Evaluate the Support required by body on plane:

A body having weight 50KN rests in limiting equilibrium on rough plane, whose slope is 30º. The plane is raised to a slope of 45º; what force, applied to the body parallel to inclined plane, will support the body on plane.

Sol.: Consider When the slope of plane be 30° The sum of forces parallel to plane = 0

µ R - Wsin30° = 0                                                                                                                                      ...(i)

The sum of forces perpendicular to plane = 0

R - Wcos30° = 0

R = Wcos30°                                                                                                                      ...(ii)

Putting value of R in equation (i) We get

µ = tan30º = 0.577                                                                                                         ...(iii)

Now consider the case when slope is 45°, Let Force P required for supporting the body. In this case

The sum of forces parallel to plane = 0

P - µR - Wsin45° = 0                                                                                                                                   ...(iv)

The sum of forces perpendicular to plane = 0

R - Wcos45° = 0

R = Wcos45°                                                                                                                       ...(v)

Putting value of R in the equation (iv) we get

P = µWcos45° - Wsin45°

P = 15.20KN                                                                               .......ANS