To find the gravitational force of the robotic helicopter on Mars, we can use the ratio of gravitational forces based on the different gravitational accelerations on Earth and Mars.
First, we know that the gravitational force \( F \) is given by the equation:
\[ F = m \cdot g \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity.
We can find the mass of the helicopter using its weight on Earth:
Given:
- Weight on Earth \( F_e = 17.65 , \text{N} \)
- Gravitational acceleration on Earth \( g_e = 9.8 , \text{m/s}^2 \)
Using the formula, we can calculate the mass:
\[ m = \frac{F_e}{g_e} = \frac{17.65 , \text{N}}{9.8 , \text{m/s}^2} \approx 1.80 , \text{kg} \]
Next, we will calculate the gravitational force on Mars using the mass we just found and the gravitational acceleration on Mars \( g_m = 3.71 , \text{m/s}^2 \):
\[ F_m = m \cdot g_m = 1.80 , \text{kg} \cdot 3.71 , \text{m/s}^2 \approx 6.68 , \text{N} \]
Thus, the gravitational force of the robotic helicopter on Mars is approximately 6.68 N.
Therefore, the correct response is:
6.68 N