A 110 kg mail bag hangs by a vertical rope 4.0 m long. A postal worker then disp

Question

A 110 kg mail bag hangs by a vertical rope 4.0 m long. A postal worker then displaces the bag to a position 1.8 m sideways from its original position, always keeping the rope taut.

Part A

What horizontal force is necessary to hold the bag in the new position?

Express your answer using two significant figures.

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Part B

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

Express your answer using two significant figures.

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Part C

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

Express your answer using two significant figures.

Explanation / Answer

part A:

let tension in the rope be T N.

angle made by the rope with vertical=arcsin(1.8/4)=26.744 degrees

balancing forces along vertical direction:

T*cos(26.744)=weight of the mail bag=110*9.8

==>T=1207.1 N

then horizontal force required=T*sin(26.744)=543.21 N

answer in two significant figure=5.4*10^2 N

part B:

work done by the rope=force * distance*cos(angle between force and displacement)

=1207.1*1.8*cos(90+26.744)

=-977.77 J

answer in two significant figures=-9.8*10^2 J

part C:

work done by the worker=horizontal force applied*distance covered horizontally

=543.21*1.8

=977.77 J

answer in two significant figures=9.8*10^2 J

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