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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 81.7-kg person straight up by means of a cable. The person has an upward acceleration of 0.729 m/s2 and is lifted from rest through a distance of 7.86 m. (a) What is the tension in the cable

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Answer:

Explanation:

Given that:

distance (z) = 7.86 m

mass of the person = 81.7 kg

Acceleration (a) = 0.729 m/s²

By using Newton's second law along the vertical axis:

[tex]T - mg = ma\\ \\ T = ma + mg \\ \\ T = m(a+g) \\ \\[/tex]

T = 81.7 (0.729 +9.8)

T = 860.22 N

The work done now is:

[tex]W_T = T\times z \\ \\[/tex]

[tex]W_T = 860.22 \times 7.86[/tex]

[tex]\mathbf{W_T =6761.3292\ N}[/tex]

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