Bosun’s Chair

A painter weighing 180 lb working from a "bosun's" chair hung down the side of a tall building, desires to

move in a hurry. He pulls down on the fall rope with such a force that he presses against the chair with only

a force of 100 lb. The chair itself weighs 30.0 lb.

(a) What is the acceleration of the painter and the chair?

(b) What is the total force supported by the pulley?

Solution by Gert Hamacher

The problem statement contains information on inner forces, so we must look at the man and the chair

separately. We neglect the masses of the rope and the pulley.

- weight of the man 180

- weight of the chair 30

- the normal (inner) force between the man and the chair 100

- the tension on the rope

- the acceleration of

m m

c c

rope

w m g lb

w m g lb

N lb

T

g

= ⋅ =

= ⋅ =

=

gravity

- the acceleration of the man/chair systema

(a) By Newton’s 2nd law:

(a.1) total force on man

rope m m

rope m man

T N w m a

T N w m a

= + − = ⋅

∴ + = + ⋅

(a.2) total force on chair

rope c c

rope c c

T N w m a

T N w m a

= − − = ⋅

∴ − = + ⋅

Subtracting Eq. (a.2) from Eq. (a.1),

( ) ( )

13

2

2 2 2 100 180 30.

180 30

m m c c

m c m c

m c m c

N w m a w m a

N w w N w wa g g g

m m w w

= + ⋅ − + ⋅

− + − + ⋅ − +∴ = = ⋅ = ⋅ =

− − −

(b) The total force supported by the pulley equals the total tension on the rope (both sides) = 2Trope. Adding

Eq. (a.1) to Eq. (a.2),

( ) ( ) ( ) ( ) ( )

13 4

2 180 30 280.3

total force supported by pulley 280 .

rope m c m c m c m c

gT w w m m a w w w w

g

lb

= + + + ⋅ = + + + ⋅ = ⋅ + =

∴ =

Trope

N wm

Man

Trope

wc N

Chair

free body diagrams