Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 20581 by Tinkutara last updated on 28/Aug/17

$$Thesurfacebetweenwedgeandblock$$$$isrough\left(Coefficientoffriction\mu \right).$$$$FindouttherangeofFsuchthat,$$$$thereisnorelativemotionbetween$$$$wedgeandblock.Thewedgecanmove$$$$freelyonsmoothground.$$

Commented by Tinkutara last updated on 28/Aug/17

Commented by ajfour last updated on 28/Aug/17

Commented by ajfour last updated on 28/Aug/17

$$Diagramaboveshowsthecase$$$$when\mathit{F}isminimumandthere$$$$isnorelativemotiinb/wblock$$$$andwedge.$$$$Ishallusepseudoforcedirected$$$$towardslefttobeabletoanalyse$$$$equilibriumofblockfromframe$$$$ofwedge.$$$$\mathrm{\Sigma }{F}_x=0$$$$\Rightarrow -\mu N\cos \theta -ma+N\sin \theta =0...\left(i\right)$$$$\mathrm{\Sigma }{F}_y=0$$$$\Rightarrow \mu N\sin \theta +N\cos \theta =mg...\left(ii\right)$$$$\Rightarrow N=\frac{mg}{\cos \theta +\mu \sin \theta }$$$$usingthisin\left(i\right):$$$$ma=\frac{mg(\sin \theta -\mu \cos \theta )}{\cos \theta +\mu \sin \theta }$$$$AsF=(M+m)a,so$$$$F_{minimum}=\frac{(M+m)g(\tan \theta -\mu )}{1+\mu \tan \theta }$$$$for{F}_{maximum},\mu \to -\mu$$$$F_{maximum}=\frac{(M+m)g(\tan \theta +\mu )}{(1-\mu \tan \theta )}.$$$$$$

Commented by Tinkutara last updated on 28/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!\mathrm{But}\mathrm{can}\mathrm{it}\mathrm{be}$$$$\mathrm{solved}\mathrm{without}\mathrm{using}\mathrm{pseudo}\mathrm{force}?$$

Commented by ajfour last updated on 28/Aug/17

$$checkagain,diagramshows$$$$situationwhenforceisminimum.$$$$Icorrectedmyanswers.$$$$withoutpseudoforce,$$$$\mathrm{\Sigma }{F}_y=0,stillthesame$$$$but\mathrm{\Sigma }{F}_x=ma$$$$\Rightarrow N\sin \theta -\mu N\cos \theta =ma$$$$thatsjustthedifference..$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com