Static Equilibrium of pedestals

[G-reg]

Homework Statement

A diver of weight 730 N stands at the end of a diving board of length L = 5 m and negligible mass. The board is fixed to two pedestals separated by distance d = 1.5 m.

What are the magnitude and direction of the force on the board from the left pedestal? (Include the sign. Take upward to be positive.)

Homework Equations

I think that it's this..

sum of forces in the y direction = 0

force of left pedestal = Fl
force of right pedestal = Fr
force of diver = mg = 730N

The Attempt at a Solution

-Fl + Fr - mg = 0
3.5Fr(mg) - (0)mg = 5Fl(mg)

is this on the right track?

 

[Delphi51]

Looks good! You have 2 equations with 2 unknowns so you can find the answer.

 

[kerimek]

Your approach is on the right track. However, in order to find the magnitude and direction of the force on the board from the left pedestal, we need to consider the torque acting on the board as well.

First, let's label the forces acting on the board: the force from the left pedestal as Fl, the force from the right pedestal as Fr, and the weight of the diver as mg.

Next, we can set up the equation for torque:

sum of torques = 0

In this case, we can choose the pivot point to be at the left pedestal. This means that the torque from the force of the right pedestal will be negative (since it is trying to rotate the board in the opposite direction) and the torque from the weight of the diver will be positive (since it is trying to rotate the board in the same direction).

Therefore, our equation becomes:

-Fl(d) + Fr(d) + mg(L/2) = 0

Solving for Fl, we get:

Fl = (Fr + mg(L/2))/d

Plugging in the given values, we get:

Fl = (0 + 730(5/2))/1.5 = 1216.67 N

The magnitude of the force on the board from the left pedestal is 1216.67 N and its direction is upward (positive).

This result makes sense because the left pedestal is supporting more weight (due to the weight of the diver and the torque from the weight) compared to the right pedestal. This is necessary for the board to remain in static equilibrium.