How Does Acceleration Affect an Astronaut's Apparent Weight Near the Moon?

[N_L_]

What is the apparent weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, and (b) accelerating toward the Moon at 2.9 m/s^2? State the "direction" in each case.

I understand part a. I got 21 Newtons towards the moon by using Fg = G * [ (m1 * m2) / d^2 ].

For part B I do not understand where / how to use the acceleration of 2.9 m/s^2...would it be the same equation?

mass of the moon: 7.35 x 10^22 kg
mass of the astronaut: 75 kg
distance: 4200 km = 4200000 meters
G = 6.67 x 10^-11

 

[topsquark]

What is the apparent weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, and (b) accelerating toward the Moon at 2.9 m/s^2? State the "direction" in each case.

I understand part a. I got 21 Newtons towards the moon by using Fg = G * [ (m1 * m2) / d^2 ].

For part B I do not understand where / how to use the acceleration of 2.9 m/s^2...would it be the same equation?

mass of the moon: 7.35 x 10^22 kg
mass of the astronaut: 75 kg
distance: 4200 km = 4200000 meters
G = 6.67 x 10^-11

Remember that "apparent weight" is a fancy term for "normal force." In the first case the normal force and the weight are going to be the same magnitude because the astronaut is not accelerating. The accelerating case is very similar to an elevator problem, where the elevator is accelerating downward at a rate less than g.

-Dan