# Static Equilibrium of scaffold

1. Mar 20, 2009

### peaceandlove

1. The problem statement, all variables and given/known data
A horizontal scaffold 2, with uniform mass m2 = 30 kg and length L2 = 2.4 m, hangs from horizontal scaffold 1, with uniform mass m1 = 53 kg. A 21 kg box of nails lies on scaffold 2, centered at distance d = 0.45 m from the left end, which is located from 0.45 m from the left end of horizontal scaffold 1 (same for the right end). What is the tension T in the right end cable of horizontal scaffold 1?

2. Relevant equations
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3. The attempt at a solution
First of all, I labeled the Tensions T_1, T_2, T_3, and T_4. T_1 is the top left, T_2 is the top right, T_3 bottom left, T_4 bottom right.

Then the Torques which I will call t are the following:

t_net,3 = d*m_b*g - 1/2 L*m_2*g + LT_4 =0
The unknown in this equation is T_4, so I solved for T_4.

Next:
t_net,4 = -L*T_3 + m_b*g*(L-d) + 1/2 L*m_2*g = 0
I solved for T_3.

Finally, I used:
t_net,1 = -T_3*d - (d+(L/2))*m_1*g - T_4(L+d) + T_2 (2d+L) = 0
to solve for T_2.

I found the answer to be 556.3727 N; however, it is apparently wrong.

2. Mar 20, 2009

### peaceandlove

Oh nevermind, I see what I did. I was accidently switching T_3 and T_4 when plugging them into the final equation.