2. In 2012, the Curiosity rover (mass m = 900 kg) landed on Mars (and is...
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2. In 2012, the Curiosity rover (mass m = 900 kg) landed on Mars (and is still at work, nearly a decade beyond its original two- year mission!) It approached the planet at 20000 km/hour. Atmospheric drag slowed it to about 1600 km/hour, then a parachute opened, which slowed to 320 km/hr (90 m/s). Rockets then completed the deceleration so it could make a gentle landing. How did NASA engineers design a parachute that they knew would work on Mars? How could they predict the minimum diameter d of the parachute that they should use on Mars by doing tests on Earth? (a) Relevant physical parameters include the acceleration due to gravity g and the atmospheric density p (considered constant on each planet: PEarth = 1.2 kg/m, PMars = 0.02 kg/m). The atmospheric viscosity is not important for this rough analysis because it is low on both planets. Develop a set of dimensionless parameters for this problem. (b) Use Matlab to confirm the vectors that span the null space that you found in part (a). You should be able to do this by entering your matrix A that represents powers of fundamental dimensions and then typing one command. Use Matlab's help resources to determine what that command is. If the result is not exactly what you found in your work by hand, explain how the results are related. Then use Matlab to confirm that one of the vectors you found in the null space actually produces the zero vector when it is multiplied by the A matrix. The goal here is for you to practice using Matlab vector operations, so do not retype any values. In one line, multiply A by the null space vector. Use a colon (:) to pull off the desired row or column of your null space result. (c) Using a model rover on Earth, what set of experiments and analysis would you do to solve the design problem of finding the correct minimum diameter? Explain clearly in a few sentences for full credit. Remember that the set of nondimensional parameters you found in part (a) not unique; to answer this and the next parts of the question you need to consider a different set. (d) The parachute used for the rover on Mars actually had a diameter of 20 m. What single test (one diameter parachute) on Earth with a 10 kg model rover could prove this to be correct for a 90 m/s Mars terminal velocity? What velocity would be measured in the Earth experiment? 2. In 2012, the Curiosity rover (mass m = 900 kg) landed on Mars (and is still at work, nearly a decade beyond its original two- year mission!) It approached the planet at 20000 km/hour. Atmospheric drag slowed it to about 1600 km/hour, then a parachute opened, which slowed to 320 km/hr (90 m/s). Rockets then completed the deceleration so it could make a gentle landing. How did NASA engineers design a parachute that they knew would work on Mars? How could they predict the minimum diameter d of the parachute that they should use on Mars by doing tests on Earth? (a) Relevant physical parameters include the acceleration due to gravity g and the atmospheric density p (considered constant on each planet: PEarth = 1.2 kg/m, PMars = 0.02 kg/m). The atmospheric viscosity is not important for this rough analysis because it is low on both planets. Develop a set of dimensionless parameters for this problem. (b) Use Matlab to confirm the vectors that span the null space that you found in part (a). You should be able to do this by entering your matrix A that represents powers of fundamental dimensions and then typing one command. Use Matlab's help resources to determine what that command is. If the result is not exactly what you found in your work by hand, explain how the results are related. Then use Matlab to confirm that one of the vectors you found in the null space actually produces the zero vector when it is multiplied by the A matrix. The goal here is for you to practice using Matlab vector operations, so do not retype any values. In one line, multiply A by the null space vector. Use a colon (:) to pull off the desired row or column of your null space result. (c) Using a model rover on Earth, what set of experiments and analysis would you do to solve the design problem of finding the correct minimum diameter? Explain clearly in a few sentences for full credit. Remember that the set of nondimensional parameters you found in part (a) not unique; to answer this and the next parts of the question you need to consider a different set. (d) The parachute used for the rover on Mars actually had a diameter of 20 m. What single test (one diameter parachute) on Earth with a 10 kg model rover could prove this to be correct for a 90 m/s Mars terminal velocity? What velocity would be measured in the Earth experiment?
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Modern Advanced Accounting In Canada
ISBN: 9781259066481
7th Edition
Authors: Hilton Murray, Herauf Darrell
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