Bonus problem 1

  • Due Feb 14 by 11:59p.m.
  • Points 0
  • Submitting a file upload
  • File Types pdf
  • Available Jan 29 at 2p.m. - Feb 15 at 11:59p.m.
This assignment was locked Feb 15 at 11:59p.m..

This bonus question is worth up to 0.5 bonus points at the end of the term.

Suppose that we have a central attracting force in LaTeX: \mathbb{R}^3 of the form

$$\vec{F} = -\frac{C}{r^k}\hat{r}$$

where LaTeX: C is a positive constant, LaTeX: k is a positive integer and as usual,  LaTeX: \vec{r}=\langle x,y,z\rangle , LaTeX: r = |\vec{r}| and LaTeX: \hat{r}=\frac{\vec{r}}{r}.

 

Find the value of LaTeX: k so that there exists a trajectory of a particle in motion acted on by the force given by a circle of some radius LaTeX: R whose center is a distance  LaTeX: R  from the origin. In other words, this circle passes through the origin.

 

To get full credit for this bonus question, the write up must include both the correct answer as well as clear and coherent reasoning as to how you obtained the answer.  

1739606399 02/14/2025 11:59pm