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 89.7-kg person straight up by means of a cable. The person has an upward acceleration of 0.524 m/s2 and is lifted from rest through a distance of 9.06 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.

Explanation / Answer

A) net force and tesion are in upward direction

T-(m*g)= m*a

Tension T = m(a+g) = (89.7)*(0.524+9.8) = 926 N

B) Work done by the tension W1 = F*S*cos(theta) = T*S*cos(0)

W1 = 926*9.06*cos(0) = 8389.56 J

C) Work done by the person's weight W2 = m*g*S*cos(180) = 89.7*9.8*9.06*cos(180) = -7964.28 J

D) Work done by the net Force = Change in kinetic energy
8389.56-7964.28 = 0.5*m*(v^2-u^2) = 0.5*89.7*(v^2-0^2)
425.28 = 0.5*89.7*v^2

v = sqrt(425.28/(0.5*89.7)) = 3.079 m/s

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