Force needed to raise a backpack

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SUMMARY

The discussion focuses on the physics of tension in a rope when a hiker pulls at an angle to raise a backpack. It clarifies that the force exerted by the hiker, labeled as ##\vec F##, is not purely vertical and emphasizes the importance of considering the entire rope's contribution, particularly the right half. Understanding the relationship between the pulling force and the tension in the rope is crucial for accurate calculations in this scenario.

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syllll_213
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Homework Statement
The question is asking how the force needed to raise the pack change, but I am unsure if my working and reasoning is right. Particularly, I am unsure if I can assume both the angles (theta) I labelled to be equivalent because I sort of assumed the force pulled by the guy to be equal to the force pulling on the backpack. Some comment on my working would be appreciated thank you TT.
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F=ma
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The diagram provided seems to have misled you a little. It shows the hiker pulling down at some angle to the vertical but labels a vertical force ##\vec F##.
How does the force with which the hiker pulls on the rope relate to the tension in the lateral section of the rope?

Also, you seem to have forgotten the contribution from the right half of the rope.
 

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