Question

When a man stands on a bathroom scale here on Earth, it reads 640 N . Assume each planet to be a perfect sphere with the following parameters.
Planet Mass, kg Radius, m
Mars 6.419×1023 3.396×106
Venus 4.869×1024 6.052×106
Saturn 5.685×1026 6.027×107
Part A: What would his mass be on Mars, Venus, and Saturn?
Part B: What is the magnitude of the gravitational force Mars would exert on the man if he stood on its surface?
Part C: What is the magnitude of the gravitational force Venus would exert on the man if he stood on its surface?
Part D: What is the magnitude of the gravitational force Saturn would exert on the man if he stood on its surface?

Answer 1

Answer:

242.19702 N

578.46718 N

681.02785 N

Explanation:

M = Mass of the corresponding planet

r = Radius of the corresponding planet

g = Acceleration due to gravity = 9.81 m/s²

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

Mass of person

$m=\frac{W}{g}\\\Rightarrow m=\frac{640}{9.81}=65.23955\ kg$

Mass is the property of an object, it is constant irrespective of the forces acting on it so the mass of the person on each planet would be the same.

Gravitational force on Mars

$F=\frac{GMm}{r^2}\\\Rightarrow F=\frac{6.67\times 10^{-11}\times 6.419\times 10^{23}\times 65.23955}{(3.396\times 10^{6})^2}\\\Rightarrow F=242.19702\ N$

Magnitude of the gravitational force Mars would exert on the man if he stood on its surface is 242.19702 N

Gravitational force on Venus

$F=\frac{GMm}{r^2}\\\Rightarrow F=\frac{6.67\times 10^{-11}\times 4.869\times 10^{24}\times 65.23955}{(6.052\times 10^{6})^2}\\\Rightarrow F=578.46718\ N$

Magnitude of the gravitational force Venus would exert on the man if he stood on its surface is 578.46718 N

Gravitational force on Saturn

$F=\frac{GMm}{r^2}\\\Rightarrow F=\frac{6.67\times 10^{-11}\times 5.685\times 10^{26}\times 65.23955}{(6.027\times 10^{7})^2}\\\Rightarrow F=681.02785\ N$

Magnitude of the gravitational force Saturn would exert on the man if he stood on its surface is 681.02785 N