Static Equilibrium: Understanding Changes in Tension and Vertical Force

[jakeginobi]

Homework Statement

If the load on the uniform beam shown below is moved to the left, how do the tension force T and the magnitude of the vertical force Fv exerted by the wall on the hinge change?

The answer is A

Homework Equations

torque = Fdsin(theta)

The Attempt at a Solution

My equation was Tsinx = fd. I understand when the object is moved to the left the distance decreases, and the angle decreases, but I don't understand how the vertical force increases exerted by the wallAlso for the 2nd question ( the ladder one) why is the answer B? What I thought was Fg_dcos theta = FN₂(d)(cos theta) + FN₁(d)(cos theta), so when the distance for FN1 increases wouldn't the force increase too?

 

[haruspex]

and the angle decreases,

What angle decreases? As I read the question, only the load is moving. The cable stays put.

 

[haruspex]

What I thought was F_gdcos theta = FN2(d)(cos theta) + FN1(d)(cos theta),

I cannot understand your notation. Is this a force equation or a moment equation? What is F_gd? Is FN2(d) the force FN2 as a function of d, the distance up the ladder, or is it a force multiplied by a distance?
(You will need to consider moments to answer the question.)

 

[jakeginobi]

I cannot understand your notation. Is this a force equation or a moment equation? What is F_gd? Is FN2(d) the force FN2 as a function of d, the distance up the ladder, or is it a force multiplied by a distance?
(You will need to consider moments to answer the question.)

Oh I meant Fg(d) and it's for the torque equation

 

[haruspex]

Oh I meant Fg(d) and it's for the torque equation

Ok. What point are you taking moments about?
You seem to be using the same d for different distances and the same θ for different angles.