https://file.aiquickdraw.com/mathbot/file/1727059336085zv6aa0aj.jpg

Let's analyze the problem in the image, which involves calculating the work done in pulling a stranded climber to safety.

### Given:
- The climber's height from the top of the rock is \( 14 \, \text{m} \).
- The total height of the rock is \( 85 \, \text{m} \), but this is not relevant to the work done, as we are only concerned with the climber's height to be raised.
- The climber's mass is \( 62 \, \text{kg} \).
- The cable weighs \( 0.6 \, \text{kg/m} \).
- Gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \).

### Work Calculation:
The formula for work done against gravity is:

\[
W = F \cdot d
\]
where:
- \( W \) is the work,
- \( F \) is the force required to lift the mass,
- \( d \) is the distance (14 m in this case).

#### Step 1: Calculate the force.
The force \( F \) is equal to the total weight, which includes both the weight of the climber and the weight of the cable over the distance of 14 meters.

1. **Weight of the climber**:
   \[
   F_{\text{climber}} = m_{\text{climber}} \cdot g = 62 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 607.6 \, \text{N}
   \]

2. **Weight of the cable**:
   The mass of the cable over the 14 meters is \( 0.6 \, \text{kg/m} \times 14 \, \text{m} = 8.4 \, \text{kg} \).
   Therefore, the weight of the cable is:
   \[
   F_{\text{cable}} = m_{\text{cable}} \cdot g = 8.4 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 82.32 \, \text{N}
   \]

3. **Total force**:
   \[
   F_{\text{total}} = F_{\text{climber}} + F_{\text{cable}} = 607.6 \, \text{N} + 82.32 \, \text{N} = 689.92 \, \text{N}
   \]

#### Step 2: Calculate the work done.
Now, we use the total force to calculate the work done in lifting the climber:

\[
W = F_{\text{total}} \cdot d = 689.92 \, \text{N} \times 14 \, \text{m} = 9658.88 \, \text{J}
\]

The correct answer for the work done should be **9658.88 Joules**.

The error in your submission was likely due to incorrect calculation of the total weight or the distance. You entered 983.92 J, but the correct order of magnitude should be in the thousands, not in the hundreds.

Would you like more details on any specific part of this calculation?

Here are 5 follow-up questions related to this problem:

1. What if the cable had a different weight per meter? How would that affect the work done?
2. How does the distance the climber needs to be raised affect the total work required?
3. How is the work affected if the gravitational acceleration changes (e.g., on another planet)?
4. What would be the work done if there was no cable weight to consider?
5. How would air resistance or friction affect the calculation of work in a real-life scenario?

**Tip**: Always double-check units and ensure your answer has the correct order of magnitude when solving physics problems involving forces and energy!

Finding the work done in pulling a stranded climber to safety. The climber is 14 meters from the top of an 85-meter rock face. The climber weighs 62 kg, and the cable weighs 0.6 kg/m. How much work is done in raising the climber, harness, and cable to the top?

Calculate the work done in raising a stranded climber 14 meters to safety, taking into account the climber's weight of 62 kg, the cable's weight of 0.6 kg/m, and gravitational acceleration. This solution demonstrates the application of the work-energy theorem.

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