The radius of Mars is 3.37×106m, and it’s mass is 6.42×1023kg. How long will it take a rock dropped from 2.0m above the surface of Mars to reach the ground?
In order to calculate the time that the rock will take to fall 2 meters on Mars, it is
necessary to first calculate the gravitational acceleration of Mars, since naturally
that quantity is different for each planet. In fact, the gravitational acceleration is
different and unique for each astronomical body, be it anything from a small asteroid
to a galactic cluster.
We use the following formula:
a = Gm/r²
a = gravitational acceleration of Mars = to be determined
G = universal gravitational constant = 6.6726 x 10-11N-m2/kg2
m = mass of Mars = 6.42×10^23 kg
r = radius of Mars = 3.37×10^6 m
a = (6.6726 x 10^-11N∙m²/kg²)(6.42×10^23 kg)/(3.37×10^6 m)²
a = 3.77 m/s²
To find the time needed for a rock to fall 2 meters on Mars,
we use the following formula:
t = elapsed time = to be determined
d = distance through which the rock falls = 2.0 m
a = gravitational acceleration of Mars = 3.77 m/s²
t = √(2d/a)
t = √(2∙2.0 m/3.77 m/s²)
t = 1.03 s Time for a rock to fall 2.0 meters on Mars
Source(s): https://www.easycalculation.com/physics/classical-…
http://www.gravitycalc.com/
The starting point is the “Universal Law of Gravitation”
F = G Mm/ R^2
-> a = GM/ R^2
(G is the universal constant of gravitation 6.67384 x 10^ -11 m3 kg-1 s-2)
Once you know the acceleration the rest is simple kinematics.
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