Force -displacement graph question

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The discussion focuses on calculating the work done in pulling a 45 kg crate upwards through a height of 12 m using two ropes, each with a mass of 0.75 kg/m. The total mass of the ropes is determined to be 18 kg, leading to an initial force of 617.4 N when both the crate and ropes are considered. After pulling the crate 12 m, the force reduces to 441 N, as only the crate's weight is relevant. The work done is calculated using the area under the force-displacement graph, resulting in a total of 6350.4 J. The calculations and graph illustrate the relationship between force and displacement during the lifting process.
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Homework Statement


A crate, having a mass of 45 kg is pulled steadily upwards by tw ropes through a height of 12 m. Each rope has mass of 0.75 kg/m. Draw the F-d graph and determine the work done in pulling the crate 12 m.

The Attempt at a Solution


Alright...

so we know that we are starting with
m1 = 45 kg
m2 = 0.75kg/m x 12 m
m2 = 9 kg x2
m2 = 18 kg

Now we need to find the force that it will have initially ...

Fn = mg
Fn = (18 kg + 45 kg)(9.8m/s^2)
Fn = 617.4 N

Now after the crate has been pulled 12 m ...
it'll only have m1 attached which is 45 kg

Fn=mg
Fn=(45kg)(9.8m/s^2)
Fn=441 N

Now i made this graph...

http://s1176.beta.photobucket.com/user/LolaGoesLala/media/ih.jpg.html

Then i used this formula..

W = (A+B/2)(d)
W = (617.4 N+ 441 N/2)(12 m)
W =6350.4 J
 
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