Answer:
the apparent weight of the astronaut is 81.032 N { towards moon }
Explanation:
Given that;
Mass of astronaut m = 80 kg
Distance of spaceship from the Earth's moon r = 2200 km = 2200 × 10³ m
Acceleration due to gravity of the moon = GM/r²
where M is mass of the moon( 7.34767309 × 10²² kg )
gravitational constant G = 6.67 × 10⁻¹¹
So,
Acceleration due to gravity of the moon g is;
g = [ (6.67 × 10⁻¹¹) × (7.35 × 10²²) ] / (2200 × 10³)²
g = 4.90245 × 10¹² / 4.84 × 10¹²
g = 1.0129 m/s²
now, we take the positive direction towards the moon if the spacecraft is moving with constant velocity, a = 0
The apparent weight is measured by the normal force FN
so,
∑F = ma
-FN + mg = ma
-FN + mg = 0
FN = mg
we substitute
FN = 80 × 1.0129
FN = 81.032 N { towards moon }
Therefore, the apparent weight of the astronaut is 81.032 N { towards moon }
