What Is the Tension in the Right End Cable of Scaffold 1?

[peaceandlove]

Homework Statement

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?

Homework Equations

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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.

 

[peaceandlove]

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

 

[nlightner]

Your approach to solving this problem is correct, but it seems that there may have been a mistake in your calculations. I would recommend double-checking your equations and calculations to ensure accuracy. Additionally, it may be helpful to draw a diagram to visualize the forces and torques acting on the scaffold system. Overall, your method is sound and with careful attention to detail, you should be able to arrive at the correct solution.