Question

At liftoff, a space shuttle with 2.0 x 10^6 kg total mass undergoes an upward acceleration of 0.60g.How do I calculate the force that the seat exerts on a 60 kg astronaut during liftoff?

Answer 1

The astronaut undergoes that acceleration of $0.6g$ too. The force that the seat exerts on a 60 kg astronaut during liftoff is the normal force. According to Newton's second law, assuming our x-axis looks upward:

$$\Sigma F=ma,\\ -mg+N=ma,\\ N=m(g+a)=m(g+0.6g)=\\ =60(9.8+0.6\cdot9.8)=940.8\text{ N}.$$

No matter what mass the space shuttle has, if we consider the astronaut inside, we only need the acceleration of the shuttle to calculate the normal force.