Question Number 165818 by MikeH last updated on 08/Feb/22
$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{weight}\:{W} \\ $$$$\mathrm{rest}\:\mathrm{between}\:\mathrm{a}\:\mathrm{smooth}\:\:\mathrm{vertical} \\ $$$$\mathrm{plane}\:\mathrm{and}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{plane}\:\mathrm{inclined} \\ $$$$\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{vertical} \\ $$$$\mathrm{plane}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{reaction}\:\mathrm{at}\:\mathrm{the}\: \\ $$$$\mathrm{contact}\:\mathrm{surfaces}.\: \\ $$
Answered by ajfour last updated on 08/Feb/22
Commented by ajfour last updated on 08/Feb/22
$${R}\mathrm{cos}\:\theta={W} \\ $$$$\Rightarrow\:\:{R}=\frac{{W}}{\mathrm{cos}\:\theta} \\ $$$${N}={R}\mathrm{sin}\:\theta=\left(\frac{{W}}{\mathrm{cos}\:\theta}\right)\mathrm{sin}\:\theta={W}\mathrm{tan}\:\theta \\ $$