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09/02/09 - Chapter 3 - Forces and Motion in One Dimension
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 | Acceleration of gravity in free fall - g
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 | Class measurement of the acceleration of gravity using ultrasonic motion detectors
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| In the absence of air resistance, all objects fall (accelerate) at the same rate (-9.8 m/s/s).
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| That means their velocity increases in the downward direction by 9.8 m/s every second.
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| Motion of an object dropped or thrown vertically
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| An object is dropped from rest from a height of 50 m. What is its velocity and height after 3 seconds?
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| After 3 seconds, the object is falling at a velocity of v = -9.8t = (-9.8m/s/s)(3s) = -29.4 m/s, and it has fallen a distance of -44.1 m. Since it started at a height of 50 m, it is now 50m - 44.1m = 5.9 m above the ground.
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| A ball is thrown upward from the ground at 20 m/s. At what time does it reach its maximum height, and what is the maximum height.
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| The object reaches its maximum height when the velocity equals zero: t = 2.04 s. The area under the triangle gives the displacement (maximum height the object reaches): 20.4 m.
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| Hanging a weight from a spring.
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| The spring stretches until it can support the weight.
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| Similarly, when you stand on the floor, the floor sags or compresses (microscopically) slightly until it can support your weight.
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| Acceleration and apparent weight
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| Your apparent weight depends on how much force you exert on a scale.
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| If you and the scale are accelerating upward, then the scale is pushing upward on your feet with a force greater than your weight (which is why you're accelerating upward), and your apparent weight is greater than your actual weight.
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| Similarly, if you and the scale are accelerating downward, then the scale is pushing upward on your feet with a force less than your weight (which is why you're accelerating downward), and your apparent weight is less than your actual weight.
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| These diagrams show all the forces acting on an object.
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| The magnitude of friction is not constant. It depends on the materials that are in contact and on the force pushing two objects together. For an object on a horizontal surface (such as a table), the force pushing the object and the table together is the weight of the object (or equivalently, the normal force N, with which the table pushes upward on the object), and the magnitude of the frictional force is proportional to the weight of the object (or the normal force). This is written as f = µmg or f = µN. µ is called the coefficient of friction and depends on the materials involved and the roughness of the surfaces. Here is the table from the bottom of p. 64 of the text which shows some sample values of µ.
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| Kinetic friction is the friction when an object is moving. For rubber on glass, µk = 0.7
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| Static friction is the friction when an object is not moving. For rubber on glass, µs = 0.9. Static friction is typically larger than kinetic friction. So it takes a little extra force to get an object to start to move, but once it breaks free, friction decreases slightly and it takes less force to keep the object moving at a constant velocity.
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| Tension forces in ropes and cables
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| Read the first part of Chapter 3, pp. 54-75.
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