Right after clearing the launch tower, the space shuttle is accelerating upward at 6 m/s/s.
Calculate the net force on an 80 kg astronaut during this acceleration and the force that the seat must exert on the astronaut during this acceleration.
To calculate the net force on the astronaut during this acceleration, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
Given:
Mass of the astronaut (m) = 80 kg
Acceleration (a) = 6 m/s²
Using the formula:
F = m * a
Plugging in the values:
F = 80 kg * 6 m/s²
F = 480 N
Therefore, the net force on the astronaut during this acceleration is 480 N.
Now, to calculate the force that the seat must exert on the astronaut, we need to consider the forces acting on the astronaut.
The two main forces are:
1. Force of gravity (weight): This is the force with which the Earth attracts the astronaut and can be calculated using the formula F = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Given:
Mass of the astronaut (m) = 80 kg
Acceleration due to gravity (g) = 9.8 m/s²
Plugging in the values:
F_gravity = 80 kg * 9.8 m/s²
F_gravity = 784 N
2. Net force (F_net): This is the force required to accelerate the astronaut upward and can be calculated using the formula F_net = m * a.
Given:
Mass of the astronaut (m) = 80 kg
Acceleration (a) = 6 m/s²
Plugging in the values:
F_net = 80 kg * 6 m/s²
F_net = 480 N
The force that the seat must exert on the astronaut is equal to the sum of these two forces:
F_seat = F_gravity + F_net
F_seat = 784 N + 480 N
F_seat = 1264 N
Therefore, the force that the seat must exert on the astronaut during this acceleration is 1264 N.