1. A window washer is standing on a scaffold supported by a vertical rope at eac

Question

1. A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 194 N and is 3.2 m long. What is the tension in each rope when the 690–N worker stands 1.14 m from one end?

smalled tension= ______

larger tension= _______

2. A solid, horizontal cylinder of mass 13.0 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.

Explanation / Answer

1) take moments around 1 end to get the tension in the rope of the other

then M = 0, take the rope tension direction as positive
moment around one end is
(690 x 1.14) +( 194 x (3.2 / 2)) = T1 x 3.2

T1=109.7/3.2
smaller tension is T1= 342.8N

Now moments around the other end

(690 x (3.2-1.14)) +( 194 x (3.2/2)) = T2 x 3.2
larger tension is T2 = 541.18N

check answers as F = 0, so

342.8 + 541.18 - 194 - 690 = 0 (approximately equals to 0)

2)   Inertia = 1/2 x 13 x (1m) 2

                  = 6.5 kgm2

6.5x7.5=48.75 kg m2/s

inertia of pulley = 0.25 x 0.9 2

                      = 0.2025 kg m2

final angular speed is =48.75/(6.5+0.2025)

V= 7.273 rad/s

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