Answer to Question #108414 in Mechanics | Relativity for rohan

Question

Joe Mauer hits the homerun of his life putting a baseball into the orbit of the Earth. The mass of the Earth is 5.98 x 1024 kg, the mass of the baseball is 0.15 kg and the distance between the center of mass of the Earth and the center of mass of the baseball is 6.8 x 106 m. Calculate the gravitational force (in N) between the baseball and the Earth.



Joe Mauer hits the homerun of his life putting a baseball into the orbit of the Earth. The mass of the Earth is 5.98 x 1024 kg, the mass of the baseball is 0.15 kg and the distance between the center of mass of the Earth and the center of mass of the baseball is 6.8 x 106 m. How fast (in m/s) is the baseball moving around the Earth?


Suppose a hypothetical planet with the same mass as the Earth’s has a radius that is 1/3 of Earth’s radius. What is the acceleration due to gravity (in m/s2) on that hypothetical planet?

Answer 1

1)

$$F=G\frac{Mm}{(d)^2}=6.67\cdot10^{-11}\frac{5.98 \cdot10^{24}(0.15)}{(6.8 \cdot10^{6})^2}=1.3\ N$$

2)

$$F=m\frac{v^2}{d}$$

$$\frac{(0.15)}{(6.8 \cdot10^{6})}v^2=1.3$$

$$v=7700\frac{m}{s}$$

3)

$$g'=G\frac{M}{(\frac{r}{3})^2}=9G\frac{M}{(r)^2}=9g=9(9.8)=88\frac{m}{s^2}$$