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