Question

A 227 kg crate hangs from the end of a rope of length L = 12.0 m. You push horizontally on the crate with a varying force F→ to move it distance d = 4.84 m to the side (see the figure). (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) 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 F→ does on the crate.

Answer 1

A)

Theta = arcsin (4.84/12) = 23.79 degree

T cos(theta) = mg

T = (227 x 9.8)/cos(23.79) = 2431.12 N

Force, F = 2431.12 sin(23.79) = 980.68 N

B)

Total work, W = 0

C)

Work, W = - mgL(1 - cos(theta))

W = - 227 x 9.8 x 12 (1 - cos(23.79)) = - 2268.29 J

D)

Work, W = 0

E)

Work, Wf = 2268.29 J

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