Answer to Question #127344 in Mechanics | Relativity for Rethabile Force

Question

Consider an alternate universe in which the magnitude of the attractive force of gravity exerted by Earth on a meteor of mass mm approaching Earth is given by F=CmmmE/r3, where C is some positive constant and r is the center-to-center distance between Earth and the meteor

A. How much work is done by the gravitational force on the meteor as it falls from very far away (infinite distance) to some height h above Earth's surface?
Express your answer in terms of some or all of the variables mm, C, mass of Earth mE, its radius RE, and h.

B.
If the meteor is moving very slowly when it is very far away, how fast is it moving when it gets to that height?
Express your answer in terms of some or all of the variables mm, C, mass of Earth mE, its radius RE, and h.

Vm=?

Answer 1

If $F=Cm_mm_E/r^3$ then $U(r)=\int_{\infty}^{r}Fdr=-Cm_mm_E/2r^2$ as $U(\infty)=0$ then

A. $W=Cm_mm_E/2h^2$

B. As $W=m_mV^2/2$ then $V_m=\sqrt{Cm_E}/h$