Please help with Yr 12 statics question?

Question

A stepladder is 2.00m high. The step is 2.50m long, uniform and weighs 60.0N. The other side is also uniform, is 2.50 m long and weighs 20.0N. The sides are hinged at the top and there is a massless tie rod 1.50m long which connects the midpoints of the sides . A 640N man stands three quarters of the way to the top. Find the forces on the two sides of the ladder by the floor and the tension in the tie rod.

[Hint: Assume the floor is smooth initially and apply the equilibrium conditions to one or both sides]

All i need help with is the last. Could you please provide a method for finding the tension in the rod.

Answer 1

I gotta do the whole thing....

Taking moments about the bottom of the other side (o), and letting R be the vertical floor reactions of the 2 legs,

3*Rs = 20*.75 + 640*1.875 + 60*2.25 → Rs = 450 N

then

Ro = (20+60+640) - Rs = 270 N

Taking moments about the top hinge,

1.5*Ro = .75*20 + 1*T →

T = 390 N