a. How much force does an $80kg$astronaut exert on his chair while sitting at rest on the launch pad?

b. How much force does the astronaut exert on his chair while accelerating straight up at $10m/s^2?$

An $80kg$ astronaut is sitting on his chair while at rest on the launch pad.

The acceleration due to gravity is taken as, $g=9.8\mathrm{m}/{\mathrm{s}}^2.$

Weight is the force that gravity will exert on him to keep him on the earth, it is the same force which he exerts on the chair.

And it is given by :-

$$\begin{gathered} F=m\times g \\ F=80kg\times 9.8m/s^2 \\ F=784\mathrm{N} \end{gathered}$$

Force exerted by the astronaut while sitting on chair at rest on the launch pad is $784\mathrm{N}.$

The astronaut on chair is accelerating at$10m/s^2.$

Acceleration while going straight up, $a=10\mathrm{m}/{\mathrm{s}}^2.$

Here the acceleration will be due to net force of forces like gravity and the reaction force of the chair . Let it be R . Acceleration at which moves straight up by localid="1649439467778" $10\mathrm{m}/{\mathrm{s}}^2.$

Net force acting on him will be R - mg .

localid="1650265993057" $$\begin{gathered} R-mg=ma \\ R=m(g+a) \\ R=80kg\times (9.8m/s^2+10m/s^2) \\ R=80kg\times 19.8m/s^2 \\ R=1584\mathrm{N} \end{gathered}$$

Reaction Force of chair on the astronaut is 1584 N . Hence force on the chair by astronaut will also be 1584 N.