The image contains several engineering mechanics problems related to static equilibrium, moments, and forces. Here is a detailed description and the approach to solving each question:

Problem 5:

Problem Statement:
To determine the weight of item 1 needed to keep the horizontal beam AB in equilibrium, given the weight of G = 346 N.

Approach:
Use the principle of moments (torque) about point A or B to find the unknown weight.
Sum of moments about the pivot point should be zero.

Problem 6:

Problem Statement:
Determine the modulus of the resultant moment at point A if $F = 150 \, \text{N}$, $q = 40 \, \text{N/m}$, and the lengths $AD = BD = 1 \, \text{m}$ and $BC = 3 \, \text{m}$.

Approach:

1. Calculate the total force generated by the distributed load $q$.
2. Find the moments generated by each force about point A.
3. Sum the moments to get the resultant moment.

Problem 7:

Problem Statement:
Determine the length $\ell$ of the frame for which the moment at point A is $M_A = 3 \, \text{Nm}$, given the intensity of the distributed load $q_{\text{max}} = 1 \, \text{N/m}$.

Approach:

1. Calculate the total force generated by the distributed load over length $\ell$.
2. Determine the position of the equivalent force.
3. Use the moment equation about A to find $\ell$.

Problem 8:

Problem Statement:
Determine the moment of force $\vec{F}$ about the axis $O_x$ if the force $F$ has a magnitude of 20 N and crosses the axes $O_x$ and $O_y$ at distances $a = 2 \, \text{m}$ and $b = 3 \, \text{m}$, respectively.

Approach:

1. Use the vector cross-product formula to calculate the moment about $O_x$.
2. The moment arm can be determined based on the given coordinates.

Would you like detailed solutions for these problems, or do you have any specific questions regarding one of the problems?

Here are 5 related questions that can help deepen your understanding:

1. How do you determine the resultant force of a distributed load?
2. What is the principle of moments, and how is it used in equilibrium calculations?
3. How does the positioning of a force affect the generated moment?
4. What are the steps to calculate the moment of a force about a given axis?
5. How can static equilibrium conditions help solve real-life engineering problems?

Tip: Always draw a free-body diagram for each problem; it simplifies the analysis by visually representing all forces and moments acting on the system.