Force angle question (i think)

[Ebola0001]

I'm not sure i know enough to know how to ask my question, but here goes.

I want to figure out how the force pushing up on a pivot gets transferred to a cylinder also pushing on that pivot, for lack of better description, here are pictures of kinda what I am asking, the numbers are more for discussion, i am really looking for "how" to find this rather than a specific answer


http://02ab560.netsolhost.com/joe/phys/phys1.jpg
http://02ab560.netsolhost.com/joe/phys/phys2.jpg
I haven't taken physics yet (next semester).

 

[Ebola0001]

ok bear with me, and stop me if I've messed something up here (very possible)

I am assuming a few things here, because i never got an answer.
1.The angle of force that the vertical load is compared to is the angle of the rigid arm
http://www.woodrell.com/joe/phys/physb-1.jpg
2.The force applied at an angle is the cosine of the angle delta between force and load
http://www.woodrell.com/joe/phys/physb-2.jpg

ok with that let me label the things i am looking at
a = 9 length of rigid arm
b = 6 distance between fixed pivots
c = height of movable pivot at rest above bottom fixed pivot
d = height of top fixed pivot above movable pivot at rest
e = horizontal distance between fixed and movable pivots
f = pi/12 angle of rigid arm at rest
g = angle delta of cylinder to angle of force on rigid arm of the force
http://www.woodrell.com/joe/phys/physb-3.jpg

so with this
c = Sin(f) * a
d = b - c
e = Cos(f) * a
g = pi/2 - arctan( d / e ) - f

so bringing those things together i get
g = pi/2 - (arctan((6 - sin(pi/12) * 9) / (cos(pi/12) * 9))) - pi/12

with that equation for the angle of the cylinder, i want to find how the force changes as the mounting point of the cylinder moves down the rigid arm closer to its fixed pivot, aligning with the angle of force, but moving in on the lever.

this melted my brain for a while, but i collapsed it down to an equation with the length of the rigid arm as x, and scaling with where the pivot is on the am

pi/2 - (arctan((6 - sin(pi/12) * x) / (cos(pi/12) * x))) - pi/12)
http://www.woodrell.com/joe/phys/physb-4.jpg

and the force it would generate at this delta angle
cos(pi/2 - (arctan((6 - sin(pi/12) * x) / (cos(pi/12) * x))) - pi/12))
http://www.woodrell.com/joe/phys/physb-5.jpg

and multiplying that by the proportion of the mounting position on the rigid arm
cos(pi/2 - (arctan((6 - sin(pi/12) * x) / (cos(pi/12) * x))) - pi/12)) * x/9
http://www.woodrell.com/joe/phys/physb-6.jpg

basically what graphing this told me was that the greatest force is achieved when the cylinder attached to the end of the arm even though the cylinder was at more of an oblique angle

the reason for all this thought is just a personal project, that will probably result in nothing more than a thought process, but i at least want to make sure i am getting it right so far

anyway... thanks for your help guys, just trying to understand this stuff better

 

[thomate1]

I appreciate your curiosity and interest in understanding the transfer of force in this scenario. From what I can gather, you are asking about how the force exerted on the pivot point in the first image is transferred to the cylinder in the second image.

First, it is important to understand that force is a vector quantity, meaning it has both magnitude and direction. In this case, the force is acting in an upward direction on the pivot point, and it is this force that is being transferred to the cylinder.

The key concept to understanding force transfer in this scenario is the principle of moments, also known as the law of the lever. This principle states that the sum of the clockwise moments (force x distance from pivot point) must equal the sum of the counterclockwise moments for an object to be in equilibrium.

In the first image, the force acting on the pivot point creates a clockwise moment, while the weight of the cylinder creates a counterclockwise moment. In order for the system to be in equilibrium, the force acting on the pivot must be equal to the weight of the cylinder multiplied by the ratio of their distances from the pivot point.

In other words, the force pushing up on the pivot is transferred to the cylinder through the lever mechanism. The longer the distance between the pivot point and the cylinder, the greater the force that can be transferred.

I hope this explanation helps you understand the concept better. I would encourage you to continue exploring physics and learning about the principles that govern the physical world. Best of luck in your studies!