A gymnast with mass m=50.0 kg suspends herself from the lower end of a hanging rope of negligible mass. The upper end of the rope is attached to the gymnasium ceiling.What is the gymnast’s weight?What is the tension at the top of the rope?

To solve this, let's break it into parts:

### 1. **The Gymnast's Weight**  
The weight of an object is given by the equation:

\[
W = m \cdot g
\]

Where:
- \( W \) is the weight,
- \( m = 50.0 \, \text{kg} \) is the mass of the gymnast,
- \( g \approx 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

Substituting the values:

\[
W = 50.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 490 \, \text{N}
\]

So, the gymnast's weight is **490 N** (Newtons).

### 2. **Tension at the Top of the Rope**  
The tension at the top of the rope is equal to the force needed to support the gymnast's weight since the rope is in static equilibrium (no movement). Therefore, the tension \( T \) at the top of the rope is simply the same as the gymnast's weight:

\[
T = W = 490 \, \text{N}
\]

Thus, the tension at the top of the rope is **490 N**.

### Summary:
- The gymnast's weight is **490 N**.
- The tension at the top of the rope is also **490 N**.

Would you like further details on the concepts of weight and tension? Here are five related questions to explore the topic further:

1. How does the tension change if the gymnast starts moving upward?
2. What would the tension be if the rope had mass?
3. How does the tension vary at different points along the rope in this scenario?
4. If the gymnast's mass were doubled, how would her weight and the tension change?
5. How would the tension differ if the gymnast were on the moon, where gravity is weaker?

**Tip:** When solving for tension in situations involving ropes and static objects, always consider all forces acting on the system to determine equilibrium conditions.

A gymnast with mass m=50.0 kg suspends herself from the lower end of a hanging rope of negligible mass. The upper end of the rope is attached to the gymnasium ceiling. What is the gymnast’s weight? What is the tension at the top of the rope?

This detailed solution explains how to calculate the weight and tension of a gymnast with mass 50.0 kg hanging from a rope. The problem uses fundamental concepts in classical mechanics, including the weight formula (W = m * g) and tension in static equilibrium. Ideal for students in Grades 9-12.

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