Question

A 61 kg diver stands at the end of a 31 kg springboard, as shown in the figure. The board is attached to a hinge at the left end but simply rests on the right support. What is the magnitude of the vertical force exerted by the hinge on the board?

Answer 1

Given is:-

mass of the diver M=61kg

mass of the springboard m =31kg

Now,

The downward forces acting on the board are weight of the board and man. The forces acting in upward direction are reaction forces by the fulcrum and hinge.

To find out the net vertical force by hinge we have to calculate Net torque around the right support.

For equilibrium position the net torque around the right support/fulcrum is zero.

Therefore

$\sum \tau = 0$

thus

$Mg.r = F_{hinge}.r$ (the torques due to the weight of board and the normal force by fulcrum will be zero because they both act on the pivot point therefore distance from force and then torque is zero.)

pivot point is the middle point

therefore

$F_{hinge} = Mg = weight of The Diver$

$F_{hinge} = 61 \times 9.8 = 597.8N$

Hence,

The vertical force exerted by the hinge on the board is 597.8 Newtons