant role unless it is not uniform.. its a simple model to use for the answer, i dont have time right now to calculate, but this is it..

 

w={(mass one)(position of one)+(mass2)(position of two)}devided by(mass one+mass two)

 

the units of mass do not matter, as they cancel out, you have left distance.. that should do it :) solve for your unkown :)

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Maybe you should think about the weight of the board a bit as well.  it is there for a reason

Azat, you are right, for some reason I have not seen the weight of the board. I'm not very well right now, I will answer later.

 

Gevo, the weight of the board does play a role, if it were to not play any, one side wont go down and the other up, when they are not the same size.

Edited by Fadix
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Ofcourse i should say there is some prework to do on this for it to be exact. You must find the center of mass of the first object my integration. Then u use the fact of the center of mass of the block as a point in space, take your fulcrum to be 0,0, and set up your axis accordingly.. then it would workk..
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Azat, you are right, for some reason I have not seen the weight of the board. I'm not very well right now, I will answer later.

 

Gevo, the weight of the board does play a role, if it were to not play any, one side wont go down and the other up, when they are not the same size.

dang.. lol. thats right :)... thats not any more work though.. you just have to find the percent of the weight contributing the force on one side, and incorporate it into that problem.. hmm..

 

dangit, im feeling like i wanna do thi snow.. lol.. but i have no time.. infact, i shouldnt be here right now.. :(

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OK Azat, I will just add few things and will answer tomorow or later.

 

The gravity center is at 4 foot for the weight. Because the first 2 foot on each others are waved out because they are in equilibrum. The rest from 2 to 6 are left from one side, the gravity center being at 4. This part weight 18 pound.

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Then I said those magic words: "ice cream." He quickly changed his mind.

 

As were riding over to the nearby creamery, he turned to me, and said, "I know that one and six is six. But, is two and five 10?"

-----------what the heck are Azat and Domino talking about?

 

* Poster's Note: Half of the time I am not sure.*

I have to be honest here... I looked it up on the net and I still don't get the answer. When technicalities about vehicles are involved I am as numb as a corpse. All I know about the subject are bells, tires and training wheels on the bicycles. Oh yes and the fact that balance is needed to operate the machinery properly, that's why your calves must be muscular and your legs agile. As far as math is concerned, I know that in the beginning of the problem multiplication is involved.

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ok screw studying.. lol.. im studying for physics anyways.. haha.. here is what i think then.. im thinking as im writing..

 

the board is 36 pounds, and 8 ft, so .25% of the weight is on the 2 foot section, thus..

 

net weight on side 1= [.25(36)]+48

then using previously stated calculation we get.

 

at fulcrum of 0 and distance of first mass at -2, and distance of second mass at +6, and the above met weight on side one..>>> this yields that the total weight of side 2 is 28.5lbs.

Now the 22.8 lbs may be a little off, infact if im not mistaken the very "exact" number would be a little less than that. But i didnt go through the integration, i kept it little simple.. for my sake.. lol.. now.. tell me how wrong i am?

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I just treated the weights and the board separately. Makes the center of mass calculations much easier.

I swared having answered you, for a reason I did not. :huh:

 

I know Sip, when I answered you first about the center of gravity, I meant I have found the answer for the solution.

 

The point here is that the center of gravity for the board in each side is not involved, because it is at the center of the board. which means at 2 feet from the "artificial center."

 

1.5 * 48 = 2 * 36

Edited by Fadix
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36/8 4.5

 

6*4.5 =27 Avg Dist from fulcrum 3 feet or 81 pound feet

 

2*4.5=9 Avg Dist from fulcrum 1 feet or 9 Pound feet

 

Cement block is how many feet from the fulcrum on Average? :)

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Domino it is not at the center

I know Azat. I don't understand, are you telling me my answer is not acurate?

 

The board has one gravity center which is on its middle. That would mean at two feet from the point(artificial center) which separate it with its other side.

 

The one I already have found first without considering the board was 1.5 * 48 = 72. Now the other would be 2 * 36 = 72. Isn't that accurate? <_<

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Sounds to me like it's already balanced. I don't know why you guys are wasting your time. :rolleyes:

Sipchik you are too bright. I have to admit when I hear this on Cartalk(by the way they mentioned you name as the owner of this seesaw) I was completely off like Domino in no mans land trying to remember physics and crap

 

----

 

Did I ever tell you guys that I was on cartalk once?

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36/8 4.5

 

6*4.5 =27 Avg Dist from fulcrum 3 feet or 81 pound feet

 

2*4.5=9 Avg Dist from fulcrum 1 feet or 9 Pound feet

 

Cement block is how many feet from the fulcrum on Average? :)

But Azat, I find the same thing.

 

The center of gravity of the entire board is in the middle of the board(reread what I said). The distance between this middle and the artificial middle(which you call "fulcrum") is two.

 

So again like I said. 2 * 36 = 1.5 * 4.8

 

Both side 72.

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Fad, I understand how you are looking at it and I think it's right.

 

The way I did it:

 

2 feet on the short side and 2 feet on the long side of the board cancel.

On the long side, we have 4 feet of board left (18 lb) on average 4 feet from the fulcrum.

On the short side we have 48 lbs of weight at 1.5 feet from fulcrum.

 

Since 18 * 4 = 48 * 1.5, everything is balanced.

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