I need help solving the problem below, I have the correct answers given but need

Question

I need help solving the problem below, I have the correct answers given but need to show all my work. The correct answers came from the book and I am struggling as to how I go about solving this problem. Thank you in advance.

The figure below hangs in equilibrium. It consist of objects held vertically by vertical strings. Object 3 weighs 1.40N and the uniform, horizontal bars weigh 0.50N each. Find (a) the weight of objects 1 and 2 and (b) the tension in the upper string. The correct answers are (a) object 1 weight = 1.5N, object 2 weight 1.40N and (b) tension = 5.3N.

I need help solving the problem below, I have the correct answers given but need to show all my work. The correct answers came from the book and I am struggling as to how I go about solving this problem. Thank you in advance. The figure below hangs in equilibrium. It consist of objects held vertically by vertical strings. Object 3 weighs 1.40N and the uniform, horizontal bars weigh 0.50N each. Find (a) the weight of objects 1 and 2 and (b) the tension in the upper string. The correct answers are (a) object 1 weight = 1.5N, object 2 weight 1.40N and (b) tension = 5.3N.

Explanation / Answer

Equilibrium of lower shaft:

m2*L/2 = m3*L/2

So, m2 = m3 = 1.4 N

Tension in lower string = m2 + m3 + 0.5 = 1.4 + 1.4 +0.5 = 3.3 N

Equilibrium of upper shaft: Here pivot point is not at geometric centre of rod and hence the moment due to weight of rod needs to be accounted.

m1*2L/3 + 0.5*(2L/3 - L/2) = 3.3*L/3

2*m1 + 0.25 = 3.3

m1 = 1.525 N

Tension in upper string = m1 + 3.3 + 0.5

= 1.525 + 3.3 + 0.5

= 5.325 N

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