# Chapter 7 - Newton's Third Law - Exercises and Problems - Page 189: 46

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.

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