1.

A block placed on a horizontal surface is being pushed by a force`F` making an angle `0` with the verticle If the friction coefficient is `mu` how much force is needed to get the block just started Discuss the situation when tan ` theta lt mu `.

Answer» 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 .


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