Question

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.

Answer 1

Given:

Mass of the helicopter is, $1000kg$

The total mass of crew and passengers is, $300kg$

Acceleration of the helicopter, $a=15m/s^2$

Total mass of the system, $m_t=1300kg$

$\left(a\right)$

The reaction force applied by the crew and passengers on the floor of the helicopter is given by:

$R-mg=ma$

$=m(g+a)$

$=300\times (10+15)=7500N$

So, the force exerted by the passengers on the floor is $7500N$

$\left(b\right)$

The reaction of the rotor on the surrounding air will be due to the mass of the helicopter as well as the passengers.

$R^{\prime }-m_{t}g=m_{t}a$

$=m_t(g+a)$

$=1300\times (10+15)=32500N$

Thus, the reaction force of the rotor on the surrounding air will be $32500N$

$\left(c\right)$

The force on the helicopter due to the surrounding air will be the reaction of the force applied by the rotor on the air. Therefore, its value will be $32500N$.