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We are tasked with finding how much load a crane can lift at a speed of 3.5 meters per minute, given that the crane operates at 18.5 horsepower (hp). The hint provides the equation for gravitational force \( F_g = mg \), where \( F_g \) is the weight, \( m \) is the mass of the load, and \( g \) is the acceleration due to gravity (approximated as \( 9.81 \, \text{m/s}^2 \)).

### Step-by-Step Solution:

1. **Convert horsepower to watts**:
   - 1 hp = 745.7 watts.
   - Therefore, \( 18.5 \, \text{hp} \) is converted to:
   \[
   P = 18.5 \times 745.7 \, \text{watts} = 13,796.45 \, \text{watts}.
   \]

2. **Convert lifting speed from meters per minute to meters per second**:
   - 3.5 m/min is converted to m/s:
   \[
   v = \frac{3.5 \, \text{m}}{60 \, \text{sec}} = 0.05833 \, \text{m/s}.
   \]

3. **Power and force relation**:
   The power \( P \) is related to the force \( F_g \) and velocity \( v \) by:
   \[
   P = F_g \cdot v.
   \]
   Using \( F_g = mg \), we can rewrite this as:
   \[
   P = mgv.
   \]

4. **Solve for mass \( m \)**:
   Rearranging the equation to solve for mass \( m \):
   \[
   m = \frac{P}{gv} = \frac{13,796.45}{9.81 \times 0.05833}.
   \]
   Simplifying:
   \[
   m = \frac{13,796.45}{0.57218} = 24,105.82 \, \text{kg}.
   \]

### Final Answer:
The crane can lift a load of approximately **24,105.82 kg** at a speed of 3.5 meters per minute.

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Would you like further details on any step, or do you have other questions?

Here are 5 related questions to expand your understanding:
1. How would the load capacity change if the crane's power was doubled?
2. What happens to the lifting capacity if the lifting speed is halved?
3. How do frictional forces affect the load capacity in real-world applications?
4. How can this formula be applied to calculate the load for a different gravitational constant (e.g., on the Moon)?
5. What other factors, apart from power, limit the crane's lifting ability?

**Tip:** Always ensure units are consistent across a problem, particularly when working with mixed unit systems like horsepower, meters, and minutes.

An 18.5-hp overhead crane is used to lift a load at a rate of 3.5 m/min. How much load can it raise at this lifting speed?

Learn how to calculate the load that an 18.5-hp overhead crane can lift at a speed of 3.5 meters per minute. This detailed solution involves power conversion, weight calculations, and Newton's second law of motion. Suitable for high school students in Grades 10-12.

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