An woman whose weight is 804 N stands on a long horizontal plank of wood 1.55 m from one end. The plank is uniform and is supported at each end by vertical posts. It has a mass of 27 kg and is 5.5 m long. With what force does the post that is closest to the woman push upward on the board

Explanation:

There will be reaction force by  each vertical post on horizontal plank . Let it be R₁ and R₂ . R₁ is reaction force by the post nearer to woman

Taking torque of all forces about the end far away from the woman

Torque by reaction force = R₁ x 5.5

= 5.5 R₁ upwards

Torque by weight of woman in opposite direction , downwards

= - 804 x ( 5.5 - 1.55 )

= - 3175.8

Torque by weight of the plank in opposite direction , downwards .

= - 27 x 5.5 / 2

= - 74.25

Torque by R₂ will be zero as it passes through the point about which torque is being taken .

Total torque

= 5.5 R₁ - - 3175.8 - - 74.25  = 0 ( For equilibrium )

5.5 R₁ = 3250

R₁ = 590.9 N .