How Do Forces Change as You Climb a Ladder?

[Inertialforce]

Homework Statement

As a person is walking up a stationary ladder, what happens to the magnitude of the forces Fn1 and Fn2?

a)

Magnitude Fn1 Magnitude of Fn2
A: decreases decreases
B: decreases increases
C: increases decreases
D: increases increases

it might be hard to see the choices here for this multiple choice question so I made a table for it in the attachment to make the choices clearer.

b) Conceptual question: Without using numbers or any numerical calculations (only letters and symbols allowed) prove that what you got for part a is correct for this question (use principles of physics and show in formulas and equations as you would if numbers were provided and you were trying to calculate it).

Homework Equations

ΣFx = ma, ΣFy = ma, and ΣT(torque) = 0

The Attempt at a Solution

a) For "part A" I would have to choose option "C" because if she walks up the ladder, doesn't Fn1 get larger because not only is she getting further and further away distance wise from Fn1 thus creating a larger torque. But she is also making the lever arm from Fn1 to her larger also, thus making the torque larger. And for the same two reasons wouldn't the magnitude at Fn2 begin to decrease as she approaches Fn2 and gets closer and closer?

b) For "part B" I know that they want me to explain and prove what I got for an answer in "part A" is correct using only letters and the principles of physics, but I do not know where exactly to start.

 

[Doc Al]

The Attempt at a Solution

a) For "part A" I would have to choose option "C" because if she walks up the ladder, doesn't Fn1 get larger because not only is she getting further and further away distance wise from Fn1 thus creating a larger torque. But she is also making the lever arm from Fn1 to her larger also, thus making the torque larger. And for the same two reasons wouldn't the magnitude at Fn2 begin to decrease as she approaches Fn2 and gets closer and closer?

No. Imagine this simpler case. Two men are lifting the ends of a long horizontal plank. There's a girl walking on the plank from one end to the other. When she's at the left end of the plank, which man--left or right--is lifting the most weight? As she walks to the right end, what happens to the force that each man must exert?

 

[Inertialforce]

No. Imagine this simpler case. Two men are lifting the ends of a long horizontal plank. There's a girl walking on the plank from one end to the other. When she's at the left end of the plank, which man--left or right--is lifting the most weight? As she walks to the right end, what happens to the force that each man must exert?

Then it would be "B" right because as she continues to walk up the ladder, her weight begins to shift more and more towards Fn2 thus increasing the force exerted at Fn2 to keep the ladder from slipping.

 

[Doc Al]

As she gets closer to the right end, the vertical component of Fn2 must increase to balance the increased torque about the left end due to her weight moving.