#### Answer

The painter should pull down on the rope with a force of 400 N

#### Work Step by Step

Let's consider the system of the painter and chair. Note that when the painter pulls down with a force $F$, the tension $T$ in the rope is equal in magnitude to the force $F$. Also note that the tension $T$ pulls up on the painter's hands, and the tension $T$ pulls up on the chair.
To find the tension $T$, we can set up a force equation for the system of the painter and chair. Let $M$ be the total mass of the system.
$\sum F = Ma$
$T+T-Mg = Ma$
$2T = M(g+a)$
$T = \frac{M(g+a)}{2}$
$T = \frac{(70~kg+10~kg)(9.80~m/s^2+0.20~m/s^2)}{2}$
$T = 400~N$
Since the force $F$ is equal in magnitude to $T$, the painter should pull down on the rope with a force of 400 N.