Answer
(a) The force the astronaut exerts on the chair is 784 N
(b) The force the astronaut exerts on the chair is 1584 N
Work Step by Step
Let $F_N$ be the force that the chair exerts on the astronaut. According to Newton's third law, the force the astronaut exerts on the chair is equal in magnitude to the force $F_N$ the chair exerts on the astronaut.
(a) When the astronaut is at rest, $F_N$ is equal in magnitude to the astronaut's weight.
$F_N = mg$
$F_N = (80~kg)(9.80~m/s^2)$
$F_N = 784~N$
The force the astronaut exerts on the chair is 784 N
(b) We can use a force equation to find $F_N$ when the astronaut is accelerating.
$\sum F = ma$
$F_N -mg = ma$
$F_N = m(g+a)$
$F_N = (80~kg)(9.80~m/s^2+10~m/s^2)$
$F_N = 1584~N$
The force the astronaut exerts on the chair is 1584 N
