Question

A house painter uses the chair-and-pulley arrangement of FIGURE P$7.45$to lift himself up the side of a house. The painter’s mass is $70kg$and the chair’s mass is $10kg$. With what force must he pull down on the rope in order to accelerate upward at $0.20m/s^2$?

Short answer

Force on the rope applied by the painter in the downward direction is$4\times {10}^{2}N$

Step-by-step solution

Given information 

The mass of the painter, $m_p=70kg$

The mass of the chair,$m_c=10kg$

Explanation

The tension in the rope is calculated as

$$\begin{gathered} 2T=\left(m_p+m_c\right)g-\left(m_p+m_c\right)a \\ =\left(70kg+10kg\right)\left(9.8m/s^2\right)-\left(70kg+10kg\right)\left(0.2m/s^2\right) \\ =384N \end{gathered}$$

Force required to accelerate the painter

$$\begin{gathered} F_{net}=T \\ {F}_{net}=3.84\times {10}^{2}N \end{gathered}$$

Force on the rope applied by the painter in the downward direction is $4\times {10}^{2}N$.