# As the bag is moved to this position, how much work is done by the rope?

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A 125kg mail bag hangs by a vertical rope 4.0m long. A postal worker then displaces the bag to a position 2.2m sideways from its original position, always keeping the rope taut.

What horizontal force is necessary to hold the bag in the new position? the answer for this is 810N

As the bag is moved to this position, how much work is done by the rope?

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As the bag is moved to this position, how much work is done by the rope?

Methods I have tried, that did not work:

• Θ = arcsin[2.2/4] = 33.367°

a) Fx = m*g*tanΘ = 125*9.8*tan33.367° = 806.7 N

b) Wr = 0.

No work is done by the rope because there is no movement in the direction of the rope length.

Work is done only by Fx and is equal to m*g*L*(1 – cosΘ) = 807.7 J

Source(s): Free body diagram
• When the position is 2.2m sideways, the rope makes an angle of arcsin(2.2/4) = 33.4 degrees. The vertical component of the tension is 125*9.8 = 1225N. Let the horizontal component of tension be Th

Tan(33.4) = Th/1225N => 1225*Tan(33.4) = Th = 806.7N which is not 810 but close

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