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Excerpt
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Explore the kinematics of constant power (as opposed to constant force).
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Photo by Lt. Col. Derik Crotts, courtesy of U.S. Army
Top-fuel dragsters like the one shown above accelerate from rest at a tremendous rate. They race on a straight 1/4 mile long track. From a standing start, they complete the quarter mile in about 4.5 seconds and reach a speed of about 330 mph by the finish line.
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Part A
Part A
Show that the statistics given in the problem introduction are inconsistent at the 10% level with the assumption that the dragster produces constant acceleration as it moves down the track.
Solution
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System:
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Dragster as
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External influence from the ground (friction) assumed to produce constant acceleration.
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Model:
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One-Dimensional Motion with Constant Acceleration.
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Approach: We are asked to prove that the model we are examining does not fit the data. To do so, we look for a contradiction. In this case, we have several ways to find the acceleration, since we have a large number of givens. Choosing our coordinates such that the race begins at xi = 0 and proceeds in the positive x direction, we have:
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Approach:
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Part B
Part B
Using the fact that a top-fuel dragster will typically weigh 2200 lbs (equivalent to a mass of 1000 kg), show that the assumption that the dragster moves down the track with a constant value for the power delivered to the car in the form of kinetic energy is consistent at (approximately) the 10% level.
Solution
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Dragster as .
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Friction interacts with the dragster in such a way as to deliver constant to the dragster's kinetic energy.
