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

Question

The concepts in this problem are similar to those inMultiple-Concept Example 4, except that the force doing the work inthis problem is the tension in the cable. A rescue helicopter liftsa 93.9-kg person straight up by means of a cable. The person has anupward acceleration of 0.819 m/s2 and is lifted fromrest through a distance of 12.4 m. (a) What is thetension in the cable? How much work is done by (b)the tension in the cable and (c) the person'sweight? (d) Use the work-energy theorem and findthe final speed of the person.

(a) Number Units Nounitsmm/skgNJW

Explanation / Answer

   a.   Tension in thecable   T   =   m* ( g + a)    m   =   massof person   =   93.9kg,   a   =   upwardsacceleration   =   0.819   m/s2          T   =   93.9* ( 9.8 + 0.819)   =   997.12   N    b.   Work done bytension   WT   =   T* displacement   =   997.12 *12.4   =   1.24 *104   J    c.   Work done byweight   WW   =   W* d   =   m * g *d   =   93.9 * 9.8 * ( -12.4)   =   -1.14 *104   J          - vesign indicates the fact that the displacement is oppposite thedirection of weight.    d.   Net workdone   =   change in k.e.          W   =   WT   +   WW   =   (1/2)* m * v2       1.24 *104   -   1.14 *104   =   0.5 * 93.9 *v2    v   =   (1000/46.95)   =   4.61   m/s    v   =   (1000/46.95)   =   4.61   m/s

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