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A block of mass m kg is pushed up agains...

A block of mass m kg is pushed up against a wall by a force P that makes an angle '`theta`' with the horizontal as shown in figure . The coefficient of static friction between the block and the wall is `mu` . Find the minimum value of P that allows the block to remain stationary .

Text Solution

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At equilibrium ,
`P "sin" theta + f = "mg" , N = P "cos" theta,`
`N = P "cos" theta , f = ("mg" - P "sin" theta)`
`muN = ("mg" - P "sin" theta)`
`muP "cos" theta = "mg" - P "sin" theta `

`P ["sin" theta + mu "cos"theta ] = "mg"`
`P = ("mg" )/(("sin" theta + mu "cos" theta))`
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