A wedge of mass M is placed on a smooth x-z plane as shown in the figure. On the rough inclined surface of the wedge a block of mass m is placed. By applying a force `vec(F)=-Fhat(k)` on the block. Given `mu = 2tan alpha`, find the minimum value of F. (In Newton) `(M=1kg,m=(1)/(10)kg,sinalpha=(sqrt(3))/(11))`

Answer

3

Explanation

ma = pseudo
N = mgcos`alpha`
`mu(mgcosalpha)=sqrt((ma)^(2)+(mgsinalpha)^(2))`
`a^(2)=(mugcosalpha)^(2)-(g^(2)sin^(2)alpha)=g^(2)(3sin^(2)alpha)`
`a=sqrt(3)gsinalpha=sqrt(3)(10)(sqrt(3))/(11)=(30)/(11)`
`F=(M+M)a=3`