1)The U.S. Army special units MH-47E helicopter has a mass of 23,000 kg, and its
ID: 1339680 • Letter: 1
Question
1)The U.S. Army special units MH-47E helicopter has a mass of 23,000 kg, and its propeller blades sweep out an area of 263 m2 It is able to hover at a fixed elevation above one landing point by pushing air downward (the air pushes up on the helicopter blades). Choose a reasonable air mass displaced downward each second and the speed of that air in order for the helicopter to hover. Assume the density of air to be 1.3 kg/m3.
2)Determine the recoil speed of Earth if all of the inhabitants of Canada and the United States simultaneously jumped straight upward from Earth's surface. Suppose the average jump height reached by the population is 0.60 m, the population of the two countries is about 3.46×108, an average mass is 50 kg. Mass of Earth is 5.98×1024kg.
Explanation / Answer
Weight = mg
W = 23000*9.8 = 2.254x10^5 N
F = v*dm/dt
dm/dt = air density*area*velocity
dm/dt = 1.3*263*v
dm/dt = 341.9*v
F = W
2.254x10^5 = v*341.9*v
v = sqrt(2.254x10^5/341.9) = 25.676 m/s
dm/dt = 25.676*341.9 = 8778.625 Kg/s
b) conservation of energy
initial energy = final energy
PE(earth) + PE(people) = KE(earth) + KE(people)
0 + mgh = 0.5*meVe^2 + 0.5*mp*Vp^2
Vp = sqrt(2gh) = sqrt(2*9.8*0.6) = 3.43 m/s
3.46x10^8*50*9.8*0.6 = 0.5*3.46x10^8*50*3.43^2 + 0.5*5.98x10^24*Ve^2
-4.238x10^7 = 5.98x10^24*0.5*Ve^2
Ve = -3.76x10^-9 m/s
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