Question

a house painter uses the chair and pulley arrangement of the figure to lift himself up the side of the house. the painters mass is 65kg and the chairs mass is 9.0kg. with what force must he pull down on the rope in order to accelerate upward at 0.25 m/s^2

Answer 1

Combine the masses to get 65 kg. Weight = Mass times gravity so Weight = ( 65kg ) ( -9.81 m/s^2 )
Weight =-647.46 Newtons.

I drew a pulley above a box with an arrow going down at 647.46 N with a rope attached to the box ( chair ) going over the pulley and back down to the side of the box.

Sum forces in the Y and remember its in motion so it doesnt equal 0 it equals mass times acceleration.

-647.46 N + 2T ( tension of the rope, 2 because your holding it on the other side in tension as well )

-647.46 N + 2T = ( 65 kg ) ( 0.25 m / s^2)
-647.46 N + 2T = 16.25 N
2T = 663.71 N
T = 331.855 N So you must pull down at 331.855 N