A-uniform-sphere-of-weight-W-rest-between-a-smooth-vertical-plane-and-a-smooth-plane-inclined-at-an-angle-with-the-vertical-plane-Find-the-reaction-at-the-contact-surfaces-

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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

$$R\cos \theta =W$$$$\Rightarrow R=\frac{W}{\cos \theta }$$$$N=R\sin \theta =\left(\frac{W}{\cos \theta }\right)\sin \theta =W\tan \theta$$

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