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Question Number 186439 by ajfour last updated on 04/Feb/23

Commented by ajfour last updated on 04/Feb/23

$$Ifinsidethefixedhollowcone,$$$$thesolidballofradiusrrevolves$$$$slidingfrictionlesslyalongthe$$$$lateralsideandthebasewith$$$$angularvelocity\omega ,thenfindthe$$$$normalreactionforcesitis$$$$exerteduponbythegroundand$$$$thelateralside.$$

Answered by mr W last updated on 04/Feb/23

Commented by mr W last updated on 04/Feb/23

$$\tan \theta =\frac{h}{R}$$$$b=R-\frac{r}{\tan \frac{\theta }{2}}$$$$F_C=mb{\omega }^2=m(R-\frac{r}{\tan \frac{\theta }{2}}){\omega }^2$$$$N_s\sin \theta =F_C$$$$N_s=\frac{m}{\sin \theta }(R-\frac{r}{\tan \frac{\theta }{2}}){\omega }^2$$$$=\frac{m\sqrt{h^2+R^2}}{h}(R-\frac{r}{\sqrt{1+\frac{R^2}{h^2}}-\frac{R}{h}}){\omega }^2$$$$N_b=mg+N_s\cos \theta$$$$=mg+\frac{m}{\tan \theta }(R-\frac{r}{\tan \frac{\theta }{2}}){\omega }^2$$$$=mg+\frac{mR}{h}(R-\frac{r}{\sqrt{1+\frac{R^2}{h^2}}-\frac{R}{h}}){\omega }^2$$

Commented by ajfour last updated on 04/Feb/23

$$prettysmoothnelegantsolution.$$$$Thankyousir!$$

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