A painter with a mass of 90 kg sits in a chair near the wall of the house he is

Question

A painter with a mass of 90 kg sits in a chair near the wall of the house he is painting. He holds on to a rope which goes over a pulley and suspends his chair as shown on the figure. He wants to move upwards, and pulls the rope with a force so large that the pressure he exerts on the chair corresponds to the weight of a mass of 50 kg, (i.e., 50 kg * 9.8 = 490 N). The mass of the chair itself is 15 kg. Disregard the mass of the pulley. Find the acceleration of painter and chair. With what force is the painter pulling on the rope (i.e., what is the string force)?

Explanation / Answer

you are told the painter pushes downward on the chair with a force of 490 N... now let's do sum of forces acting on the chair:

T - mg - 490 = ma

Where T is the tension in the rope

simplify this to T - 15*9.8 - 490 = 15*a

or

T = 15a + 637

Now do the same thing for the painter. The rope pulls up on him, the chair pushes up on him, and gravity pulls down on him, so

T + 490 - Mg = Ma

or

T + 490 - 90*9.8 = 90a

so

T = 90a + 392

set the two T equations equal to each other

15a + 637 = 90a + 392

solve for a

75a = 245

a = 3.27 m/s^2

Then plug this into either equation

T = 90*3.27 + 392 = 686 Newtons is the tension in the rope

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