- #1

myelevatorbeat

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## Homework Statement

A bag of cement hangs from three wires as shown. Two of the wires make angles theta1 and theta2, respectively, with the horizontal.

a)Show that, if the system is in equilibrium, then:

T1=Fgcostheta2/sin(theta1+theta2)

b) Given that Fg=325 N, theta1=10.0degrees, and theta2=25.0degrees, find the tensions T1, T2, and T3 in the wires.

## The Attempt at a Solution

Part A:

(Fnet)x=max (a=0)

T2cosx2+T1cosx1=0

T2=-T1cosx1/cosx2

(Fnet)y=may (a=0)

T1sinx1+T2sinx2-Fg=0

I substituted in the equation I got for T2 which gave me:

T1sinx1+T1cosx1sinx2/cosx2-Fg=0

I rearranged the above equation to solve for T1 and got:

Fgcostheta1/sinx1cosx2+sinx2

I assume I need a cosx1 in the denominator so it can be changed to sin (x1+x2) but I'm not sure where I get the cosx1 from? Did I skip it in one of the equations?

Now for Part B:

Fg=325 N (cause it's the weight of the cement bag)

x1=10.0 degrees

x2=25.0 degrees

I plugged them into the above equations that I had found:

T1=Fgcosx2/sin(x1+x2)

T1=325 N x cos 25.0 degrees/sin (10.0degrees + 25.0degrees)

T1=514 N

T2= -T1cosx1/cosx2

T2= -514 x cos10.0degrees/cos25.0degrees

T2=-558

I don't understand why tension 2 would be negative though. I would asume they would all be upwards vertical forces. Maybe I solved one of the equations wrong?

I feel like I should just drop the negative sign, but I don't know if that would be correct.