5.27 A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s^-2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the

(a) Force on the floor by the crew and passengers

 

(b) Action of the rotor of the helicopter on the surrounding air

 

(c) Force on the helicopter due to the surrounding air

<p>Given</p><p>Mass of the helicopter m₁ = 1000 kg</p><p>Mass of the crew and passenger m₂ = 300 kg</p><p>The vertical acceleration of the helicopter, a = 15 m/s² and acceleration due to gravity g = 10 m/s²</p><p>The total mass of the system, m = m₁ + m2 = 1000 + 300 = 1300 kg</p><p><strong> (a)</strong> Force on the floor by the crew and passengers :</p><p>R – m₂g =m₂a</p><p>R = m₂ (g+a) = 300 <span title="Click to copy mathml"><math><mo>*</mo></math></span>&nbsp; ( 10 + 15 ) N = 7500 N</p><p>&nbsp;</p><p><strong> (b)&nbsp;</strong>Action of the rotor of the helicopter on the surrounding air</p><p>R' – mg = ma</p><p>R' = m (g+a) = 1300&nbsp;<span title="Click to copy mathml"><math><mo>*</mo><mfenced separators="|"><mrow><mrow><mi></mi><mn>10</mn><mo>+</mo><mn>15</mn><mi></mi></mrow></mrow></mfenced><mi>N</mi><mi></mi></math></span>&nbsp;= 32500 N</p><p>&nbsp;</p><p><strong> (c)</strong> Force on the helicopter due to the surrounding air</p><p>It is the reaction of the force applied by the rotor on the air. As action and reaction are equal and opposite (Newton's 3rd law), the force of reaction, F = 32500 N, acting vertically upwards.</p>

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