A block placed on a horizotnal surface is being pushed by a force F making an angle `theta` with the vertical. If the friction coefficient is `mu`. How much force is needed to get the block just started. Discuss the situation when `tan thetaltmu`.

Explanation

In limitting equilibrium force of friction `f = mu R`
In equilibrium along the horizontal `F sin theta = mu R`
and along the verticle `F cos theta + mg = R = (F sin theta )/(mu`
`:. Mg = F(( sin theta )/(mu) - cos theta)`
or `F = (mu mg)/(sin theta - mu cos theta)`
If tan `theta lt mu`
`(sin theta - mu cos theta lt theta)`
`:. F` is negative So for angles less angles less than `tan^(-1) mu` on cannot push the block ahed howsoever large the force may be .