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Let's break down the problem in steps as per the given questions:

### a) Representation of all the existing forces:

There are three main forces in this situation:
1. **The weight of the lantern**: This force acts vertically downward and has a magnitude of 50 N (since the weight is given as 50 N). This is the gravitational force pulling the lantern down.
2. **Tension in the left rope**: There is a tension force acting upward along the left rope.
3. **Tension in the right rope**: Similarly, there is a tension force acting upward along the right rope.

In the diagram, these two ropes are angled inward toward the point where they connect to the lantern.

### b) Magnitude of the forces on the ropes and the parallelogram rule:

Using the parallelogram rule, we can determine the relationship between the tensions in the ropes. The rule suggests that the vector sum of the tension forces in both ropes must equal the downward force due to the weight of the lantern (50 N). The direction and magnitude of the forces in the ropes depend on the angles at which they are inclined.

- If we consider the tensions \( T_1 \) (left rope) and \( T_2 \) (right rope), and the angle between the ropes, the parallelogram formed by these vectors must balance the vertical weight.
- The vertical component of each tension force (coming from the ropes) must add up to 50 N, which is the downward force due to the lantern’s weight.

### c) Determining the force on each rope:

To find the exact forces in each rope (the tensions), we need to know the angles the ropes make with the horizontal. Let’s call these angles \( \theta_1 \) and \( \theta_2 \).

Using trigonometry, we know that the sum of the vertical components of the tensions must equal the lantern’s weight:
\[
T_1 \sin(\theta_1) + T_2 \sin(\theta_2) = 50 \, \text{N}
\]

If the ropes are symmetric (i.e., \( \theta_1 = \theta_2 \)), then the forces in both ropes will be the same, and the equation simplifies to:
\[
2T \sin(\theta) = 50 \, \text{N}
\]
where \( T \) is the tension in each rope. Solving for \( T \):
\[
T = \frac{50}{2 \sin(\theta)}
\]

Once the angle is known, you can calculate the exact tension in each rope.

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Would you like to provide the angles or ask further about how to handle specific angles in this problem?

### Here are 5 relative questions to expand on this information:
1. How do you find the tension in each rope when the angles are known?
2. Can you explain how the parallelogram rule applies to more complex systems with more than two ropes?
3. What happens to the tension in the ropes if the angles between them decrease?
4. How does the symmetry of the system affect the forces on each rope?
5. How would the forces change if the lantern's weight increased?

**Tip**: Always resolve forces into vertical and horizontal components when dealing with systems involving angles.

The rope supports a lantern that weighs 50 N.
a) Make a representation of all the existing forces.
b) What can you say about the magnitude of the forces on the ropes? Use the parallelogram rule to defend your answer.
c) Determine the force on each rope.

This problem involves calculating the tension forces in two ropes supporting a 50 N lantern using vector addition and the parallelogram rule. It includes a detailed analysis of force representation and determination of individual rope forces using trigonometry.

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