A 606.3 N window washer is standing on a uniform scaffold supported by a vertical rope at each end.?
A 606.3 N window washer is standing on a
uniform scaffold supported by a vertical rope
at each end. The scaffold weighs 194.1 N and
is 3.42 m long. Assume the window washer
stands 1.33 m from one end.
What is the force on the farther rope?
Answer in units of N
What is the force on the closer rope?
Answer in units of N
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Verified answer
Using the principle of moments where the sum of forces in one direction is equal to the sum of forces in the opposite direction. The sum of upward forces which are the tensions in the ropes should be equal to the sum of downward forces which are the weights of the window washer and the scaffold.
Also the anti-clock wise forces should be equal to the clockwise forces.
So, first The tensions Px and Py are equal to 606.3N and 194.1N
Px + Py = 606.3N + 194.1N = 800.4N
Now, taking moments about one side of the scaffold which is the Px side we have
194.1 * 1.7 + 606.3 * 1.33 = 1136.349
Anti-clockwise moment is Py * 3.42
Since the clockwise moments are equal to the anti-clockwise moments we could equate the two.
1136.349 = 3.42Py --> Py = 1136.349/3.42 = 332.3N(that is the force on the farther rope)
Now, substitute the value for Py into the first equation to solve for Px(the force on the closer rope)
Px + 332.3 = 800.4 --> Px = 800.4 - 332.3 = 468.1N
NB: you could also take moments about the opposite side to solve for Px