Example of equilibrium of body on the rough inclined, Mechanical Engineering

Example of Equilibrium of body on the rough inclined:

Magnitude of minimum force 'p' that is required to move the body up the plane. At the time when 'p' is acted with the angle of φ.

1938_Equilibrium of body on the rough inclined.png

Resolving the forces which are Parallel to Plane OA:

Pcosφ  - µW.sinα  = 0                                                                                                                ...(i)

Resolving all the forces Perpendicular to Plane OA:

Psinφ W.cos  α = 0                                                                                                                ...(i)

Putting value of 'R' from (ii) in equation (i) we get

W.[(µ.cosα + sinα )/( µ.sinφ + cosφ )]

Now putting µ = tanφ , on solving

W.[sin(α   + φ  )/cos(φ-  θ )]                                                               ...(iii)

Now is minimum at cos(φ - θ ) is max

i.e., cos(φ   -  θ ) = 1 orφ     -θ   = 0     i.e., φ    =θ

PminW.sin( θ +φ )

Posted Date: 10/17/2012 7:14:40 AM | Location : United States

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