Determine contact reactions and force, Mechanical Engineering

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.

1614_Determine contact reactions and force.png

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 RA  and RB  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'

RA/sin(90° + 30°) = RB/sin(90° + 60°)

= 140/ sin(180° - 90°)

By further solving

RA = 121N                                                           .......ANS

RB = 70N              .......ANS

Posted Date: 10/16/2012 6:01:19 AM | Location : United States







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