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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.

Determine the magnitudes of the two components of 'F' directed along the axes of AB and AC. Set 'F' = 500 N.

Solve a statics problem involving the resolution of a vertical force of 500 N into two components along the members of a two-member frame. Learn how to apply vector resolution and the law of sines to calculate the forces along AB and AC.

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