To calculate the normal force acting on the astronaut, we need to consider the forces acting on him:

1. Gravitational force (weight): $F_g = m \cdot g$
2. Normal force due to the rocket's acceleration: $F_n$ which is the apparent weight experienced due to the combined effect of gravity and the rocket's acceleration.

Step-by-Step Calculation:

1. Given values:

   • $m = 82.9 \, \text{kg}$ (mass of astronaut)
   • $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity)
   • $a = 37.2 \, \text{m/s}^2$ (rocket's upward acceleration)

2. Gravitational force: $F_g = m \cdot g = 82.9 \cdot 9.8 = 812.42 \, \text{N}$

3. Normal force: The normal force is caused by the apparent weight experienced by the astronaut due to the rocket's upward acceleration: $F_n = m \cdot (g + a)$ Substituting the values: $F_n = 82.9 \cdot (9.8 + 37.2) = 82.9 \cdot 47.0 = 3896.3 \, \text{N}$

4. Direction: The normal force is acting upward (positive direction) since it opposes gravity and is in the direction of the rocket's motion.

Final Answer:

$F_n = +3896.3 \, \text{N}$

Would you like further explanation or any additional examples?

---

Related Questions:

1. How does the normal force change if the rocket's acceleration increases?
2. What would the normal force be if the astronaut's mass increased by 10%?
3. How does the astronaut's apparent weight compare to his real weight in this scenario?
4. What happens to the normal force when the rocket reaches a constant velocity?
5. How does the calculation change if the rocket accelerates downward?

Tip: Always consider the direction of forces to ensure the correct sign and avoid errors in physics calculations.