To determine the centripetal force acting on the airplane, we use the formula for centripetal force:

$F_c = \frac{m v^2}{r}$

Where:

• $m$ is the mass of the airplane ($3 \, \text{kg}$),
• $v$ is the velocity ($1 \, \text{m/s}$),
• $r$ is the radius of the circular path ($5 \, \text{m}$).

Step-by-step calculation:

1. Substitute the values into the formula: $F_c = \frac{3 \times (1)^2}{5}$

2. Simplify the numerator: $F_c = \frac{3 \times 1}{5}$

3. Divide: $F_c = 0.60 \, \text{N}$

Final Answer:

The centripetal force acting on the airplane is 0.60 N.

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Would you like a detailed explanation of why this formula works or its real-world implications? Let me know!

Here are some related questions to deepen your understanding:

1. What happens to the centripetal force if the mass of the airplane doubles?
2. How does increasing the velocity affect the centripetal force?
3. What forces contribute to tension in the guideline in this scenario?
4. Can centripetal force exist without tension? If so, how?
5. How would reducing the radius to half impact the centripetal force?

Tip: Always ensure units are consistent (e.g., mass in kg, speed in m/s, and radius in meters) to avoid calculation errors.