WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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The question here is by what factor does
the drag force increase
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when the car increases its speed
from 65 kilometers an hour
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to 110 kilometers an hour?
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So the drag force formula is one-half times
drag coefficient times density of air times
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the cross-sectional area of the object
times its speed squared
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and I put a subscript only on the speed
because that's the only
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factor that changes between
the two scenarios—
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the first and the second scenario—
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so we have speed 1 and we have speed 2.
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So when we divide these two drag forces,
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all these factors are going to cancel
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and we are left with only *v 2 squared*
divided by *v 1 squared*
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and that can be written as *v 2*
over *v 1* all squared.
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I noticed that it's not necessary to change
the units into meters per second
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although that's normally what
we would do to have
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*mks* units—meters, kilograms
and seconds—
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but in this case, the units just have to be
the same so that they cancel
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and we'll be left with an answer of 2.9.
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So we can say that the drag
force in case two
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is increased by a factor of 2.9 compared
to the drag force in scenario one.