Torque

[IlyaR]

What am I doing incorrectly?

If the point of rotation is in the middle of Y, then the force on the right side of Y generates
2M (4N)= 8NM= 1M (Nail Force)= 8N

Intuitively I understand that if you pry the right side up, the hinge will be on the left side, thus 4M(4N)= 1M( Nail Force), but from my understanding you can choose the point of rotation anywhere and still arrive at the correct answer, is this wrong?

Thanks!

Does the board on bottom's normal force count as torque (The 12N)?

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[enervate]

You're not accounting for the force/torque exerted by Board X. If you tried to with your fulcrum point, you'd have two unknown forces: one for the Force by Board X and another for the Force by the Nail.

Your equation should look like this:

(F_y * r_y) = (F_x * r_x) + (F_n * r_n)

...and, when you plug in known variables:

(4 N * 2 m) = (F_x * 2 m) + (F_n * 1 m)

Which works out given the values provided in the answers. Only problem is that you have two variables and one equation. One must be eliminated by placing the fulcrum at that point.

 

[IlyaR]

That makes much more sense. Is the force exerted by X arbitrarily placed at the end of board Y? Wouldn't the force be the same at every single point between the left end of Y, to it's midpoint?

Thanks again!

 

[enervate]

That's something I had difficulty with as well. Imagine lifting the board without the nail; it will rotate about the end. Roughly the same thing will happen with the nail there as well.

Why? I don't know. I can't explain it.

 

[Romz]

That's something I had difficulty with as well. Imagine lifting the board without the nail; it will rotate about the end. Roughly the same thing will happen with the nail there as well.

Why? I don't know. I can't explain it.

I like to imagine the nail as glue.

Just because we add glue/a nail at that position, it doesn't change the fulcrum of our board if the substance were not there. The tricky thing is that we see this verticle line and imagine it to serve as a balancing point or something.

Would adding a weak glue to your board change it's "natural" fulcrum? Imagine applying force at one end to the board; we could imagine strings of glue coming off as the board rotates among it's end. I relate this effect to the nail in the board.The glue/nail only serves as a downward force, as is depicted by the nail in the answer.


Hope this helps.