Force and Stress 1. i) Calculate the total upward force in kilonewtonson the bas

Question

Force and Stress 1. i) Calculate the total upward force in kilonewtonson the base of a continent that is 30 km thick, has an area of 4.0 x 107 km- and has a mean density of 2.85 g/cm3 What is the total stress (assume it is a principal stress) at the base of the slab - in megapascals? in kilobars? Useful: 1 dyne1gcm/sec? 1 Newton - 105 dynes Gravitational acceleration 980 cm/sec2 ii) What contact area would you need when jacking (con gato) a vehicle to general the same pressure? Assume jacking-lifting 1 ton.

Explanation / Answer

i)

Density = mass/volume

mass = density x volume

mass = 2850 x 30 x 4 x 107 x 109(1 gm/cm3 = 1000 kg/m3and 1 km3 = 109 m3)

mass = 3.42 x 1021 kg

now force = mass x acceleration (here we'll take acceleration due to gravity as mass is attracted by the same acceleration)

force = 3.42 x 1021 x 9.81 (taking acceleration due to gravity in S.I. units that is m/s2)

force = 3.35502 x 1022 Newtons

stress = force/ area

stress = 3.35502 x 1022 /4 x 107 x 106 (1 km2 = 106 m2)

stress = 838,755,000 pascal or newton/meter2

stress = 838,755,000/106 = 838.755 megapascal

stress =838.755 x 10 bar = 8387.55 bar = 8.38755 kilobar

ii)

1 US ton = 907.185 kg

Let the area be "y" meter2

stress = 838,755,000 pascal = (907.185 x 9.81)/ y

y = (907.185 x 9.81)/ 838,755,000

y = 1.061035 x 10-5 meter2

Therefore the area should be 1.061035 x 10-5 meter2

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