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Welcome to new problems.
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This time we're dealing with center of mass.
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So if you think about a typical object like this one, what's going to happen is we have the middle, we have the middle, which is the provides md, and md is the center of gravity.
00:29
Md is the center of gravity.
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If it's a geometric figure like this one, which is the tangana, then what's going to happen is this middle part will also be the center of mass.
00:45
So we can define it as the center of mass.
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And for the most part, if you have two objects, if you have two objects, then they have specific masses.
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This is m1.
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This is m2, for example.
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And then you take a point of reference.
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Then the distance from m1 up until the point of reference is going to be up until the point of reference.
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And so to get the center of mass, you take the product of the object's mass, m1, and its distance plus the second object and its distance from the point of reference, and then you divide it by the sum of these two objects.
01:36
So that's the idea behind the center of mass.
01:39
So now we do have a problem and this is a new problem we're looking at.
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Think about a pier.
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So it's almost like if you go to the beach we have this santa monica, santa monica pier.
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And if this is the pier and we have a raft, you know, a raft is like a simple boat.
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We have a raft that's close to the pier.
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We'll say this is this happens to be our raft right there this is our raft and obviously we have to make it float otherwise if it's synced were kind of messed up the distance from the pier up until the raft happens to be 0 .5 meters and then the length of the raft is the same as 6 .0 meters so we have we have a woman, we have a woman that stands on this side of the raft.
02:53
So we have a woman that stands on this side of the raft.
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And she has a weight, she has the weight, or rather she has a mass.
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The mass, her mass is the same as 120 kilograms.
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This is her mass.
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The other thing that happens, or actually her mask, not 120 her mass is her mask is fixed so just remember that and then of course the raft also has its own mass which we're gonna call mri so mri is the mass of the raft and this one happens to be 120 kilograms that's the mass of the raft it's 120 kilograms so this is before this she works towards and then the second instance is towards what's going to happen in the second instance.
04:15
So obviously as we start to walk something has to happen to the wrap.
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Something has to happen.
04:28
It means that probably going to get closer and the distance, the distance of the distance we're looking for is the same as it's going to be a specific thing you know what's going to happen then what's going to happen to this distance this is the distance we're now looking for this gap right here you know if we start to walk towards towards the pier like that it means our boat is probably or raft is probably going move towards the edge of so that's what you're looking at and then in part a we're saying determining the distance or we could say the new distance between the the last and the pierce so we want to get the new distance and then in part d we're saying that relatives are relatives to the so either the two things we're looking at and so we do have the numbers we have the length of the both and so if we decide if we decide that this is our origin, we decide that this is our origin, then it simply means that the distance of the woman from the origin up until half the region is the same of 6 .5 meters.
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So we're going to call xw 6 .6.
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And then for the boat, for the boat it's 6 meters, but the center, the center of the center of the of the boat is at 3 meters.
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So the distance from the origin up until the center of the raft is going to be 3 .5 meters.
07:35
That's the distance because we're taking this 3 meters and then you're adding it to 0 .5 meters.
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That's what to be.
07:43
We know the mass of the woman is 60 kilograms and the mass of the white.
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We're 20 kilograms.
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So we're going to go ahead and walk on this problem.
07:56
The center of mass the center of mass the center of mass offices the mass of the mass of the wall distance plus the mass of the raft times are distance from the origin and then the mass of the woman plus of the raft so we're going to go ahead and plug in these numbers 6123 .5 meters and then we have plus 120 kilograms so the center of mass of 15.
08:42
Become 4 .5 meters from the area.
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4 .5 meters from the energy.
08:58
So if this is the fear, this is the raft, this is the graph, this is the rap and this is the rap what's going to happen is that from this end up until her position, the her new position, the woman has moved a distance, that's a distance to and so if that's a case, if you can recall, the center of mass, the center of mass, stays the same with no external, we don't have any external force...