Lecture214Week4 - This Week Circular motion Going round the...

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This Week Circular motion Going round the bend Riding in a ferris wheel, the vomit comet Gravitation Our solar system, satellites (Direct TV) The tides, Dark matter, Space Elevator 12/09/11 Physics 214 Fall 2011 1
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12/09/11 Physics 214 Fall 2011 2 Circular Motion Circular motion is very common and very important in our everyday life. Satellites, the moon, the solar system and stars in galaxies all rotate in “circular” orbits. The term circular here is being used loosely since even repetitive closed motion is generally not a perfect circle. At any given instant an object that is not moving in a straight line is moving along the arc of a circle. So if we understand motion in a circle we can understand more complicated trajectories. Remember at any instant the velocity is along the path of motion but the acceleration can be in any direction .
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12/09/11 Physics 214 Fall 2011 3 Circular motion If the velocity of an object changes direction then the object experiences an acceleration and a force is required. This is centripetal acceleration and force and is directed toward the center of the circle. This is the effect you feel rounding a corner in a car a = v 2 /r F = ma = mv 2 /r
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12/09/11 Physics 214 Fall 2011 4 Balance of forces We need to understand the forces that are acting horizontally and vertically. In the case shown the tension or force exerted by the string has components which balance the weight in the vertical direction and provide the centripetal force horizontally. T v = W = mg T h = mv 2 /r
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12/09/11 Physics 214 Fall 2011 5 Cars When a car turns a corner it is friction between the tires and the road which provides the centripetal force. If the road is banked then the normal force also provides a force. For a banked track there is a velocity for which no friction is required. F f Above W = mg F f F f Rear
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12/09/11 Physics 214 Fall 2011 6 Vertical circles If v = 0 then N = mg As v increases N becomes smaller When v 2 /r = g the car becomes weightless. Same as the “vomit comet” mg – N = mv 2 /r Ferris wheel g At the bottom N - mg = mv 2 /r At the top Mg – N = mv 2 /r + is always toward the center of the circle W = mg N v
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Free fall versus Weightless 12/09/11 Physics 214 Fall 2011 7 Near the earths surface there is a force F = mg which is called the weight of an object. Since the force of gravity is always present then this force always is present. There are situations where if we were standing on a scale the apparent weight, the reading on the scale, could be smaller or larger than the real weight. In an accelerating elevator In the case of free fall our apparent weight is zero In an elevator and the cable snaps. The case of being weightless corresponds to the case where one is moving in a circle and the force of gravity is exactly equal to the centripetal force required. Since the force of gravity is vertical the type of cases where weightlessness happens are At the top of a ferris wheel if mg = mv 2 /r At the top of a hump back bridge if mg = mv 2 /r
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Planes and satellites 12/09/11 Physics 214 Fall 2011 8 http://www.avweb.com/news/airman/184318-1.html
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