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STATICS - EXAMPLE

    Example

 

A lunar lander module has a mass of 250 slugs on earth. Calculate (a) its mass in SI units, and (b) its weight in SI units.

If the module lands on the moon, where g is 5.30 ft/s2, determine (c) its weight in SI units, and (d) its mass in SI units. Calculate all the answers to four significant digits. Recall the gravitation constant, g, is 9.807 m/s2 (32.17 ft/s2) on the earth's surface (average) and 1.622 m/s2 (5.321 ft/s2) on the moon's surface (average).

   
  Solution


 

Units table in the appendices can be used for this example. From that table 1, slug is equal to 14.59 kg.

     a) 250 slugs (14.59 kg / 1 slugs)
           = 3,647.5 kg
           = 3,648 kg

The final answer is expressed with four significant digits.

Weight is mass multiplied by the acceleration due to gravity (W = mg). In SI system g is 9.807 m/s2

     b) W = 3,647.5 kg (9.807 m/s2)
              = 35,771.01 kg-m/s2
              = 35,770 N
              = 35.77 kN

     

 

 

 

When the module is on the moon, g is 5.321 ft/s2. Its weight can be found by multiplying the mass by the gravitational acceleration (both in US units)

    c) Wm = mgm = 250 slugs (5.321 ft/s2)
                = 1,330 lb

To convert the final answer to SI unit, the units table from the appendix can be used again. 1 lb is 4.448 newton. (Please note that the final answer needs to be expressed in four significant digits)

     1,330 lb (4.448 N / 1 lb)
       = 5,915.8 N
       = 5.916 kN

The same result can be found by multiplying the weight on earth by the ration of gravitational accelerations.

    Wm=We (gm / g)
           = 35.77 kN (5.321 ft/s2) / (32.17 ft/s2)
           = 5.916 kN

d) The mass is independent from the gravity and will remain constant.

   
 
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