Sunday, April 24, 2022

3557 - MATH - for a space shuttle launch?

  -  3557  -  MATH  -  for a space shuttle launch?-  Math exercise to calculate the fuel spent of a Space Shuttle launch.   The Space Shuttle is retired so we will miss those launches from Kennedy Space Center.  The Shuttle itself carries 55,000 pounds of fuel  At 8 pounds per gallon that is 6,900 gallons of fuel taken aloft. 


---------------------  3557 -  MATH  -  for a space shuttle launch?

-   It is not quite enough fuel to carry it to the Moon.  It would need 65,000 pounds of fuel to make a one way trip to the Moon.  See Review 1270 for a review of “ The Space Shuttle’s Last Flight”.

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-  The Shuttle is not designed to make a trip to the Moon.  It is designed for a low Earth orbit of 236 miles high traveling at 17,180 miles per hour.  1270 Review explains how this orbit is achieved by obtaining a velocity that balances Kinetic Energy ( the energy of motion) with the Gravitational Potential Energy of elevation.  Do the math.

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-  The Shuttle jettisons the main fuel tank used at launch.  It gets the Shuttle off the launch pad and to 50 miles altitude.  The Launch Fuel Tank is a cylinder 8.4 meters in diameter and 29.6 meters long.

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-  How many gallons of fuel does the launch tank carry?

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--------------  Volume  =  area of the cylinder cross section *  height

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--------------  V  =  pi * r^2  * h

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-------------  V  =  3.14  * ( 4.2)^2  *  29.6  

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------------   V  =  1,600 meters^3

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------------  one liter  =  1000 cm^3

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-----------  V  =  1,000,000,000 centimeters^3

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-----------  V  =  1,000,000 liters

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----------- one liter  =  0.26 gallons

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---------------  V  =  420,000 gallons

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-  You are part of the launch crew and the flight controllers would like to know after launch when there is only 1/8 of a tank of fuel left.  Your job is to place a detector fuel gauge in the tank to give his reading.  Where do you put the gauge?

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---------------   1/8 volume left  =  1/8 ( 1,600 meters^3)  =  200 m^3

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---------------  V  =  pi* r^2 * h

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--------------   200  =  3.14 * (4.2)^2 * height

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--------------  height  =  3.6 meters.

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-  You install the fuel gauge 3.6 meters above the bottom of the tank.

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-  The launch vehicle burns 1000 gallons of fuel per second.  How long do we wait to get the fuel gauge to send the signal after blast off?

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-  The tank will have burned through 7/8th of the volume of fuel.

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----------------------  7/8  *  420,000 gallons  =  367,500 gallons

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---------------------  367,500 gallons /  1000 gallons / second  =  367.5 seconds.

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-  The fuel gauge signal should arrive in 6.1 minutes after launch.  An announcement will be made shortly, stay tuned.

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April 24, 2022      MATH  -  for a space shuttle launch?            1410   3557                                                                                                                                              

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--------------------- ---  Sunday, April 24, 2022  ---------------------------






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