Question

Leonardo da Vinci proposed a flying machine that would work like a screw in order to lift the pilot into the air. The 'screw' is being rotated by the pilot. The machine and the pilot together have a total mass of $120kg$.. Which useful output power must the pilot provide to move vertically upwards at a constant speed of \[2.5m{{s}^{-1}}\]?
\[\begin{align}
  & A.48W \\
 & B.300W \\
 & C.470W \\
 & D.2940W \\
\end{align}\]

Answer 1

Hint: The equation of power is to be considered here. The force which is acting on the flying machine will be gravitational force. And the velocity is also given in the question. Substitute this in the equation of power. Give the proper units too.

Complete answer:
Let us consider the output power to be \[P\].
The output power is given by the equation,
\[P=F\cdot V\]
Here in the question, it is given that,
Total mass of the machine is \[m\]
That is,
\[m=120kg\]
Therefore the force acting on the machine will be,
\[F=mg=120\times 9.8=1176N\]
In which\[g\]IS the acceleration due to gravity.
And now let us find out the output power \[P\].
The velocity at which the machine is moving,
\[V=2.5m{{s}^{-1}}\]
Output power is
\[P=F\cdot V\]
Substituting the values in the equation will give,
\[P=1176\times 2.5=2940W\]
Hence the output power of the flying machine will be given as
\[P=2940W\]

So, the correct answer is “Option D”.

Note:
Power is defined as the measure of amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is given as watt, equal to one joule per second. In early years, power is sometimes known as activity. Power is considered to be a scalar quantity in which it depends on magnitude only. As the dot product of two vector quantities are taken, the output power will be scalar.