To find the gravitational force of the helicopter on Mars, we can use the following relationship between gravitational force and acceleration due to gravity:
\[ F = m \cdot g \]
Where:
- \( F \) is the gravitational force,
- \( m \) is the mass of the helicopter,
- \( g \) is the acceleration due to gravity.
First, we need to calculate the mass of the helicopter using its weight on Earth:
Given:
- Weight on Earth \( F_{Earth} = 17.65 , N \)
- Acceleration due to gravity on Earth \( g_{Earth} = 9.8 , m/s^2 \)
We can rearrange the formula to solve for the mass:
\[ m = \frac{F_{Earth}}{g_{Earth}} = \frac{17.65 , N}{9.8 , m/s^2} \approx 1.8 , kg \]
Now, we can find the gravitational force on Mars using this mass and the acceleration due to gravity on Mars:
Given:
- Acceleration due to gravity on Mars \( g_{Mars} = 3.71 , m/s^2 \)
Now calculate the weight on Mars:
\[ F_{Mars} = m \cdot g_{Mars} = 1.8 , kg \cdot 3.71 , m/s^2 \approx 6.68 , N \]
Therefore, the gravitational force of the helicopter on Mars is approximately 6.68 N.