Determine contact reactions and force:
Figure given below shows a sphere resting in smooth V shaped groove and subjected to a spring force.
The spring is compressed to length of 100mm from its free length of 150mm. If stiffness of spring is 2N/mm, determine contact reactions at A and B.
The spring is compressed from 150mm to 100mm. So it is exiting compressive force, which is acting vertically downward on sphere.
As,
Spring force(F) = K.x
Given K = 2N/mm
x = 150 - 100 = 50mm
F = 2 × 50 = 100N ...(i)
Let R_{A} and R_{B} be the contact reaction at Point A and B.
Here wt of sphere and F are the collinear force, both act down ward so net force is = 100 + 40, acting downward.
Apply lamis theorem at 'O'
R_{A}/sin(90° + 30°) = R_{B}/sin(90° + 60°)
= 140/ sin(180° - 90°)
By further solving
R_{A} = 121N .......ANS
R_{B} = 70N .......ANS