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Basic Physics (Tension; Displacement; Force etc.)

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A 230kg crate hangs from the end of a rope of length L-12.0m. You push horizontally on the crate with a varying force F to move it distance d=4.00m to the side (see attached picture).
(a) what is the magnitude of F when the crate is in this final position?
During the crate's displacement, what are (b) the total work done on it, (c) ...

**Please see attachment for diagram and complete question.

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The expert examines tension, displacement and force on hanging crates.

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Here, let  be the angle the line L makes with the vertical. , which gives

There will be a tension force in the string, which will be counteracted by F.
T = F sin
The force F cos will be the force responsible for bringing the block back to its equilibrium position.
If ...

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