Statics Mechanics: Looking for the flaw in my logic

[Femme_physics]

Yep...back to old statics. Not because I have a test (already passed it in flying colours) just for fun seeing what I can solve and can't...now I ran into this:

Homework Statement

http://img705.imageshack.us/img705/1533/pulleyf.jpg

Statics:

The weight is 50kg. Find force P to hold it in equilibrium.

The Attempt at a Solution

http://img18.imageshack.us/img18/5787/pulleya.jpg Somehow I got the result in minus, trying to find where is the logic in this. Or, otherwise, where is the flaw in my logic.

 

[I like Serena]

Hey Fp!

Only saw this thread just now.

Weren't you giving lessons in mechanics nowadays?

Anyway, you are assuming that all cables give the same tensional force.
They don't.
It's not all the same cable.
There are 3 cables, each with its own tensional force.

 

[Femme_physics]

I am giving lessons in mechanics, but with a very focused set of materials that I'm well-practiced with. In our course we never gone through several cables connected to system of pulleys. In fact, we hardly gave pulleys much time. At most we had one cable if I recall correctly.

Where do you see 3 cables?

 

[Femme_physics]

Ah... Got it, thanks. Once I realized the nail was separating the ropes, it was pretty straightforward. :) I thought originally the rope goes through holes in the pulleys... http://img844.imageshack.us/img844/8541/pull1g.jpg
http://img190.imageshack.us/img190/2194/pull2.jpg

 

[Femme_physics]

And I just solved 2 more such exercises correctly. Don't make me prove myself :) Just needed to understand one "Graphical" principle!

 

[ehild]

Very good! You are

ehild

 

[I like Serena]

Good!

If you feel up to the challenge... what would happen if there was indeed 1 cable and holes in the pulleys?

 

[Femme_physics]

Well then P would equal 1/6 of the weight. :)

 

[I like Serena]

Well then P would equal 1/6 of the weight. :)

Suppose P would equal 1/6 of the weight, what would be the resultant force on the leftmost pulley?

 

[Femme_physics]

Suppose P would equal 1/6 of the weight, what would be the resultant force on the leftmost pulley?

2/6 of the weight

 

[I like Serena]

2/6 of the weight

That would mean that ƩFy is not zero... what would that mean?

 

[Femme_physics]

That would mean that ƩFy is not zero... what would that mean?

Of course ƩFy is zero. The resultant force at Y of the rightest pulley is 2/6... Of the middle pulley is also 2/6...and the right 2/6... these are the up vectors in the Y direction...the down vector is just the weight...so of course it ends up being ƩFy=0

 

[I like Serena]

Of course ƩFy is zero. The resultant force at Y of the rightest pulley is 2/6... Of the middle pulley is also 2/6...and the right 2/6... these are the up vectors in the Y direction...the down vector is just the weight...so of course it ends up being ƩFy=0

Which up vectors do you mean?

I see only 2 downward tensional forces on each pulley and the pulleys are not attached to anything else (since we assumed that the cables were not attached to the pulleys).

 

[Femme_physics]

Which up vectors do you mean?

http://img444.imageshack.us/img444/8613/pulls.jpg

Each pulley has two!

 

[I like Serena]

Each pulley has two!

Ah, I meant that I didn't see any up vectors on for instance pulley A.

 

[Femme_physics]

Wait a second...That was a trick question! If there are no pins attaching the pulleys to the rope they're going to slide down!

 

[I like Serena]

Wait a second...That was a trick question! If there are no pins attaching the pulleys to the rope they're going to slide down!

Yep. The whole thing would collapse!

 

[Femme_physics]

:) Thanks for the stimulation!

 

[I like Serena]

:) Thanks for the stimulation!

I'm just thinking of those poor cardboard men that were standing below that weight!

 

[Femme_physics]

LOL! Remeber them eh? :)