A test pilot is forced to land his airplane in the ocean. A helicopter comes to

Question

A test pilot is forced to land his airplane in the ocean. A helicopter comes to rescue him and drops a cable with a harness attached. The pilot puts on the harness and the cable is used to pull him up. Assume a thin cable of negligible mass. Assume the wet pilot has a mass of 60kg. Ignore atmospheric effects. a) If the cable can withstand a maximum tension of 1080N, what is the minimum time required to accelerate the pilot from being at rest in the water to being lifted towards the helicopter at a steady speed of 2.75m/s? b) When the pilot gets within 1 meter of the helicopter this lift speed is steadily decreased until he reaches the helicopter and stops. What is the tension in the cable during this portion of the lift? c) If the helicopter hovers 28 m above the surface of the water, how long does it take to lift the pilot from the water to the height of the helicopter? d) If the helicopter has a mass of 2850kg and the main rotor has 5 blades, how much lift force must each blade produce during each of the three phases (lift from water, lift at constant speed, slow down and stop) of the pilots motion?

Explanation / Answer

Let the maximum acceleration be a.

T=mg+ma=1080

60*(9.8+a)=1080

a=8.2m/s^2

time=v/a=2.75/8.2=0.3354s

b)a2=v^2/2s=2.75^2/2*1=3.78m/s^2

T=mg-ma2=60*(9.8-3.78)=361.2N

c)Distance for the first part=v^2/2a=2.75^2/2*8.2=0.46m

t=time for each of the three phases=t1+t2+t3=0.3354+(28-1-0.46)/2.75+2.75/3.78=10.71s

d)Lift force by each blade during lift from water=(T1+mg)/n=(1080+2850*9.8)/5=5802N

During constant speed motion, lift force per blade=mg/n=(60*9.8+2850*9.8)/5=5703.6N

During slow down, left force/blade=(T2+mg)/n=(361.2+2850*9.8)/5=5658.2N

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