It has been said that dinosaurs became extinct when about 65 million years ago,
ID: 2298326 • Letter: I
Question
It has been said that dinosaurs became extinct when about 65 million years ago, a large asteroid hit the Earth surface. Dust caused by this collision blocked the sunlight reaching the Earth's surface and many forms of life became extinct due to the cold. Fearing this threat, how large is the radius of an asteroid should you be looking for if the dangerous asteroid size is approximately the same as the one that killed the dinosaurs? Available data suggests that about 18% of that asteroid's mass ended up as a dust spread evenly over Earth after eventually settling out of the upper atmosphere. About 0.0180 g/cm^2 of dust, which is chemically different than the Earth's rock, covered the Earth's surface. Typical asteroids have a density of about 1.9 g/cm^3. Now imagine that scientists drill a hole from the North Pole to the South Pole of Earth and you happen to jump into the hole. What will be the period of your oscillation going from the North Pole to the South Pole and back up to the North Pole? Radius of Earth: 6370 Km Mass of Earth: 6Times10^24kg Density= M/VExplanation / Answer
A.
given
R2=Earth radius Ra=Asteroid radius
?=asteroid density ?=asteroid mass/m^2 on Earth
S=Earth surface
asteroid mass on Earth is
m=?S
original asteroid mass is
M=m/0.18=?S/0.18
asteroid original volume is
V=M/?=?S/(0.18?)
V=4/3?Ra^3
S=4?Re^2
then
4/3?Ra^3=4??Re^2/(0,18?)
from which
Ra=[3?Re^2/(0,18?)]^1/3 [radius of asteroid]
the minimum energy released is
E=?M
where
?=fusion latent heat
considering the asteroid as a rock
?~50Kcal/kg~210 kJ/kg
M=?S/(0.18?)
?=0.18kg/m^2
S=4?Re^2
then
M=4?Re^2/?
Re=6.37x10^6 m
?=1.9x10^3 kg/m^3
M=4?*4.06x10^13/1.9x10^3=2,68x10^11 kg
then
E=2.1x10^5*2,68x10^11 = 5.63x10^16 J
the speed is
v=(2E/M)^1/2
v=6.5x10^2 m/s = 1950 km/h [underestimated]
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