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Unformatted text preview: ME163 Mechanical Vibrations (Winter 2009) HW7 Due 2.26.09 in class25% if late within 24 hours50% if later than that 1. Shock Response. NASA landed the Mars Lander Spirit on Jan 4th 2004 as shown in the video in class. In the final decent of the rover, it was surrounded by cushions inflated with air. This allowed it bounce like a ball on each impact till it came to a rest. The cushions have both a spring effect and damping effect, but for this homework problem, consider the damping to be zero. The following data is known: (a) The mass of the rover is 180[ kg ]. (b) The gravity of Mars is 38 percent of earths gravity. (c) The booster rockets and the parachutes (used to slow down the rover) were cut off at a height of 10[ m ], after which it falls freely. We want to determine the necessary stiffness of the cushions knowing that the maximum acceleration the rover can sustain is 5 × 9 . 81[ m s 2 ]. Given that at the instant the rover is dropped it has an initial velocity of 10[ m s ], find the effective stiffness needed. From pg. 180 in the book, we know the expression for the maximum acceleration experienced during the impact is  ¨ x g Mars  = radicalbigg 1 + ( vω n g Mars ) 2 where v is the velocity just before impact. We know we can find the velocity by using v 2 = v 2 + 2 g Mars x h We are given v = 10 m/s , g Mars = 0 . 38 × 9 . 81 and x h = 10 m . Taking the square of the first equation and rearranging terms ω 2 n = (  ¨ x g Mars  2 1) g 2 Mars v 2 = k m Thus we get k = 13 . 7034 * m = 2466 . 6 N/m....
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 Winter '08
 Mezic,I
 Laplace, gM ars

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