Rock climbing with forces along a "cam clamp" axle

[aspodkfpo]

Homework Statement

Why is the downward force Ff all on the axle of the cam is converted (through the cam’s rigidity) to an outward force Fr on the rock, which acts along the line from the axle of the cam to the point of contact with the rock and how are you able to relate cos Ff and N to those angles on the cam?

Relevant Equations

Ffall = 2Fr sinφ
N = Fr cosφ

https://www.asi.edu.au/wp-content/uploads/2016/10/Physics_ASOE2015solutions.pdf
Q`12b)
Unable to understand how they deduct the relation between Ffall and N via the angles.
Unable to tell why this would act along the axle of the cam to the point of contact with the rod and be relatable to each other via the angle?

The model that I have in my head is that the gravitational force equals to the frictional force and there is a normal force, and that the gravitational force and the normal force do not relate to each other like this.

 

[haruspex]

Why is the downward force Ff all on the axle of the cam is converted (through the cam’s rigidity) to an outward force Fr on the rock, which acts along the line from the axle of the cam to the point of contact with the rock and how are you able to relate cos Ff and N to those angles on the cam?

Can you attempt to draw the FBD for one lobe of the cam and post it?

 

[aspodkfpo]

Can you attempt to draw the FBD for one lobe of the cam and post it?

Specifically I don't see why Fn + Fg would equal a force that just happens to be at phi angle to the vertical. (this image should be rotated 90 degrees for the actual model)

 

[haruspex]

View attachment 268016
Specifically I don't see why Fn + Fg would equal a force that just happens to be at phi angle to the vertical. (this image should be rotated 90 degrees for the actual model)

$F_g$ should act at the pivot, and there should be another force at the pivot from the other lobe.
$F_f$ should act at the rock surface.
Your $F_N$ arrow wanders around a bit. It should be normal to the rock surface, not passing through the angle on the other side of the cam.

 

[aspodkfpo]

$F_g$ should act at the pivot, and there should be another force at the pivot from the other lobe.
$F_f$ should act at the rock surface.
Your $F_N$ arrow wanders around a bit. It should be normal to the rock surface, not passing through the angle on the other side of the cam.

Statement 1 and 2, we're taught to draw fbd from the centre of mass in schools now LOL.
Statement 3 and 4, can't draw something without the wobbles with a mouse, it's meant to be normal.
Still don't see why Fn + Fg would equal a force that just happens to be at phi angle to the vertical.

 

[haruspex]

we're taught to draw fbd from the centre of mass in schools now

Then how do you figure out torque balance?

don't see why Fn + Fg would equal a force that just happens to be at phi angle to the vertical.

Because if not then torques would not balance and the cam would rotate.