Answer to Question #279669 in Physics for Yana

Question

1. What is the force exerted by Big Ben on the Empire State building? Assume that Big Ben has a mass of 10^8 kilograms and the Empire State building 10^9 kilograms. The distance between them is about 5000 kilometers and Big Ben is due east of the Empire State building

2. How far apart are the centers of two objects with masses of 4,100kg and 6,500kg. The graviational attraction between them is 86 N.

3. The moon has a mass of 7.35 x 10^22 kg and a radius of 1.738 x 10^6 m. At what speed must a rocket be launched from the moon's surface so as not to fall back to the moon.

4. What must be the radius of a star of mass 2 x 1030 kg so that the escape speed from this star is equal to 2 x 10^8 m/s

Answer 1

1) $F=GMm/R^2=2.69·10^{-7}\text{ N}$

2) $R=\sqrt{GMm/F}=4.55\text{ mm}.$

3) $v=\sqrt{GM/R}=1680\text{ m/s}.$

4) $R=2GM/v^2=6673\text{ m}.$