# Chapter 7 - Newton's Third Law - Exercises and Problems: 6

(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

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