Question

The continents of Europe (or more exactly, Eurasia) and North America are separating at a speed of about 3 cm per year.

a) Assuming they were once together and have moved at a constant speed, estimate roughly how long has it taken the continents to reach their current separation (in years)?

b) Estimate roughly the kinetic energy of North America moving at 3 cm per year (in erg or J).

Answer 1

a) present distance between europe and north america= 6725km=6725x10⁵cm

speed of separation=3cm/yr

i.e in 1 year the distance between the continents increases by 3 cm

then the number of years it took for the separation to be 6725x10⁵cm=6725x10⁵/3=2242x10⁵years=2.242x10⁸years

b) kinetic energy=1/2MV²

now mass can be also written as M= volumexdensity

let A be the surface area of north america and t be the thickness

then volume, v=At and hence mass M=At where =density

so K.E=1/2AtV²

velocity is given as 3cm/year=0.03/(60x60x24x365)m/s=9.51x10^-10m/s

surface area of north america=24.71x10⁶km²=2.471x10¹³m²

thickness varies from 100km to 200km. let it be 150km=150x10³m

density varies from 2700-2900Kgm^-3, let it be =2800kgm^-3

substituting all the values we get K.E=1/2x(2.471x10¹³x150x10³x2800)x(9.51x10^-10)²=4693J