Answer
The net force on the system is $965~N$ and this net force is directed upward.
Work Step by Step
We can find the person's mass:
$mg = 640~N$
$m = \frac{640~N}{9.80~m/s^2}$
$m = 65.3~kg$
Let $F_N$ be the upward force exerted on the person by the elevator. We can find the person's upward acceleration:
$F_N - mg = ma$
$a = \frac{F_N-mg}{m}$
$a = \frac{700~N-640~N}{65.3~kg}$
$a = 0.919~m/s^2$
Let $M$ be the total mass of the system. We can find the net force on the system:
$\sum F = Ma$
$\sum F = (1050~kg)(0.919~m/s^2)$
$\sum F = 965~N$
The net force on the system is $965~N$ and this net force is directed upward.
