Question

Help on centripetal force's formula! See photo attached.

Answer 1

the relation between centripetal force and kinetic energy, is:
\[\huge {F_0} = \frac{{2{{\left( {KE} \right)}_0}}}{{{r_0}}}\]
now, from the text of the problem the new kinetic energy and the new radius are:
\[\huge {\left( {KE} \right)_1} = \frac{{{{\left( {KE} \right)}_0}}}{2},\quad {r_1} = 2{r_0}\]
so, after a substitution, we get:
\[\huge {F_1} = \frac{{2{{\left( {KE} \right)}_1}}}{{{r_1}}} = \frac{{2\frac{{{{\left( {KE} \right)}_0}}}{2}}}{{2{r_0}}} = ...?\]
please complete

Answer 2

Is it \(\huge \frac{ KE }{ 2R }\)?

Answer 3

\[\huge F_{centripetal}= \frac{ \frac{ mv^2 }{ 2 } }{ 2R }
= \frac{ mv^2 }{ 4R } = \frac{ F }{ 4 }?\]

Answer 4

I'm not sure. Yikes!

Answer 5

It should be F/2

Answer 6

from my computation above, we get:
\[\Large {F_1} = \frac{{2{{\left( {KE} \right)}_1}}}{{{r_1}}} = \frac{{2\frac{{{{\left( {KE} \right)}_0}}}{2}}}{{2{r_0}}} = \frac{1}{4}\frac{{2{{\left( {KE} \right)}_0}}}{{{r_0}}} = \frac{{{F_0}}}{4}\]