What is the magnitude of the apparent weight of a 76 astronaut 3200 from the center of the Earth's Moon in a space vehicle accelerating toward the Moon at 3.6 ?
To find the magnitude of the apparent weight of the astronaut, we need to consider the gravitational force acting on them and the acceleration of the space vehicle.
First, let's determine the gravitational force acting on the astronaut. The gravitational force can be calculated using Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.674 x 10^-11 N*m^2/kg^2),
m1 and m2 are the masses of the two objects (astronaut and moon),
r is the distance between the two objects (distance from the center of the moon to the astronaut).
The mass of the astronaut is given as 76 kg, and the distance from the center of the Moon is given as 3,200 m.
Next, we need to consider the acceleration of the space vehicle. The apparent weight of an object is the force experienced by the object due to acceleration. In this case, the space vehicle is accelerating toward the Moon at 3.6 m/s^2. We need to calculate the net force acting on the astronaut.
Using Newton's second law of motion:
F_net = m * a
Where:
F_net is the net force,
m is the mass of the astronaut,
a is the acceleration.
Now, we can calculate the magnitude of the apparent weight of the astronaut by finding the difference between the gravitational force and the net force:
Apparent Weight = Gravitational Force - Net Force
Substituting the values and calculating, we can determine the magnitude of the apparent weight of the astronaut.