The-surface-between-wedge-and-block-is-rough-Coefficient-of-friction-Find-out-the-range-of-F-such-that-there-is-no-relative-motion-between-wedge-and-block-The-wedge-can-move-freely-on-smooth-gr

FacebookTweetPin

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

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

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

FacebookTweetPin