Boom problem using rotational equilibrium methods

[qnney]

URGENT! Boom problem using rotational equilibrium methods

Hi!

Here is a picture of the problem I'm about to explain... http://i96.photobucket.com/albums/l168/synovial/boom.jpg

My professor did not give us numbers to use, just variables.

The goal of the problem is to find the 3 unknowns: T, V, and H. The given variables are the entire length of the boom (L--not pictured), mass of the boom, mass of the load, $$\Theta$$, x, and p.

The rope is connected to distance x from the end. The load hangs at distance p from the end. The boom's center of gravity is in the middle.

I know that I am supposed to find all of the forces in the X and Y directions, but I can't seem to calculate the torques correctly.

$$\Sigma$$F_x = 0
0 = H -Tcos$$\Theta$$

$$\Sigma$$F_y = 0
0 = V + Tsin$$\Theta$$-W_boom-W_load

$$\Sigma$$$$\tau$$F_a = 0
0 = $$\tau$$_{T perpindicular} + $$\tau$$_V + $$\tau$$_H + $$\tau$$_{W boom} + $$\tau$$_{W load}

Can someone please help me? Thanks!

 

[MaxL]

qnney--always start torque problems by picking a good pivot point! Where do you want yours to be? (HINT: Put it at the point where you have the most unknown forces acting).

Don't hesitate to ask more questions if you get stuck again!

 

[qnney]

I think a good place for the pivot point would be at the intersection of the V and H forces. Does this work?

 

[MaxL]

That's what I used.

 

[qnney]

Ok, so far I think I've figured out:

Sum of the torques = 0
0 = -Tsin$$theta$$(L-p) + Wboom(L/2) + Wload (L-x)

 

[MaxL]

Er... well, that's not consistent with the drawing you made OR with the description of the problem, but it's close.

The issue seems to be with your radii. The tension connects to the beam at a radius of (L-x) according to the text of the problem, and at (L-p-x) according to the picture. By both accounts, the load connects to the beam at a radius of (L-p)

It looks like you just got a bit mixed up, but otherwise, you seem to be on the right track.

 

[qnney]

Thanks so so much! I wasn't so sure if I was getting those right.

So now I think I can solve for T in this problem and then plug that value back into the $$\Sigma$$F_x and $$\Sigma$$F_y equations to get V and H.

:)

 

[MaxL]

Looks like you're on the home stretch now!

 

[qnney]

Thanks for your help!

 

[MaxL]

Hey, no problemo!