Equilibrium Ladder Question, can get 1st part but not 2nd

[sweetpete28]

Equilibrium Ladder Question, can get 1st part but not 2nd!

A symmetrical ladder of mass M = 20.8kg leans against a smooth frictionless wall so the top of the ladder is height h = 6.58m above the floor and the bottom of the ladder is distance d = 2.19 m from base of wall. The floor is also frictionless so a horizontal wire connects bottom of ladder to wall so ladder does not slip.With nobody on ladder, here is what I did to get T, magnitude of tension in wire:

ƩF = 0

F wire = F wall

L of ladder = sq. root of 6.58^2 + 2.19^2 = sq. root of 48.0925 = 6.9348m

Angle θ b/t wire and ladder --> tan θ = 6.58 / 2.19; so θ = 71.59°

Center of mass for ladder = 6.9348 / 2 = 3.46743m

mg down = (20.8)(9.81) = 204.048 N

(6.93487 x sin 71.59°)(F wall) - (3.46743 cos 71.59°)(204.048) = 0

F wall = 33.9 N, so F wire = 33.9 N

Now, suppose wire will snap when the magnitude of the tension is T = 197 N. What is x, the distance a man of mass m = 78.3 kg can climb up along ladder before the wire snaps?

mg down = (78.3 + 20.8) x 9.81 = 972.171

(6.93487 times sin 71.59)(197) = (x cos 71.59)(972.171)

and I get x = 4.22m but this is wrong...

What am I doing wrong here? I know I did first part right (without man on ladder) but what I am doing wrong for this part??

 

[darkys]

For the second part, you need to take into account the torque due to the man climbing up the ladder. The torque is equal to the mass of the man multiplied by the distance of the man from the wall (which is x). You can then use this torque to calculate the force of tension in the wire. This will be different from the tension in the wire when there is nobody on the ladder. The equation for torque is: Torque = F x dSo, you can rearrange this equation to get: F = Torque / dThen, you can substitute in the values for Torque (the mass of the man multiplied by x) and d (which is x) to get the tension in the wire. Once you have the tension in the wire, you can set it equal to 197N and solve for x.