The mass of a planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600N on Earth, what would he weigh on this planet.
The ANSWER IS 96N, how to I get to this?
given constants:
Radius of Earth: 6.37E6 meters
Mass of earth: 5.98E24 meers
Universal gravitational constant: 6.67E-11 Nm^2/kg^2
2007-12-12 02:48:38 · 5 answers · asked by bazjhi 1 in Science & Mathematics ➔ Physics
Newton's Law of Gravity says that the local acceleration of gravity at the surface of the Earth is
g = G M / r²
where G is the Newton Gravity Constant, M the mass of the Earth, and R the radius of the Earth.
Now plug in the values for your planet: m = M / 100 and r = R / 4...
G ( M / 100 ) / ( R / 4 )²
( 16 / 100 ) GM / R²
So the acceleration of gravity on this planet is .16 that of Earth.
2007-12-12 03:02:16 · answer #1 · answered by jgoulden 7 · 2⤊ 0⤋
Force=Weight = Gm1m2/R²
G is gravitational constant
m1 mass of planet
m2 mass of person
R Radius
m2xg=Gm1m2/R²
g=(6.67E-11)(1/100 x 5.98E24) / (1/4 x 6.37E6)²
g=1.572780572
g is gravity acceleration
Weight = mass x g
mass = 600 /9.8
g = 1.572780572
Weight = (600 /9.8) x (1.572780572 )
Weight = 96.29268809 N
2007-12-12 02:58:23 · answer #2 · answered by Murtaza 6 · 0⤊ 0⤋
Gravity is an inverse square relationship. Assuming the distance is constant, when you decrease the mass by 2 you decrease the gravity by 2x2 or 4. And if you decrease the mass by 4 you decrease the gravity by 4x4 or 16.
2016-04-08 22:41:34 · answer #3 · answered by Anonymous · 0⤊ 0⤋
you need not the constants
according to attraction law the weight is
w=km*m'/r'^2 k =univgrav const ,m mass of the person
where m' is mass of planet P, r' its radius
on earth w= k*m*m(mass earth)/r(earth)^2
on planet P w' =k*m(mass planet P)/r(planet P)^2
w'= 0.01 k*m*mass earth/(1/16) r(earth)
so w'/w = 0.16
w'=0.16*600=96 N
2007-12-12 03:02:37 · answer #4 · answered by maussy 7 · 1⤊ 0⤋
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Suppose mass of earth = M
Radius of earth = R
Acceleration due to gravitation of earth =ge =GM/R^2
The mass of a planet is 1/100 that of Earth and its radius is 1/4 that of Earth.
mass of planet = M /100
Radius of planet = R/4
Acceleration due to gravitation of planet =gp =G(M/100) / (R/4)^2
Acceleration due to gravitation of planet =gp =0.16 [GM / R^2]
Acceleration due to gravitation of planet =gp =0.16 g
Weight of person on earth =mge=600 N
Weight of person on earth =mge
Weight of person on planet =mgp
Weight of person on planet /Weight of person on earth =mgp/mge
Wt. of person on planet / Wt. of person on earth =gp/ge
Wt. of person on planet / Wt. of person on earth =0.16ge/ge
Wt. of person on planet / Wt. of person on earth =0.16
Wt. of person on planet =0.16 Wt. of person on earth
Wt. of person on planet =0.16 *600=96 N
Wt. of person on planet = 96 N
He will weigh 96 N on this planet.
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2007-12-12 03:21:39 · answer #5 · answered by ukmudgal 6 · 0⤊ 0⤋