Confused about forces - can anyone help?

[peanutaxis]

In the first diagram below, there is a horizontal board and it is attached to a vertical board via a pivot, P, but is also hooked via a nail (red), and the vertical board is resting on the ground.

If I am pulling on the horizontal board with force Fp, and the whole setup doesn't move, then the forces on the vertical board are Fp, Ff, and F?. Since it is not moving Fp + Ff + F? = 0, and also the torques on the vertical board - due to Ff and F? - about P are equal and opposite (I should have made Ff look smaller).

In the second diagram (also nothing is moving) the nail and hook are now moved to the bottom. Fp is still the same, and Ff is also the same since the weight of the system and the frictioned ground are the same. Even F? is the same since the vertical board is still not rotating so the torques due to Ff and F? will still add to zero. But now F? is in the same direction as Fp, and so the horizontal forces aren't going to sum to zero anymore.

Intuitively, it shouldn't make any difference where you place the nail and hook. Wherever you place them, they will create the same torque about P, but all of a sudden it doesn't make sense in the second diagram.

What the heck is going on?:huh::huh:

 

[Vodkacannon]

Yea who made this diagram? It dosen't seem consistent.

 

[peanutaxis]

What's not consistent about it? In the first the vertical board experiences F? to the right, where the nail is. And in the second the vertical board experiences a F? to the left where the nail is.

 

[Drakkith]

How is there any torque around P if you are just pulling it straight on?

 

[peanutaxis]

How is there any torque around P if you are just pulling it straight on?

Without the nail and hook, there would be a torque on the vertical plank - due to Ff - and it would rotate CCW.

With the nail and hook the torque due to Ff is balanced by the torque due to F?

The question is, how on Earth to balance the horizontal forces overall, given that it shouldn't matter where the nail and hook is.

 

[Nugatory]

What the heck is going on?:huh::huh:

You've made a subtle error in your interpretation of F_p. (It might be easier to think of the hook and the pivot as two pins holding the two boards together and analyzing the forces on them, rather than thinking of a pivot and a hook).

I grab on to the horizontal board and tug on it with some force - let's call it F_h where the h stands for "handle", as if there's a handle on the horizontal board that I'm pulling on. Note that F_h and F_f are the external forces on the two-board system; if they are balanced the two boards won't move.

Now the important part: F_h is NOT the force at the pivot, F_p. Instead, the forces are related by (using the convention that left is the positive direction):
F_h = -(F_p + F_?). Depending on where the hook is relative to the pivot, F_? can be positive or negative, whatever is needed to generate a torque around the pivot that cancels the torque from F_f and then F_p will be whatever value is needed to make F_h come out to the the known horizontal force you're applying.