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Published byBenjamin Tucker Modified over 3 years ago

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Acceleration And related topics: average velocity, instantaneous velocity, acceleration due to gravity

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Acceleration (a) Your concept of acceleration is probably lacking. When the velocity of an object is changing it is accelerating. acceleration = rate of in velocity Acceleration is the derivative of velocity as a function of time. a = v/t Using physics variables, how would you write that formula in calculus?

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2 ways a body can accel. in mag. (speed up or slow down) in direction (traveling in a curved path)

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Annotation of velocity Initial velocity = v o or v i Final velocity = v or v f Other velocities = v 1,v 2,v 3 ……

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Average velocity When an object is accelerating we can not speak of velocity as we do when an object has constant velocity. We must speak in terms of average velocity during a time interval. Acceleration is always implied.

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Average velocity - formulas V ave = d t /t t V ave = (v f +v o )/2 V ave = (v 1 + v 2 + v 3 + … + v n )/n

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Acceleration formulas - table 3- 3 p.68 v = v o + at d = v o t + 1/2at 2 v 2 = v o 2 + 2ad Derivations These are the forms of the equations I want you to use. These are slightly different than those given in your text. Write these formulas on your formula note card.

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Dimensions of acceleration MKS? CGS? Discuss what the dimensions mean.

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Uniform acceleration Constantly changing velocity - magnitude or direction.

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Instantaneous velocity Velocity @ one instant in time. Define instant Velocity for which the displacement is measured over shorter & shorter time intervals. V ins = v ave over a short time interval Acceleration is always implied.

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V ins cannot be measured w/ 100% accuracy Since v ins is only used with accel. Motion, velocity is changing within an instant. No matter how short the time interval is a shorter time interval will yield a value of v ins.

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100% accuracy cont. V ins would be absolutely correct if it were so instantaneous that the displacement were meas. over the exact path. This would be impossible. Either constant of direction or t = 0, then d/0 = undefined or d = 0 the 0/0 = 0 and the object is obviously moving. Therefore, v ins cannot be meas. W/ 100% accuracy.

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More v ins v ave = v ins only in the special case of constant v. Vins can change in 2 ways: - speed - direction

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Consider v ins & 100% accuracy when direction not speed is changing

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With circular motion speed is the limit of v ins

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v ins & 100% accuracy cont. Therefore it is impossible to measure v ins w/ 100% accuracy due to changes in either speed or direction. When direction is involved v ins > v ave

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Instantaneous acceleration Also exist Involves velocity & time instead of displacement & time.

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Acceleration due to gravity (g) g = the accel. due to gravity. g is a function of the mass of the body causing the accel.. Therefore since the mass of the earth is constant, g is also constant. g gravity. Gravity is the force that causes g and F a, although F a.

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g g = - 9.8 m/sec 2 = - 980 cm/sec 2 = -32 ft/sec 2 Notice g is only in 2 sign. dig.

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g formulas v = v o + at ---> v = v o + gt d = v o t + 1/2at 2 ----> d = v o t + 1/2gt 2 v 2 = v o 2 + 2ad ----> v 2 = v o 2 + 2gd

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g exercise 1. Present the data from the handout in a data table. 2. What general conclusion do you draw from your data? 3. From your data, hypothesize about the value of g at sea level on the equator. 4. What does the value of g at the N pole compared to other locations tell you? 5. Name a U.S. city with a N latitude of 45°. 6. What is our approx. latitude?

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Data table Location & the value of g. LocationValue of g (m/s 2 ) N pole-9.832 Sea level @ 45 o N latitude -9.806 Denver-9.796

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