Question

A 92.0-N uniform, horizontal board 14.0 m long rests on two supports, each 1.00 m from the

end of the board. A 385-N block is placed on the board 3.00 m from one end as shown below.

Find the force exerted on the board by each support.

Answer 1

The Free Body Diagram is,

Since the object is in static equilibrium the Total force acting on the board will be zero and also Moment about any point will be 0. Taking the forces along vertical direction (mg = 92 N and Mg = 385), we can write, ( upwards is +ve and downwards is -ve)

Now, on taking moment about Point where N₁ acts (anti clockwise moment is +ve and clockwise moment is -ve). About this point the force mg and Mg creates clockwise moment at distances 6m and 10m (the force mg acts at midpoint of the board, since the board is uniform) and N₂ generates anti-clockwise moment at a distance of 12 m. So we can write the total moment about the point as,

Therefore N₁ can be calculated as,

So the normal reactions N₁ and N₂ are 366.83 N and 110.17 N respectively.