WEBVTT
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the situation in this question is the following. This
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car is moving to the right until it meets a
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hell which is inclined at 18 degrees with respect the
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horizontal. This car is moving at 95 kilometers per
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hour. We then have to discover what is the
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minimal radios off this transition section such that the car
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do not leave the road. So these is the
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radios, it's the radios off the circle and we
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have to discover what is the minimum value off are
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such that the car do not fly away went passing
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through this transition. For that, let us analyze
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closer. Why is this transition region so lives as
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room it in the transition region? Notice that the
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transition is nothing else than a section off a circle
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. So during the transition the car is under giving
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a circular motion. Then we can treat it as
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usual. The condition that the car never leaves the
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road translates to the condition that the normal is bigger
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than or at most equals 20 So the condition is
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the following. The normal forced must be bigger than
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or at most equals 20 But now what does the
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normal force has to do with the radios off the
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circle. For that, you have to remember a
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few beats about this and typical force. So whenever
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an object is undergoing a surgical emotion, but there
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is a centripetal force acting on that object on that
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centripetal force is given by the mask off the object
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times the velocity off that object squared, divided by
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the radios off the trajectory. But then what does
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this centripetal force has to do? The normal force
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. It happens that the centripetal force is the net
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force that is acting on the radio, their action
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, which is the direction that passed through the center
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off the trajectory. Then you can see that in
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any situation, the normal force is part off the
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centripetal force. But obviously the normal forest isn't the
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wolfing. There is actually a component off the weight
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force that is composing the centripetal force. Let me
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call this component the radio component off the weight force
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. And it is like this does this level.
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You are the other component off the weight force Would
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be these one, then genteel component. Wait,
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I'm calling the beauty. I noticed that this Ando
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is the same Anno as these one because we have
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to parlor lines that are crossed, my, uh
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, straight line. Then we can also say that
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this angle is equal to teeter and then we are
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able to relate the weight with the radio component off
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the weight. It was in that triangle we have
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the following. This is the triangle. And then
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these is the 90 degree angle is the hypotenuse business
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WR and this is W t these this Tita,
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you can see that the co sign off Peter in
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that context is given by the address in sight.
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So the radio component divided by their party news which
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is the full weight then the radio component is equal
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to the weight times the curve. Sign off,
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Tita. The reform. We can write this centripetal
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force as follows at any point off this conference,
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this centripetal force is given by the radio component off
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the weight force which is pointing to the center.
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Sure, it's positive. Mind is the normal force
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that is pointing outwards. These easy. It goes
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to the mass times velocity squared, divided by the
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radios. Then in the limiting situation where the normal
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is very very close to zero so that we can
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say that it is effectively zero. We can say
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the following the radio component off the weight force must
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be equal to M B squared, divided by r
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So the radius must be equals two m v squared
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divided by the radio component off the weight force Using
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the equation for the radio component off the weight force
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that we had just directed. We get the following
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em These weird divided by W times The co sign
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off detail Remember that the weight force is given by
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the mass off the object times the acceleration of gravity
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So these can be written as m v squared,
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divided by AM G times Nico's sign off, Tita
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, We can simplify the masses and then we get
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an equation for the radios. The create parade Ian's
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is V squared, divided by G times. Niccum
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, sign off, Tita, We already knew what
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his V we knew What is G? Actually we
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remember that he is approximately 9.8 meters per second squared
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. So the only thing that we are left to
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discover is the value off this angle, Tita,
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for that we have to use the geometry of the
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situation. Notice the following this angle between these lines
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and these line is 18 degrees. But the angle
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between the black line on this red line is 90
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degrees. I can extend this line so that it's
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easier to see. As you can see, there
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is a 90 degree angle here them. With that
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in mind, we can better mind. What is
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this angle? Because we know that this world angle
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is 90 degrees, then these angle must be 90
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minus 18 degrees, which results in 72 degrees.
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These is this angle, but notice that the angle
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between the radio direction on this blue line is also
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90 degrees. So these angle is an angle off
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19 Reese. Therefore, we conclude that teeter plus
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72 degrees must be equals to 90 degrees on.
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The only possibility for the result is that Tito is
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also equals to 18 degrees. Now that we know
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teeter, we can finish the question So the radios
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is given by 95 kilometers per hour. We should
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covert these 95 kilometers per hour two meters per second
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. For that, we divide it by 3.6.
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So the velocity is 95 divided by 3.6 meters per
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second and this is squared and then we divide by
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9.8 times. They could sign off 18 degrees and
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these results in the radios off approximately 75 meters,
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which is the minimal radios off the transition region.