A bucket hangs from a rope. The other end of the rope is held by a woman. The te
ID: 1451866 • Letter: A
Question
A bucket hangs from a rope. The other end of the rope is held by a woman. The tension in the rope is 64.6 N in each case. All movements take place with constant velocity. What is the work done by the rope in each of the following cases?
a.) She moves 5 m horizontally without changing the height of the bucket.
b.) She lifts the bucket 0.27 m.
c.) She lowers the bucket 0.27 m.
d.) She pulls the bucket up an incline, moving it 1.3 m vertically and 0.5 m horizontally.
e.) She lowers the bucket down the same incline by the same distance as in part (d).
Explanation / Answer
(a)
If the change in height is zero, then the work done by the tension is zero. In the case of the horizontal motion, the angle between the tension in the rope and displacement is 90 degree. thus, the total work done is zero.
(b)
the work done is,
W=T*d =64.6 N *0.27 m =17.442 J
(c)
W=-T*d =-64.6 N *0.27 m =-17.442 J The tension and displacement are in opposite direction.
(d)
the work done is,
W=T*y+T* x*cos90
=(64.6 N)*1.3 m+0
=83.98 J=84 J
(e)
the work done is,
W=-T*y+T* x*cos90
=-(64.6 N)*1.3 m+0
= - 83.98 J = - 84 J
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