A 194 kg crate hangs from the end of a rope of length L = 14.5 m. You push horiz

Question

A 194 kg crate hangs from the end of a rope of length L = 14.5 m. You push horizontally on the crate with a varying force to move it distance d = 3.83 m to the side. (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) T sin theta = F g T = tension in rope and m g = 194 * 9.8 = 1901 N T cos theta = m g F = sideways force on crate tan theta = F / m g dividing equations sin theta = 3.83 / 14.5 theta = 15.3 deg F = 1901 * tan 15.3 = 521 N b) h = 14.5 - 14.5 cos theta h = height raised h = .514 m W (total) = m g h = 1901 * .514 = 977 J c) Work by gravity = - m g h = -977 J d) the crate moves in a circular arc perpendicular to the rope so the rope does no work e) Wb = Wc + Wd + We We = 977 + 977 - 0 = 1954 J

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