A rescue helicopter lifts a 78.5-kg person straight up by means of a cable. The
ID: 1285191 • Letter: A
Question
A rescue helicopter lifts a 78.5-kg person straight up by means of a cable. The person has an upward acceleration of 0.741 m/s2 and is lifted from rest through a distance of 13.9 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
A rescue helicopter lifts a 78.5-kg person straight up by means of a cable. The person has an upward acceleration of 0.741 m/s^2 and is lifted from rest through a distance of 13.9 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 personExplanation / Answer
a) T = m*(g+a)
= 78.5*(9.8+0.741)
= 835.3 N
b) W(T) = T*d
= 835.3*13.9
= 11610.9 J
c) W(g) = -m*g*d
= -78.5*9.8*13.9
= -10693.27 J
d) Wnet = 11610.9 - 10693.27
= 917.63 J
Wnet = 0.5*m*(v^2-u^2)
here u = 0
Wnet = 0.5*m*v^2
v = sqrt(2*Wnet/m)
= sqrt(2*917.63/78.5)
= 4.835 m/s
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