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 89.6-kg person straight up by means of a cable. The person has an upward acceleration of 0.623 m/s2 and is lifted from rest through a distance of 12.2 m. (a) What is the tension in the cable? How much work is done by (b) the tension in the cable and (c) the person's weight? (d) Use the work-energy theorem and find the final speed of the person. Number units Number units

Explanation / Answer

a)

T = tension force upward

mg = weight of person downward

a = upward acceleration = 0.623

Force equation is given as

T - mg = ma

T - 89.6 x 9.8 = 89.6 x 0.623

T = 933.9 N

b)

d = displacement = 12.2 m

work done by tension force

Wt = T d = 933.9 x 12.2 = 1.14 x 104 J

c)

work done by weight = - mgd = - 89.6 x 9.8 x 12.2 = - 1.07 x 104 J

d)

Vi = initial velocity = 0 m/s

using work- kinetic energy theorem,

(T - mg) d = (0.5) m (Vf2 - Vi2)

(933.9 - 89.6 x 9.8) (12.2) = (0.5) (89.6) (Vf2 - 02)

Vf = 3.89 m/s

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