I see you've uploaded an image containing multiple physics and statics problems. I will solve these step by step. Let's start with Problem No. 1:

Problem 1:

A vertical force $F = 500 \, N$ acts downward at point $A$ on a two-membered frame. We are tasked with determining the magnitudes of the two components of $F$ directed along the axes of AB and AC.

Step 1: Setup the coordinate system

• $F_{AB}$ is the force component along member AB.
• $F_{AC}$ is the force component along member AC.

The angles given are:

• Angle between AB and the horizontal: $45^\circ$
• Angle between AC and the horizontal: $30^\circ$

Step 2: Use the method of components

The vertical force $F$ is resolved into components along AB and AC using the direction cosines of the members.

• For member AB: $F_{AB} = F \cdot \cos(\theta_{AC}) / \sin(\theta_{AB} + \theta_{AC})$
• For member AC: $F_{AC} = F \cdot \cos(\theta_{AB}) / \sin(\theta_{AB} + \theta_{AC})$ where $F = 500 \, N$, $\theta_{AB} = 45^\circ$, and $\theta_{AC} = 30^\circ$.

I will now calculate these values.For Problem No. 1, the magnitudes of the force components are:

• Force along $AB$ ($F_{AB}$): $448.29 \, N$
• Force along $AC$ ($F_{AC}$): $366.03 \, N$

Would you like to proceed to the next problem, or would you like more details about this one?

Here are 5 related questions you might be interested in:

1. How do you derive the component formulas used in this problem?
2. Can the force components ever be greater than the original force?
3. What if the angles $\theta_{AB}$ and $\theta_{AC}$ were different?
4. How would this change if the force $F$ was not vertical?
5. How do forces in frames interact when members are not pinned?

Tip: When resolving forces in frames, always ensure you account for the correct geometry and angle conventions.