Question and Answers Forum

All Questions      Topic List

Mechanics Questions

Previous in All Question      Next in All Question      

Previous in Mechanics      Next in Mechanics      

Question Number 53145 by ajfour last updated on 18/Jan/19

Commented by ajfour last updated on 18/Jan/19

$$Ifentirestringlengthisl,find\theta$$$$intermsofl,a,r,andR.$$$$Orfindlfroma,r,R,and\theta .$$

Commented by tanmay.chaudhury50@gmail.com last updated on 18/Jan/19

Answered by ajfour last updated on 18/Jan/19

$$l=a+R(\pi +\theta +2\cot \frac{\theta }{2})$$$$+r(\frac{\pi }{2}-\frac{\theta }{2}+\tan \frac{\theta }{2}-\frac{2}{\sin \theta })$$$$\left(myanswer\right).$$

Answered by mr W last updated on 18/Jan/19

Commented by mr W last updated on 18/Jan/19

$$AB=a$$$$\stackrel{⌢}{BC}=r(\frac{\pi }{2}-\frac{\theta }{2})$$$$CD=HD-HC=\frac{R}{\tan \frac{\theta }{2}}-\frac{r}{\tan \theta }$$$$\underset{⌣}{DE}=R(\pi +\theta )$$$$EF=HE-HF=\frac{R}{\tan \frac{\theta }{2}}-\frac{r}{\sin \theta }$$$$\Rightarrow l=a+r(\frac{\pi }{2}-\frac{\theta }{2})+\frac{R}{\tan \frac{\theta }{2}}-\frac{r}{\tan \theta }+R(\pi +\theta )+\frac{R}{\tan \frac{\theta }{2}}-\frac{r}{\sin \theta }$$$$\Rightarrow l=a+r(\frac{\pi }{2}-\frac{\theta }{2}-\frac{1}{\tan \theta }-\frac{1}{\sin \theta })+R(\pi +\theta +\frac{2}{\tan \frac{\theta }{2}})$$

Commented by Otchere Abdullai last updated on 18/Jan/19

$$thusmyprofW$$

Commented by ajfour last updated on 18/Jan/19

$$ThankyouverymuchSir.$$

Commented by mr W last updated on 18/Jan/19

$$wehadsomedifferenceinourresults.$$$$doyouknowthereasonsir?$$

Commented by ajfour last updated on 18/Jan/19

$$yes,theyarethesame,$$$$\tan \frac{\theta }{2}-\frac{1}{2\sin \frac{\theta }{2}\cos \frac{\theta }{2}}=-\frac{1}{\tan \theta }$$$$hence\tan \frac{\theta }{2}-\frac{2}{\sin \theta }=-\frac{1}{\tan \theta }-\frac{1}{\sin \theta }{}^{.}$$

Commented by mr W last updated on 18/Jan/19

$$thankssirfortheexplanation!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com