sorry, couldn't think of a better title(adsbygoogle = window.adsbygoogle || []).push({});

anyways, i'm somewhat stuck on 2 questions i have in my homework assignment

first one:

Three blocks are supported using the cords and two pulleys. If they have weights of WA = WC= W, WB= kW, determine the angle (theta) for equilibrium.

Given:

k = 0.25

http://www.mydatabus.com/2z/lnubb.pn/mybsaccownt/blocksandcords.bmp

alright, for the first one, i thought it would be easy and i thought i had a good plan

Wa = Wc = W Wb = kW and k = 0.25

i want equilibrium so, sum of the forces in x = 0, sum of forces in y = 0

so then i break everything into components to add the x and y forces respectively

in the y the two forces going up should equal the force going down

Wsin(fi) + 0.25Wsin(theta) = - W

W cancels and i end up with

sin(fi) + 0.25sin(theta) = -1

here is where my math skills fail me, instead of trying to write theta or fi in terms of the other one (i get some ugly things), i see what i can do with the other part

forces in the x, only two of them, so:

Wcos(fi) = -0.25Wcos(theta)

once again, the W cancels, and i dared to solve for one angle in terms of the other

cos(fi) = -0.25cos(theta)

fi = arccos(-0.25)*theta

fi = 104*theta

theta = fi/104 <---theta will be really really tiny, that's ok, because block b has to fight block c in the x direction and block c has 4 times the mass

anyways, this is where i pretty much got stuck,

have i done something screwy, or is it just a lack of trig knowledge?

and

Determine the mass of each of the two cylinders if they cause a sag of distance d when suspended from the rings at A and B. Note that s=0 when the cylinders are removed.

Given:

d = 0.5m

l1 = 1.5m

l2 = 2m

l3 = 1m

k = 100N/m

g = 9.81m/s^2

http://www.mydatabus.com/2z/lnubb.pn/mybsaccownt/springsandmass.bmp

for the 2nd problem

i got stuck pretty early on

i started drawing a FBD at point A, i had t1, t2, and m1

then i started second-guessing my strategy and came to the conclusion that i had no real idea what i was going to do with that

i trigged out some angles, wrote some equations of equilibrium, but...when i saw 5 unknowns, i backed down and decided i'd check if i am on the right path before taking on that beastly chore

i'll just briefly outline where i was headed

Fxa = t1cos48.59 - t2

Fya = t1sin48.59 -m1g

Fxb = t3cos48.59 - t2

Fyb = t3sin48.59 - m2g

i must admit, t2 confuses me in the FBD, i need to have it opposing t3 and t1, which means it opposes itself, hmm

i also tried something like

m1 + m2 = 2kd/g and i get the combined mass of m1 and m2 is 10.2 kg, but surely, it can't be that simple

alright...that's where i am :)

any help would be appreciated

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# Homework Help: Forces, blocks, cords, and springs

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