On Mars, the acceleration due to gravity is 3.73m/s. If you brought ball that wa

Question

On Mars, the acceleration due to gravity is 3.73m/s. If you brought ball that was 14 kg on Earth, what would its mass be on Mars? What would its weight be on Mars? The period of the Earth's rotation is 365.2425 days, and the Earth is 1.49 times 10^11 m. Using this information, determine the mass of the sun. 3. A white dwarf is an old star that has collapsed in upon itself. At the end of our sun's life cycle, it will collapse down to a radius of roughly 10 km. What is the acceleration due to gravity on the surface of the sun today? What will the acceleration due to gravity be on the surface once it has collapsed into a white dwarf? The mass of the sun is m = 2 times 10^30 kg and today has a radius of r = 695,700 km.

Explanation / Answer

1. Mass is the inertia of ball that doesn;t change.

mass = 14 kg

Weight = mass x acc due gravity = 14 x 3.73 = 52.22 N

2.
Time period = 2 pi / w

w = 2pi / T = 2pi / (365.2425 x 24 x 3600 s ) = 1.991 x 10^-7 rad/s

for circular motion,

G M m / r^2 = m w^2 r

G M / r^3 = w^2

(6.67 x 10^-11 x M ) / (1.49 x 10^11)^3 = (1.991 x 10^-7)^2

M = 1.967 x 10^30 kg

3. accelartion due to gravity = G M / R^2

initially :

a_g = (6.67 x 10^-11 x 1.967 x 10^30 ) / (695700 x 10^3)^2

a_g = 270.95 m/s^2

finally :

a_g = (6.67 x 10^-11 x 1.967 x 10^30 ) / (10000)^2

a_g = 1.312 x 10^12 m/s^2

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