Static equilibrium - girl on diving board

[smashd]

Homework Statement

A diving board of length L is supported at a point a distance x from the end, and a diver weighing w₁ stands at the free end (Figure 1) . The diving board is of uniform cross section and weighs w₂.

(Figure 1)​

1. Find the force at the support point.
2. Find the force at the end that is held down.

Homework Equations

$\sum\tau_{z} = 0$

$\sum F_{x} = 0$

$\sum F_{y} = 0$

The Attempt at a Solution

So first I found the x & y components of the forces on the diving board. Oh, I also defined n₂ as the normal force on the left end of the board, and n₁ as the normal force at the support point. Up is positive and down is negative.

$\sum F_{x} = 0$

$\sum F_{y} = 0 = n_{1} - n_{2} - w_{1} - w_{2}$

Now to take the torque about an axis, since I have a lot of unknowns here. Here I've chosen the left normal force as the axis of rotation. Counter-clockwise is positive and clockwise is negative.

$\sum\tau_{n_{2}} = 0 = n_{1}(L - x) - w_{2}(\frac{L}{2}) - w_{1}(L)$

Now I'm stuck and can't solve the two problems. I have a lot of unknowns and no other equations in my toolbox afaik. Help please!

 

[SteamKing]

Use the moment equation to find n2 in terms of w1 and w2. Then you can use the force equation to find n1 in terms of w1 and w2. That's all you can do with this problem.