Uncovering the Mystery: How a Wheel and Axle Multiply Force in Simple Machines

[Infrasound]

Here is something that has been bothering me for quite a while...

Growing up, I was always taught that a wheel and axle decreased effort by multiplying the input force. In other words, the axle actually exerts more force than the wheel, just over a shorter distance.

This makes sense and conserves overall work, yet I am not completely satisfied with my current level of understanding.

WHY does the axle exert more force? How did the force get multiplied? To me, the "because it is can be exerted over a shorter distance" holds no ground, becuase it does not explain the balancing of two opposite but unequal forces using a wheel and axle. If they are indeed balanced, then the force is not exerted over a distance.

Sometimes I feel as if I am the only one who just does not get it.

How does the force increase?

 

[Infrasound]

Perhaps there is something obvious that I am not considering?

Do I have a serious mental disorder that is not allowing me to understand something simple?

I feel like I have lost it here.

 

[Doc Al]

Do you understand how a lever works? The wheel & axle can be viewed as a first class lever. A small force at the edge of the wheel translates into a large force at the axle, and vice versa. (Of course, the torque is the same.)

 

[Infrasound]

Yes, I understand that it is really just a first class lever, but WHY does the force translate to a different amount? To me, the force being applied over a smaller distance is just an inherent side effect, not the cause of the force being different at the two different radii. Thats what I wan't to know. How can the force be different if two different loads can be in balance? It's not moving then, so force is NOT being exerted over a distance.

I don't want this to be a situation where I have to use the "It just does" excuse. Let me get my barf bucket!