The concepts in this problem are similar to those in Multiple-Concept Example 4,

Question

The concepts in this problem are similar to those in Multiple-Concept Example 4, except that the force doing the work in this problem is the tension in the cable. A rescue helicopter lifts a 87.5-kg person straight up by means of a cable. The person has an upward acceleration of 0.777 m/s2 and is lifted from rest through a distance of 9.25 m. What is the tension in the cable? How much work is done by the tension in the cable and the person's weight? Use the work-energy theorem and find the final speed of the person.

Explanation / Answer

a)
tension in the cable T = m(g+a) = 87.5(9.8+0.777) = 925.4875 N
b)
work done by tension = 925.4875*9.25 = 8560.759375 J
c)
work doen by weight = - mg h = -87.5*9.8*9.25 = - 7931.875 J
d)
from work energy heroem work = K2-K1
0.5*mv^2 = 8560.75
v = 13.988 = 14 m/s

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