A 271 kg crate hangs from the end of a rope of length L = 12.6 m. You push horiz

Question

A 271 kg crate hangs from the end of a rope of length L = 12.6 m. You push horizontally on the crate with a varying force to move it distance d = 2.69 m to the side (see the figure). (a) What is the magnitude of when the crate is in this final position? During the crate's displacement, what are (b) the total work done on it, (c) the work done by the gravitational force on the crate, and (d) the work done by the pull on the crate from the rope? (e) Knowing that the crate is motionless before and after its displacement, use the answers to (b), (c), and (d) to find the work your force does on the crate.

Explanation / Answer

a) let inclination of wire be θ,T be tension in wire and m be mass of block

so net horizontal forces are

Tsinθ=F      sinθ=2.69/12.6

Tcosθ=mg

T=2718 N

F=580.37 N

b) the total work done is given by the work done against gravity since change in kinetic is 0 and gravity is the only other force

work done against gravity =271*9.8*0.29

                                    =771.5 J

c) the work done by gravitational force on crate= -771.5 J

d)it is zero since the length of the rope doesnt change and work is only done when displacement has a component along direction of force which is tension in this case

e)the work done by force on crate =771.5 J

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