How Do Forces and Tension Affect Equilibrium on a Staircase?

[songoku]

Homework Statement

AC and CE = 4 m. BD is a string that has length 1 m and located in the middle. A person weighs 500 N climbs the stair as far as 3 m. Mass of AB is 100 N and mass of CE is negligible. If the floor is smooth, find
a. the tension BD
b. forces on stair by floor

Homework Equations

torque
equilibrium

The Attempt at a Solution

Is there force at point C? I think there is but I don't know the direction. On AC, there is horizontal force by BD so in order to be equilibrium, there must be force on C. C must have horizontal component to balance BD, but does C have vertical component?

Thanks

 

[collinsmark]

Homework Statement

AC and CE = 4 m. BD is a string that has length 1 m and located in the middle. A person weighs 500 N climbs the stair as far as 3 m. Mass of AB is 100 N and mass of CE is negligible. If the floor is smooth, find
a. the tension BD
b. forces on stair by floor
[...]

Homework Equations

torque
equilibrium

The Attempt at a Solution

Is there force at point C? I think there is but I don't know the direction. On AC, there is horizontal force by BD so in order to be equilibrium, there must be force on C. C must have horizontal component to balance BD, but does C have vertical component?

Thanks

Well, you know that the net force at point C is zero. Otherwise C would be accelerating. Since it is not, you know that the net force is zero.

That said, I think you're supposed to assume that the force on AC exerted by CE, and the force on CE exerted by AC (both at point C) are both restricted to the horizontal direction.