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Question: Answered & Verified by Expert
A helicopter of mass $2000 \mathrm{~kg}$ rises with a vertical acceleration of $15 \mathrm{~ms}^{-2}$. The total mass of the crew and passengers is $500 \mathrm{~kg}$. Give the magnitude and direction of the $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) force on the floor of the helicopter by the crew and passengers.
(b) action of the rotor of the helpicopter on the surrounding air.
(c) force on the helicopter due to the surrounding air.
PhysicsLaws of Motion
Solution:
2213 Upvotes Verified Answer
As given that, mass of helicopter $\left(m_1\right)=2000 \mathrm{~kg}$
Mass of the crew and passengers $m_2=500 \mathrm{~kg}$
Acceleration (of helicopter) in vertical direction
$a=15 \mathrm{~m} / \mathrm{s}^2(\uparrow)$ and $g=10 \mathrm{~m} / \mathrm{s}^2(\downarrow)$
(a) Force $\left(F_1\right)$ on the floor of the helicopter by the crew and passengers will be equal to apparent -weight (left).
$$
\begin{gathered}
F_1=m_2(g+a)=500(10+15) \mathrm{N} \\
=500 \times 25 \mathrm{~N}=12500 \mathrm{~N}
\end{gathered}
$$
(b) Action of the rotor of the helicopter on the surrounding air will be equal to the reaction force $\left(F_2\right)$ by Newton's third law due to which helicopter along with crew and passenger rises up to acceleration
$$
\begin{aligned}
&F_2=\left(m_1+m_2\right)(g+a) \\
&=(2000+500) \times(10+15)=2500 \times 25 \\
&=62500 \mathrm{~N} \text { (downward) }
\end{aligned}
$$
(c) Force $\left(F_3\right)$ acting on the helicopter (by reaction force) due to the surrounding air
= reaction of force applied by helicopter
$$
F_3=62500 \mathrm{~N} \text { (upward), }
$$
as Action force
$$
F_2=-62500 \mathrm{~N} \text { (downward). }
$$

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