A block of mass `m` is placed at rest on a horizontal rough surface with angle of friction `phi`. The block is pulled with a force `F` at an angle `theta` with the horizontal. The minimum value of `F` required to move the block is

Options

A. `(mgsinphi)/(cos(0-phi))`
B. `(mg cos phi)/cos(0-phi)`
C. `mg tan phi`
D. `mg sin phi`

Explanation

`tan phi=mu`
`impliesmuN=Fcosthetaimpliesmu(mg-Fsintheta)=Fcostheta`
`impliesmumg=F(costheta+sintheta)`
`implies F=(mumg)/((costheta+musintheta xx sintheta/costheta))`
`impliesF=(mumg xx costheta)/cos(theta-phi)`
`impliesF=(mgsintheta)/cos(theta-phi)`