Question

Compare the power at which each of the following is moving upwards against the force of gravity?
(i) A butterfly of mass 1.0 g that flies upward at a rate of $0.5m{s}^{-1}$
(ii) A 250 g squirrel climbing up on a tree at a rate of $0.5m{s}^{-1}$

Answer 1

We know, $power=\frac{workdone}{time}$
Let m be the mass of the object, g be the acceleration due to gravity, h be the height (distance) and t be the time taken.
Therefore, power $p=\frac{mgh}{t}$
We know, velocity, $v=\frac{distance}{time}=\frac{h}{t}$
$\Rightarrow$ power, $p=mgv$
Acceleration due to gravity, $g=10m{s}^{-2}$
(i) Given mass, $m=1g=\frac{1}{1000}=0.001kg$ and velocity, $v=0.5m{s}^{-1}$
Power, $p=0.001\times 10\times 0.5=0.005=5\times {10}^{-3}W$

(ii) Given, mass, $m=250g=\frac{250}{1000}=0.25kg$ and velocity, $v=0.5m{s}^{-1}$
Power, $p=0.25\times 10\times 0.5=1.25W$
Hence, the power with which the squirrel is climbing is much higher than that of a butterfly flying