A 284 kg crate hangs from the end of a rope of length L = 14.9 m. You push horiz

Question

A 284 kg crate hangs from the end of a rope of length L = 14.9 m. You push horizontally on the crate with a varying force  to move it distance d = 2.52 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

d= 2.52 m

L = 14.9 m

sin(theta) = d/L =2.52/14.9 = 0.169= 9.737 degrees

a) let the tension be T

the Tcos(theta) balcances the mg

so, Tcos(theta) = 284*9.8

=>T = 2823.87 N

and the horizontal force = Tsin(theta) = 2823.87 N* sin(theta) = 477.591N

(b) Since there is no change in kinetic energy, the net work on it is zero.

(c)height raised = del(h) = L ( 1- cos(theta) ) = 0.2235 m

so , potential energy change = work done = mg*del( H) = 284*9.8 * 0.2235 m= 622.0452 J

(d) The tension vector is everywhere perpendicular to the direction of motion, so its work is zero
(since cos 90° = 0).

e) total work done = work done by gravitational force = 622.0452 J

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