WEBVTT
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this'll questions were asked to show that the work done
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by a constant force field wants people to see on
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the path that we were given. Is that a
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circle of radius one? So we have X squared
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. Uh, that's why I swear it is well
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to one. And we know to pure amateur eyes
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circle. So we just said x equal to co
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sign T like will sign t and he goes from
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0 to 5 and then our are It's just society
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off site tea and then our prime It's negative sign
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t common cause so we could stick the derivative off
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CO sign T. All right now And now what
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? We're told that West units that are forced feel
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this cost. So we're gonna set our force field
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after two equal income and just constants were eman n
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are constants of CN STS, right. So now
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we know that the work is the integral along the
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curve of f dot are. And then now what
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we're gonna do is we're gonna write everything in terms
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of cheap. So that's where the work will simply
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be the integral from 0 to 5. Well,
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I m call much of the vector and public end
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, uh, about product with the vector Negative Sign
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Club coastline. So this is just the product,
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and what we get is the integral for you're a
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to buy a negative M Sigh Inti Bus and Co
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sci fi. The M ISS constant the MND and
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are constants so we can pull them to the outside
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. And the integral scientist is simply negative co sign
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teeth. But remember, there's a negative in front
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of the magic schools away, and the Integral co
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signed you've just signed. All right, so now
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we're gonna plug in to buy and then subtract,
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Subtract from that the value at zero. So this
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is an who sign to Pai minus co signs you're
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also co cited by is just one no sign zeros
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. Also one bus and sign of two pi zero
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sign of 00 So we get em. Times one
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minus one. She just zero an an time zero
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minus. Here with this is against you. So
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the work done by a constant force field is zero
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. So we showed that now part B were given
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of the force field. This k Times X were
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X is a vector field given by Ex cover life
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. So now what we do is we just,
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uh, multiply like a So our vector field becomes
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Horsfield. I'm sorry becomes k X, come off
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the line. And then what we get is we
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know from our privatisation about that X is just close
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I inti and why you signed. All right,
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now we're asked to find the work, and we
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have to show that it's is you. So you
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know that the work is just the integral along the
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curb See off at stock d are another way to
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write that is the integral from 0 to 2.
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Yes, I'm 0 to 2 pi at which is
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x co sign D comma. That's our case goes
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I e chronic A sci fi Don't our prime tea
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that they are crime. We also found that above
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have been part is just negative Sign t close I
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, Inti and then DT So now we're gonna find
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adult Frana. So that's just negative, K.
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So we're just gonna multiply this first term this first
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turn and then after that, this second term times
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this second. So we get negative co scientist negative
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Keiko site. He's fine teeth was scarce. Scientific
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o society. So these to cancel we're just left
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with zero. So again now we showed that the
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work for this new force field, which is Ah
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, Kate, Times X, where X is just
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, uh the vector X cover line is also equal
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to tears of the work in Syria.