Woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N. The board is supported at each end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the woman standing

Explanation:

Let us assume that W is the weight of the board and is the weight of women standing.

And, at the left end supporting force is F and at the right end supporting force is 3F.

So, when this system is in equilibrium then upward force will be equal to the downward force as follows.

              4F = 100 N + 500 N

                 F =

                    = 150 N

For system to be in static friction another condition is that net torque acting on the left end will be equal to zero.

Hence,         = 0

          = 0

Putting the given values into the above formula as follows.

          = 0

        = 0  

                    x = 6.4 m

Therefore, at the left side distance from the women is 6.4 m.

And, distance from the right end will be as follows.

               8 m - 6.4 m = 1.4 m