To find the gravitational force of the robotic helicopter on Mars, we can use the formula for gravitational force:
\[ F = m \cdot g \]
Where:
- \( F \) is the gravitational force,
- \( m \) is the mass of the helicopter,
- \( g \) is the acceleration due to gravity.
First, we need to find the mass of the helicopter using its gravitational force on Earth.
Given:
- Gravitational force on Earth, \( F_{\text{Earth}} = 17.65 , \text{N} \)
- Acceleration due to gravity on Earth, \( g_{\text{Earth}} = 9.8 , \text{m/s}^2 \)
We can rearrange the formula to solve for mass (\( m \)):
\[ m = \frac{F_{\text{Earth}}}{g_{\text{Earth}}} \]
Substituting the known values:
\[ m = \frac{17.65 , \text{N}}{9.8 , \text{m/s}^2} \]
Calculating the mass:
\[ m = 1.80 , \text{kg} \]
Now, we can calculate the gravitational force on Mars using the mass we just found and the acceleration due to gravity on Mars (\( g_{\text{Mars}} = 3.71 , \text{m/s}^2 \)):
\[ F_{\text{Mars}} = m \cdot g_{\text{Mars}} \]
Substituting the values:
\[ F_{\text{Mars}} = 1.80 , \text{kg} \cdot 3.71 , \text{m/s}^2 \]
Calculating the gravitational force on Mars:
\[ F_{\text{Mars}} \approx 6.68 , \text{N} \]
So, the gravitational force of the robotic helicopter on Mars is 6.68 N.