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Old Mar 23rd 2016, 12:38 PM   #1
Join Date: Jan 2015
Posts: 96
Work-energy theorem problem (reprise)

Hi everybody,
Sorry I've not been on the site for a while but I have been ill and spent some time in hospital. I've just come back and I am revisiting the last problem I posted on the system and I'm afraid I still don't see how to solve it even with the hints a couple of you sent me. I will quickly go over the problem again and some of the help I was given below.

Problem - A 120-kg mail bag hangs by a vertical rope. A worker then displaces the bag to a position 2.0 m to the side from the original position, always keeping the rope taut.
What horizontal force is necessary to hold the bag in the new position ?

Note :- We have to use energy balance methods to solve this problem.

I'm sorry but I cannot provide a diagram as I don't know how to draw one within this message environment. Suffice to say the bag moves in an arc outwards and up. The horizontal distance is 2.0 m and the upwards displacement is the height.
As part of the help I received when I posted the original problem was help in sorting out the geometry of the displacement but i am afraid it served to confuse me as I cannot see how these values (height, chord length, arc length and angle made at the centre of the circle) help me in using the Energy method to solve the problem.

I wonder if I can prevail on someone give me help in seeing how this all fits together because all I can see at present is a collection of disconnected bits of information and cant see how they come together. Thank you.

Note :- I initially decided to use the equation linking work, kinetic and
potential energies during the displacement as follows -

K(1) + U(G1) + W(other) = K(2) + U(G2)
where K(1) and K(2) are kinetic energy at start and end of displacement
U(G1) and U(G2) are potential energy at start and end of displacement
W(other) is work done by horizontal force in displacing the bag.
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Old Mar 25th 2016, 09:18 AM   #2
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Join Date: Jun 2010
Location: NC
Posts: 402
Supported Bag

Hi Jack...

I suppose Earth is below, the "free" end of the rope is attached to some manner of support, and initially the rope is taut because the bag hangs vertically, directly below the support some distance, say "L." Is this it?

Now suppose a "push-type" force arrives. Since a pushed "bag" will flop every which way, we model the bag as a BODY. A force acting on a BODY acts "at a point" so the BODY won't be moving left or right as it is displaces from the vertical.

Now there are many forces that
can do this. I think we want the "Least" force. (This could be "least at the beginning, least finally...) I think we want the least final force.

Logically one direction the force might be applied would be always tangent to the quarter-circle the BODY moves through - at constant distance from the support. The force will be very small to start, Later, located two meters to the side, the force will be vertical-upward and equal to the BODY weight, finally.. We can get the Least Force thus.

I don't know how the Work-Energy Eqn would yield the force.

In closing, here's a URL you might enjoy. JP


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