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

 

[kyle8921]

N*m^2/kg^2

In order to calculate the apparent weight of the astronaut in a space vehicle that is accelerating towards the Moon at 2.9 m/s^2, we need to take into account the gravitational force and the acceleration force acting on the astronaut. The gravitational force is given by the equation Fg = G * [ (m1 * m2) / d^2 ], where G is the gravitational constant, m1 is the mass of the Moon, m2 is the mass of the astronaut, and d is the distance between the center of the Moon and the astronaut.

In this case, the gravitational force will be directed towards the center of the Moon, since the astronaut is 4200 km from the center of the Moon. This force will remain constant throughout the astronaut's journey towards the Moon.

However, the acceleration force will change as the space vehicle accelerates towards the Moon. The acceleration force is given by the equation F = m * a, where m is the mass of the astronaut and a is the acceleration towards the Moon. This force will also be directed towards the center of the Moon, since the acceleration is in that direction.

To calculate the apparent weight of the astronaut, we need to add these two forces together. The result will be the net force acting on the astronaut, which can be used to calculate the apparent weight using the equation F = m * g, where g is the gravitational acceleration on the Moon's surface.

Therefore, the apparent weight of the astronaut in the space vehicle accelerating towards the Moon will be the sum of the gravitational force and the acceleration force, directed towards the center of the Moon. This will result in a larger apparent weight compared to the astronaut's weight on Earth or in a space vehicle moving at constant velocity, since the acceleration force adds to the gravitational force.