Statics - Two Supports
A rectangular wooden board with length and width is attached to a wall at its top left corner by a frictionless hinge support.
There is also a simple support attached to the wall which contacts the board. The board's length is aligned with the vertical.
If, in static equilibrium, the magnitude of the total reaction force at the hinge is twice the weight of the board, the distance from the simple support to the hinge is What is the value of
The answer is 12.
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Since there is no friction, the force at the support point, F h , will be horizontal.
The total torque around the hinge is F h d − m g ( w / 2 ) = 0 .
We solve this for F h to get F h = m g w / 2 d .
The vertical component of the force at the hinge balances the weight, F y = m g .
The horizontal component balances the push at the support point F x = F h = m g w / 2 d .
The magnitude of the force is F = 2 m g and F 2 = 4 ( m g ) 2 = ( m g ) 2 + ( m g w / 2 d ) 2 .
We get 4 = 1 + ( w / 2 d ) 2 and d = w / 3 3 = w / 1 2 .