You are part of a team that is designing a space probe that will land on the surface of a distant planet. The surface of the new planet can support a maximum force of 155 N. If the gravitational acceleration on the new planet is 11.6

, what is the maximum allowable weight of the probe when it is finished being constructed on earth? (Answer tolerance: ± 1 N)

To find the maximum allowable weight of the probe on Earth, we need to relate the force the probe will exert on the distant planet's surface to its weight on Earth.

### Step 1: Understand the relationship between weight, mass, and force
The force that the surface of the planet can support is related to the mass of the probe by the gravitational acceleration on that planet:
\[ F_{\text{max}} = m \cdot g_{\text{planet}} \]

Where:
- \( F_{\text{max}} = 155 \, \text{N} \) (maximum force the planet's surface can support)
- \( g_{\text{planet}} = 11.6 \, \text{m/s}^2 \) (gravitational acceleration on the distant planet)
- \( m \) is the mass of the probe.

### Step 2: Calculate the mass of the probe
\[ m = \frac{F_{\text{max}}}{g_{\text{planet}}} = \frac{155 \, \text{N}}{11.6 \, \text{m/s}^2} \]
\[ m \approx 13.36 \, \text{kg} \]

### Step 3: Determine the weight of the probe on Earth
The weight of the probe on Earth is given by:
\[ W_{\text{Earth}} = m \cdot g_{\text{Earth}} \]

Where \( g_{\text{Earth}} \) is the gravitational acceleration on Earth, approximately \( 9.8 \, \text{m/s}^2 \).

\[ W_{\text{Earth}} = 13.36 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ W_{\text{Earth}} \approx 130.93 \, \text{N} \]

So, the maximum allowable weight of the probe when it is finished being constructed on Earth is approximately **131 N** (considering the answer tolerance of ±1 N).

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How would the weight of the probe change if the gravitational acceleration on the distant planet were higher?
2. What is the significance of the probe's mass in designing other aspects of the mission, such as fuel requirements?
3. How would the design change if the probe needed to operate on a planet with a much weaker gravitational field?
4. What factors should be considered in addition to gravitational force when designing a probe to land on another planet?
5. How does Earth's gravitational force compare to that of other planets in our solar system?

**Tip:** Always account for gravitational differences when planning missions to other planets, as they significantly impact the weight and force exerted by objects.

Learn how to calculate the maximum allowable weight of a space probe on a distant planet's surface. Understand the relationship between gravitational acceleration, force, weight, and mass. Suitable for students and professionals interested in physics and space exploration.

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