Question

Compare the power at which each of the following is moving upwards against the force of gravity? (given $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

(i) A butterfly of mass $1.0\mathrm{g}$ that flies upward at a rate of $0.5{\mathrm{ms}}^{-1}$.

(ii) A $250\mathrm{g}$ squirrel climbing up on a tree at a rate of $0.5{\mathrm{ms}}^{-1}$.

Answer 1

Step 1: Given data

Acceleration due to gravity $\mathrm{g}=10{\mathrm{ms}}^{-2}$

Butterfly's mass $\left({\mathrm{m}}_{\mathrm{b}}\right)=1\mathrm{g}={10}^{-3}\mathrm{kg}$

Speed of butterfly $\left({\mathrm{v}}_{\mathrm{b}}\right)=0.5{\mathrm{ms}}^{-1}$

Squirrel's mass $\left({\mathrm{m}}_{\mathrm{s}}\right)=250\mathrm{g}=0.25\mathrm{kg}$

Speed of squirrel $\left({\mathrm{v}}_{\mathrm{s}}\right)=0.5{\mathrm{ms}}^{-1}$

Step 2: Formula used

Force of gravity $=\mathrm{m}\times \mathrm{g}$

Power $\left(\mathrm{P}\right)=\mathrm{F}\mathrm{x}\mathrm{v}$

Where,

$\mathrm{g}$ is the force of gravity

$\mathrm{m}$ is mass

$\mathrm{P}$ is power

$\mathrm{F}$ is force

$\mathrm{v}$ is velocity

Step 3: A butterfly of mass $1.0\mathrm{g}$ that flies upward at a rate of $0.5{\mathrm{ms}}^{-1}$

Force of gravity on butterfly $\left({\mathrm{F}}_{\mathrm{h}}\right)={\mathrm{m}}_{\mathrm{b}}\times \mathrm{g}$

${\mathrm{F}}_{\mathrm{h}}={10}^{-3}\times 10={10}^{-2}\mathrm{N}$

Power $\left({\mathrm{P}}_{\mathrm{b}}\right)={\mathrm{F}}_{\mathrm{b}}\mathrm{x}{\mathrm{v}}_{\mathrm{b}}$

${\mathrm{P}}_{\mathrm{b}}={10}^{-2}\mathrm{N}\times 0.5{\mathrm{ms}}^{-1}$

${\mathrm{P}}_{\mathrm{b}}=0.005\mathrm{W}$

Step 4: A $250\mathrm{g}$ squirrel climbing up on a tree at a rate of $0.5{\mathrm{ms}}^{-1}$

Force of gravity on squirrel,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{s}}={\mathrm{m}}_{\mathrm{s}}\times \mathrm{g} \\ {\mathrm{F}}_{\mathrm{s}}=0.25\mathrm{x}10 \\ {\mathrm{F}}_{\mathrm{s}}=2.5\mathrm{N} \end{gathered}$$

Power will be:

$\left({\mathrm{P}}_{\mathrm{s}}\right)={\mathrm{F}}_{\mathrm{s}}\times {\mathrm{v}}_{\mathrm{s}}$

$$\begin{gathered} {\mathrm{P}}_{\mathrm{s}}=2.5\mathrm{N}\times 0.5{\mathrm{ms}}^{-1} \\ {\mathrm{P}}_{\mathrm{s}}=1.25\mathrm{W} \end{gathered}$$

As a result, the squirrel uses more energy to climb than a butterfly does to fly at the same speed.