question_answer 82)

                  A helicopter of mass 2000 kg rises with a vertical acceleration of \[15\,m{{s}^{-2}}\]. The total mass of the crew and passengers is 500 kg. Give the magnitude and direction of the \[(g=10\,m{{s}^{-2}})\]                 (a) force oil the floor of the helicopter by the crew and passengers.                 (b) action of die rotor of the helicopter on the surrounding air.                 (c) force oil the helicopter due to the surrounding air.

Answer:

                  We are given that                 mass of the helicopter, \[{{m}_{1}}=1000\,kg\]             mass of the crew and the passenger, \[{{m}_{2}}=300\,kg\]             vertical acceleration of the helicopter                 \[a=15\,m/{{s}^{2}}\]                 acceleration due to gravity, \[g=10\,m/{{s}^{2}}\]                 (a) Let \[{{R}_{1}}\] be the force on the floor by the crew and the passengers.                 \[{{R}_{1}}={{m}_{2}}(a+g)=300\,(15+10)N\]             =7500 N, downwards                 (b) Let \[{{R}_{2}}\] be the action of the rotor of the helicopter on the surrounding air. (Clearly,                 \[{{R}_{2}}=({{m}_{1}}+{{m}_{2}})(a+g)\]                              \[=(1000+300)(15+10)N\]                             = 32500 N, downwards                 (c) According to Newton?s third law of motion, force on the helicopter due to surrounding air i.e.,                 \[{{\mathbf{R}}_{\mathbf{2}}}\mathbf{=32500}\,\mathbf{N,}\]upwards.