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A block placed on a horizontal surface i...

A block placed on a horizontal 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`.

Text Solution

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In limiting equilibrium `f=muN`
In equilibrium, along the horizontal `F sintheta=muN` and along the vertical
`F costheta+mg=N`
`rArrF=(mumg)/(sin theta-mu cos theta)`
If `tan thetaltmu, (sintheta-mucos theta)lt0` (or) F is negative. So for angles less than `tan^(-1)mu or tanthetaltmu`,one can not push the block ahead, however large the force may be.
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